Air-fuel ratio control system for internal combustion engine

Abstract: An air-fuel ratio control system for an internal combustion engine utilizes a pre-stored standard relation between an air-fuel ratio indicative sensor signal and a standard air-fuel ratio indicative value for deriving the standard air-fuel ratio indicative value based on the sensor signal. The system further utilizes a pre-stored modified relation between the standard air-fuel ratio indicative value and a for-control air-fuel ratio indicative value for deriving the for-control air-fuel ratio indicative value based on the derived standard air-fuel ratio indicative value. In the modified relation, the for-control air-fuel ratio indicative value varies corresponding to a variation of the standard air-fuel ratio indicative value within a given range across the standard air-fuel ratio indicative value representing the stoichiometric air-fuel ratio. On the other hand, the for-control air-fuel ratio indicative value is held constant outside the given range. The system performs an air-fuel ratio feedback control based on a deviation between the derived for-control air-fuel ratio indicative value and a target air-fuel ratio indicative value.

Description: BACKGROUND OF THE INVENTION Field of the Invention The present invention relates to an air-fuel ratio control system for an internal combustion engine. More specifically, the present invention relates to an air-fuel ratio feedback control system for an internal combustion engine which enables the center of the air-fuel ratio control to follow up a target air-fuel ratio in an improved manner. Description of the Prior Art Conventionally, there has been proposed an air-fuel ratio control system for an internal combustion engine in which an air-fuel ratio control is performed by comparing an output signal of an oxygen sensor with a reference value representing a stoichiometric air-fuel ratio so as to determine whether a mixture gas is LEAN or RICH. In the air-fuel ratio control system of this type, a feedback correction coefficient is largely skipped up or down when the monitored air-fuel ratio changes between LEAN and RICH, and then the feedback correction coefficient is gradually changed by an integral action so as to maintain the monitored actual air-fuel ratio at the stoichiometric value. However, the air-fuel ratio control system of this type has a problem of its poor follow-up characteristic for controlling the air-fuel ratio toward the stoichiometric value. This is particularly significant when a base of the air-fuel ratio control is deviated such as due to uneven individual characteristics of fuel injectors so that the above-noted skip and integral action based control can not quickly follow up such a deviation. In order to eliminate this problem, there has been proposed another type of the air-fuel ratio control system as disclosed in such as Japanese First (unexamined) Patent Publication No. 1-121541 and United States Patent No. 4,917,067 which is an equivalent of the former. In this system, the air-fuel ratio control is performed using a pre-stored characteristic which defines a substantially linear relation between an output signal of the oxygen sensor and a for-control air fuel ratio. In this pre-stored characteristic, the for-control air-fuel ratio varies evenly corresponding to variations of the oxygen sensor output signal irrespective of a value of the oxygen sensor output signal being close to or remote from the stoichiometric value. Accordingly, as the value of the oxygen sensor output signal is deviated from the stoichiometric air-fuel ratio, a value of the for-control air-fuel ratio is also deviated from the stoichiometric value. In this prior art system, since the for-control air-fuel ratio is derived from the oxygen sensor output signal using the above-noted pre-stored characteristic and the air-fuel ratio feedback control is performed based on a deviation between the for-control air-fuel ratio and a target air-fuel ratio, the follow-up controllability of the system is improved. However, though the prior art air-fuel ratio control system improves the follow-up controllability as described above, there is another problem that due to an unexpected occurrence of shift or unevenness in level of the oxygen sensor output signal which may be caused due to the individual proper characteristic of the employed oxygen sensor or due to measuring temperatures or the like, the control performance of the system inevitably becomes unreliable. This adversely affects the exhaust emission and the follow-up controllability of the system. Fig. 12 shows this unevenness or shift of the oxygen sensor output. As seen in Fig. 12, the oxygen sensor output signal VOX is considered to be stable during a given air-fuel ratio range across the stoichiometric air-fuel ratio, on the other hand, the oxygen sensor output signal VOX is significantly unstable outside the given air-fuel ratio range. This instability causes the above-mentioned problem. Further, the dynamic characteristic of the oxygen sensor at the time of inversion from RICH to LEAN differs from that at the time of inversion from LEAN to RICH. Generally, a response time of the oxygen sensor is longer to change its output voltage from RICH to LEAN than to change its output voltage from LEAN to RICH. As a result, in the prior art system, the center of the air-fuel ratio control tends to be shifted to the LEAN side so that the exhaust emission is deteriorated. Under an engine idling, it is required to set the control amplitude small so as to provide the idling stability, that is, engine speed variations should be set small. However, since the prior art system executes the same control both at the engine idling and at the engine non-idling, the control amplitude at the engine idling becomes large to deteriorate the idling stability. In order to overcome this problem, in the foregoing prior art air-fuel ratio control system using the skip and integral action, the feedback correction coefficient is held fixed after the skip action to prevent reflection of the integral action onto the feedback correction coefficient so as to suppress the control amplitude. This, however, deteriorates the follow-up controllability of the system. Further, due to the individual proper characteristic of each engine, the optimum center of the air-fuel ratio control which can control the exhaust emission into the regulated range differs for each engine. Accordingly, particular means is necessary for shifting the control center to the optimum value reqired for each engine. In the prior art system, however, since no such a means is provided, the engine's individual characteristic can not be dealt with. Further, in the air-fuel ratio control, the required control characteristics differ at an engine transitional condition such as at an immediate acceleration and at an engine steady condition such as at a normal driving. Specifically, at the engine transitional condition, the target air-fuel ratio is largely deviated from the stoichiometric air-fuel ratio so that the quick follow-up of the control is required, on the other hand, at the engine steady condition, the actual air-fuel ratio should be stably maintained at the stoichiometric value without being adversely affected by the individual characteristic of the oxygen sensor. However, the prior art system performs the same control both at the engine transitional condition and at the engine steady condition so that the system is unable to provide the air-fuel ratio control which matches the driving conditions of the engine. SUMMARY OF THE INVENTION Therefore, it is an object of the present invention to provide an improved air-fuel ratio control system for an internal combustion engine that has an improved follow-up controllability and that can adjust the center of the air-fuel control to reduce the exhaust emission. This object is solved by the features of claim 1. Other advantages of the invention result from the dependent claims. BRIEF DESCRIPTION OF THE DRAWINGS The present invention will be understood more fully from the detailed description given hereinbelow and from the accompanying drawings of the preferred embodiments of the invention, which are given by way of example only, and are not intended to be limitative of the present invention. In the drawings: Fig. 1 is a sectional view showing a schematic structure of an internal combustion engine; Fig. 2 is a block diagram showing a structure of a control unit and its peripheral devices; Fig. 3 is a flowchart of a first air-fuel ratio feedback control routine according to a first preferred embodiment of the present invention; Fig. 4 is a block diagram for explaining the air-fuel ratio feedback control executed by the flowchart of Fig. 3; Fig. 5 is a characteristic map showing a relation between an output voltage of an oxygen sensor and a standard excess air ratio; Fig. 6 is a characteristic map showing a relation between the standard excess air ratio and a for-control excess air ratio at an engine non-idling; Fig. 7 is a characteristic map showing a relation between the standard excess air ratio and the for-control excess air ratio at an engine idling; Fig. 8 is a characteristic map showing a common characteristic between the maps of Figs. 6 and 7; Fig. 9 is a characteristic map showing a particular characteristic selected from Fig. 6; Fig. 10 is a timechart showing variations of the for-control excess air ratio; Fig. 11 is a timechart showing a dynamic characteristic of the oxygen sensor, a differential correction and a PID correction; Fig. 12 is a characteristic map showing an output characteristic of the oxygen sensor; Fig. 13 is a sectional view showing a structure of an internal combustion engine, wherein upstream and downstream oxygen sensors are provided; Fig. 14 is a block diagram for explaining an operation of a second preferred embodiment of the present invention; Fig. 15 is a flowchart showing a first linearize characteristic correction routine according to the second preferred embodiment; Fig. 16 is a characteristic map showing a relation between an output voltage of the downstream oxygen sensor and a mean excess air ratio; Fig. 17 is characteristic map showing a relation between a deviation and a correction amount; Fig. 18 is a graph for explaining a correction of the characteristic of a correction linearizer; Fig. 19 is a timechart showing an effect of the correction shown in Fig. 18 relative to time-domain variations in the output of the downstream oxygen sensor; Fig. 20 is a graph for explaining a correction of the characteristic of the correction linearizer; Fig. 21 is a characteristic map showing a relation between the output voltage of the downstream oxygen sensor and the correction amount; Fig. 22 is a flowchart of a second linearized characteristic correction routine according to a third preferred embodiment of the present invention; Fig. 23 is a timechart showing effects realized by the second linealized characteristic correction routine and a third linearized characteristic correction routine, relative to time-domain variations in the output of the downstream oxygen sensor; Fig. 24 is a flowchart of the third linearized characteristic correction routine which is a modification of the second linearized characteristic correction routine; Fig. 25 is a flowchart showing a second air-fuel ratio feedback control routine; Fig. 26 is a flowchart showing a control constant correction routine cooperative with the second air-fuel ratio feedback control routine of Fig. 25, according to a fourth preferred embodiment of the present invention; Fig. 27 is a characteristic map showing a relation between a deviation and a correction amount in the fourth preferred embodiment; Fig. 28 is a timechart showing a relation between the output of the downstream oxygen sensor and the correction amount; Fig. 29 is a timechart showing time-domain relation among the output of the downstream oxygen sensor, skip amounts and an feedback air-fuel ratio dependent correction coefficient; Fig. 30 is a timechart showing time-domain relation among the output of the downstream oxygen sensor, integral constants and the feedback air-fuel ratio dependent correction coefficient; Fig. 31 is a timechart showing time-domain relation among the output of the downstream oxygen sensor, delay times, the output of the upstream oxygen sensor, a condition of a flag and the feedback air-fuel ratio dependent correction coefficient; and Fig. 32 is a characteristic map showing a relation between the output of the downstream oxygen sensor and the correction amount. DESCRIPTION OF THE PREFERRED EMBODIMENT Referring now to the drawings, an air-fuel ratio control system for a vehicular internal combustion engine according to a first preferred embodiment of the present invention will be described with reference to Figs. 1 to 12. Fig. 1 schematically shows the engine 1 and Fig. 2 is a block diagram showing an electronic control unit (ECU) 30 along with its peripheral input and output devices. The engine 1 includes an induction system 3, a combustion chamber 5 and an exhaust system 7. The induction system 3 includes, as known elements, an air cleaner (not shown), a throttle valve 9, a surge tank 11, an intake air pressure sensor or an intake vacuum sensor 13, a throttle position sensor 15 and an intake air temperature sensor 17 etc. The intake vacuum sensor 13 is disposed in the surge tank 11 to monitor an intake vacuum. The throttle position sensor 15 includes a throttle opening degree sensor 15a and an idle switch 15b. The idle switch 15b turns on at the engine idling. The exhaust system 7 includes, as known elements, an oxygen sensor or an O₂ sensor 19, an ignition coil 21, a distributor 23, an engine speed sensor 25, a cylinder detection sensor 27, an engine coolant temperature sensor 29 etc. The oxygen sensor 19 is of an electromotive-force-type and detects an oxygen concentration in the exhaust gas. The oxygen sensor 19 represents a sudden change in its output across the stoichiometric air-fuel ratio. The engine speed sensor 25 produces the number of pulses in proportion to an engine speed NE. The engine coolant temperature sensor 29 is mounted to a cylinder block la and detects a temperature of the engine coolant or the engine cooling water which is circulated to cool the engine cylinder block 1a. Signals from the above-referred sensors indicative of various engine operating conditions are fed into the ECU 30. The ECU 30 includes as a main component a microcomputer 31 having a CPU 31a, a ROM 31b and a RAM 31c etc. The microcomputer 31 is connected at its input/output port to the idle switch 15b, the engine speed sensor 25, the cylinder detection sensor 27, the ignition coil 21, a heater energization control circuit 33 and a drive circuit 35 etc. The ignition coil 21 is connected to the distributor 23 which is in turn connected to an ignition plug 41. The heater energization control circuit 33 controls an electric power supplied from a battery 37 to a heater 19b of the oxygen sensor 19. When the heater 19b is energized, a detection element 19a of the oxygen sensor 19 is heated. The drive circuit 35 is for actuating a fuel injection valve 39. The input/output port of the microcomputer 31 is connected via an analog-to-digital converter (A/D converter) 42 to the intake vacuum sensor 13, the throttle opening degree sensor 15a, the intake air temperature sensor 17 and the engine coolant temperature sensor 29 ect. which respectively produce analog signals. The A/D converter 42 is further input with an output of the heater energization control circuit 33, a terminal voltage of a current detection resistor 43 and an output of the detection element 19a of the oxygen sensor 19. The ECU 30 detects the operating conditions of the engine 1 based on the outputs from the above-described sensors and the heater energization control circuit 33 etc. and controls the operation of the engine 1. Fig. 3 shows a flowchart of a first air-fuel ratio feedback control routine, and Fig. 4 shows a block diagram for explaining the air-fuel ratio feedback control executed based on the flowchart in Fig. 3 in detail. The first air-fuel ratio feedback control routine as shown in Fig. 3 is executed by the CPU 31a of the ECU 30 as a timer interrupt per 20msec. A first step 100 determines whether a given condition for the air-fuel ratio feedback control is established. This determination is made based on, for example, engine coolant temperature data, fuel cut-off data and acceleration enrichment data. If answer at the step 100 is NO, i.e. the given condition is not established, then the routine goes to END to be terminated for a subsequent cycle of the interrupt routine. On the other hand, if answer at the step 100 is YES, then the routine goes to a step 110 which reads out an output voltage VOX from the oxygen sensor 19. At a subsequent step 120, a standard excess air ratio λ1 is derived based on the output voltage VOX read out at the step 110. The excess air ratio represents a rate of an actual air amount included in the mixture gas relative to an air amount included in the mixture gas of the stoichiometric air-fuel ratio. Accordingly, the excess air ratio at the time of the stoichiometric air-fuel ratio is set to 1.0. The standard excess air ratio λ1 is a value derived by estimating an air amount included in the monitored actual mixture gas based on the output voltage VOX which is indicative of an oxygen concentration in the exhaust gas or in the exhaust passage. Subsequently, a step 130 determines whether the idle switch is ON, i.e. whether the engine 1 is under the idling condition. If answer at the step 130 is NO, i.e. the idle switch is OFF, the routine goes to a step 140. At the step 140, a for-control excess air ratio λ2 which corresponds to the standard excess air ratio λ1 derived at the step 120 is derived using a characteristic map for the engine non-idling. At a subsequent step 150, the for-control excess air ratio λ2 derived at the step 140 is subtracted from a target excess air ratio λ0 to derive and set a deviation Δλ. The target excess air ratio λ0 represents an excess air ratio in the mixture gas of a target air-fuel ratio which is determined depending on the operating condition of the engine. For example, when the target air-fuel ratio is the stoichiometric air-fuel ratio, the target excess air ratio λ0 is 1.0. Subsequently, a step 160 determines whether the vehicle is under an immediate acceleration. If answer at the step 160 is NO, i.e. the vehicle is not under the immediate acceleration, the routine goes to a step 170 where calculation parameters for a PID (proportional, integral and differential actions) control are derived. On the other hand, if answer at the step 160 is YES, i.e. the vehicle is under the immediate acceleration, the routine goes to a step 180 where calculation parameters for a PI (proportional and integral actions) control are derived. Referring back to the step 130, if answer at the step 130 is YES, i.e. the idle switch 15b is ON, i.e. the engine is idling, then the routine goes to a step 190. At the step 190, a for-control excess air ratio λ2 which corresponds to the standard excess air ratio λ1 derived at the step 120 is derived using a characteristic map for the engine idling. Subsequently, at a step 200, the for-control excess air ratio λ2 is subtracted from a target excess air ratio λ0 to derive and set a deviation Δλ. At a subsequent step 210, calculation parameters for a PI (proportional and integral actions) control are derived. Finally, from one of the steps 170, 180 and 210, the routine goes to a step 220. At this step, a feedback air-fuel ratio dependent correction coefficient FAF is calculated, which will be described later in detail. When the step 220 is processed, the current cycle of the first air-fuel ratio feedback control routine is terminated. Based on the calculated FAF, the air-fuel ratio feedback control is performed in a known manner. Now, the air-fuel ratio feedback control performed by the flowchart of Fig. 3 will be described in detail with reference to the block diagram of Fig. 4 which is equivalent to the control routine of Fig. 3. The output voltage VOX of the oxygen sensor 19 is input to a linearlizer 50 which corresponds to the steps 110 and 120 in Fig. 3. The linearlizer 50 has a characteristic map as shown in Fig. 5. In practice, the data identified by this characteristic map is pre-stored in the ROM 31b. This characteristic map defines a relation between the output voltage VOX of the oxygen sensor 19 and the standard excess air ratio λ1. According to this characteristic map, the linearlizer 50 derives the standard excess air ratio λ1 which corresponds to the output voltage VOX received from the oxygen sensor 19. The derived standard excess air ratio λ1 is fed to a correction linearlizer 51 for the engine non-idling condition and a correction linearlizer 53 for the engine idling condition. The correction linearlizer 51 corresponds to the step 140 in Fig. 3, and the correction linearlizer 53 corresponds to the step 190 in Fig. 3. The correction linearlizer 51 has the characteristic map for the engine non-idling condition as shown in Fig. 6(A) or (B), and the correction linearlizer 53 has the characteristic map for the engine idling condition as shown in Fig. 7. In practice, the data identified by these characteristic maps is also pre-stored in the ROM 31b. The characteristic maps of Fig. 6(A) or (B) and Fig. 7 respectively show relations between the standard excess air ratio λ1 and the for-control excess air ratio λ2 and partly include a common basic relation between the standard excess air ratio λ1 and the for-control excess air ratio λ2. This common basic relation is shown in Fig. 8. As seen in Fig. 8, this common basic relation is that the for-control excess air ratio λ2 is held to be constant outside a given air-fuel ratio range having a width of 1% across the standard excess air ratio λ1 being 1.0 which represents the stoichiometric air-fuel ratio. Specifically, irrespective of variations in the standard excess air ratio λ1, the for-control excess air ratio λ2 does not vary outside the given air-fuel ratio range having the width of 1%, that is, 0.5% for each side across the standard excess air ratio λ1 being 1.0. This given air-fuel ratio range corresponds to the foregoing given air-fuel ratio range as shown in Fig. 12. Specifically, the unexpected unevenness or shift in level of the output voltage VOX due to the individual characteristic of the employed oxygen sensor or due to the measuring temperatures is highly revealed outside the above-noted given air-fuel ratio range. On the other hand, within the above-noted given air-fuel range, such unevenness or shift in level of the output voltage VOX is small enough to be ignored, which has been confirmed by the inventors of the present invention through various experiments. For this reason, the common basic relation is established in the characteristic maps both for the engine non-idling condition and for the engine idling condition so as to inhibit the unexpected unevenness or shift of the oxygen sensor output voltage VOX from reflecting upon the for-control excess air ratio λ2 during the execution of the air-fuel ratio feedback control. Now, the difference between the characteristic maps for the engine non-idling condition [Fig. 6(A) or (B)] and the engine idling condition (Fig. 7) will be described. As shown in Fig. 6(A) or (B), in the characteristic map for the engine non-idling condition, the for-control excess air ratio λ2 is shifted or biased in an upward or downward direction or in a rightward or leftward direction, that is, toward the RICH side or the LEAN side. Specifically, such a shift or bias is established only for the for-control excess air ratio λ2 which corresponds to the standard excess air ratio λ1 within the above-described given air-fuel ratio range in which the for-control excess air ratio λ2 varies depending on variations of the standard excess air ratio λ1. "RICH" or "LEAN" respectively means that the mixture gas is rich or lean with respect to the stoichiometric air-fuel ratio. On the other hand, as shown in Fig. 7, in the characteristic map for the engine idling condition, a variation rate of the for-control excess air ratio 12 relative to a variation of the standard excess air ratio λ1 is reduced in comparison with a basic variation rate of the for-control excess air ratio λ2 represented by a dotted line. Such a reduced relation is established only for the for-control excess air ratio λ2 which corresponds to the standard excess air ratio λ1 within the above-described given air-fuel ratio range except for small width ranges respectively adjacent to the RICH and LEAN side ends of the above-noted given air-fuel ratio range. Referring back to Fig. 4, the correction linearlizer 51 and the correction linearlizer 53 respectively output the for-control excess air ratio λ2 corresponding to the standard excess air ratio λ1 using the characteristic maps respectively for the engine non-idling condition and the engine idling condition. The for-control excess air ratio λ2 output from the correction linearlizer 51 is fed into a deviation calculation circuit 55, and the for-control excess air ratio λ2 output from the correction linearlizer 53 is fed into a deviation calculation circuit 57. Each of the deviation calculation circuits 55 and 57 outputs the deviation Δλ between the for-control excess air ratio λ2 and the target excess air ratio λ0. Based on the calculated deviation Δλ, the subsequent air-fuel ratio control is performed. Before describing the subsequent air-fuel ratio control, reference is made to how the characteristic maps for the engine non-idling condition and the engine idling condition reflect upon the control characteristic of the air-fuel ratio. As shown in Fig. 8 and as described before, both at the engine non-idling and at the engine idling, the for-control excess air ratio λ2 is held constant outside the given air-fuel ratio range of the standard excess air ratio λ1. However, when the for-control excess air ratio λ2 is held constant, the for-control excess air ratio λ2 has already increased to a sufficiently large value or decreased to a sufficiently small value. On the other hand, when the standard excess air ratio λ1 is within the given air-fuel ratio range, the for-control excess air ratio λ2 varies depending on variations of the standard excess air ratio λ1. Accordingly, since the air-fuel ratio control is performed based on the deviation Δλ between the for-control excess air ratio λ2 and the target excess air ratio λ0, the high follow-up characteristic of the air-fuel ratio control is ensured over all the ranges of the standard excess air ratio λ1. On the other hand, since the for-control excess air ratio λ2 stops varying when the standard excess air ratio is outside the given air-fuel range, the unexpected unevenness or shift in level of the output of the oxygen sensor 19 is inhibited from reflecting onto the air-fuel ratio control. Accordingly, the highly reliable control performance is ensured to improve the exhaust emission. At the engine non-idling, the following control characteristic is attained when the standard excess air ratio λ1 is within the given air-fuel ratio range: Fig. 9 shows one example of Fig. 6, wherein the for-control excess air ratio λ2 is biased toward the LEAN side as shown by a solid line. A dotted line shows the basic relation between the standard and for-control excess air ratios λ1 and λ2 with no such a bias. When the biased relation identified by the solid line is available in the correction linearlizer 51, the for-control excess air ratio λ2 is output from the correction linearlizer 51 as shown by a solid line in a timechart of Fig. 10. On the other hand, when the basic relation identified by the dotted line is available in the correction linearlizer 51, the for-control excess air ratio λ2 is output from the correction linearlizer 51 as shown by a dotted line in the timechart of Fig. 10. In Fig. 10, when the for-control excess air ratio λ2 is represented by the dotted line, a value 1.0 of the for-control excess air ratio λ2 which corresponds to the stoichiometric air-fuel ratio makes an area of the RICH side equal to an area of the LEAN side. In other words, when the area of the RICH side is considered to be positive and the area of the LEAN side is considered to be negative, a mean value of them becomes zero. On the other hand, in the case of the solid line, the value 1.0 of the for-control excess air ratio λ2 which corresponds to the stoichiometric air-fuel ratio λ2 does not make the respective areas equal to each other, but makes an area of the LEAN side larger than an area of the RICH side. This means that the center of the air-fuel ratio control is shifted toward the RICH side to compensate such a bias toward the LEAN side. Obviously, if the for-control excess air ratio λ2 is biased toward the RICH side as opposite to Fig. 9, then the center of the air-fuel ratio control is shifted toward the LEAN side to compensate the bias toward the RICH side. Accordingly, by changing or resetting an amount and a direction of such a bias or shift of the for-control excess air ratio λ2, a delicate adjustment of the center of the air-fuel ratio control is accomplished. As a result, even if the optimum air-fuel ratio for the exhaust emission differs due to the individual characteristic of each engine, the center of the air-fuel ratio is easily adjusted to the required optimum air-fuel ratio by resetting the above-noted bias of the for-control excess air ratio λ2. At the engine idling, the following control characteristic is attained when the standard excess air ratio λ1 is within the given air-fuel ratio range: As shown in Fig. 7 and as described before, a variation rate of the for-control excess air ratio λ2 identified by the solid line is set smaller than the reference variation rate identified by the dotted line. Such a reduced relation is established only for the for-control excess air ratio λ2 which corresponds to the standard excess air ratio λ1 within the above-described given air-fuel ratio range except for the small width ranges respectively adjacent to the RICH and LEAN side ends of the above-noted given air-fuel ratio range. Within such small width ranges, a variation rate of the for-control excess air ratio λ2 is set larger than the reference variation rate and is immediately increased. As a result, the variation rate of the for-control excess air ratio λ2 can be set smaller than a variation rate of the actual excess air ratio to diminish the control amplitude so that the high idling stability is attained. Further, when the standard excess air ratio λ1 deviates far from the stoichiometric value to get close to the RICH or LEAN side end of the given air-fuel ratio range, the for-control excess air ratio λ2 is immediately increased or decreased to provide the high follow-up characteristic. Now, referring back to Fig. 4, the air-fuel ratio control based on the derived deviation Δλ will be described hereinbelow in detail. The deviation Δλ output from the deviation calculation circuit 55 is fed to a PID controller 59 and a PI controller 61, respectively. The PID controller 59 is for the steady engine condition and the PI controller 61 is for the immediate acceleration. The PID controller 59 performs the feedback control identified by the following transfer function Gc(S): Gc S = Kp·(1+ 1 KiS )· 1+Kd·S 1+k·Kd·S where, Kp is a proportional constant, Ki is an integral constant, Kd is a differential constant and k is a differential weight constant. In the equation (1), a differential factor (1 + Kd·S)/(1 + k·Kd·S) represents an approximate expression. In practice, the step 220 of the first air-fuel ratio feedback control routine in Fig. 3 calculates the feedback air-fuel ratio dependent correction coefficient FAF in accordance with the following equation (2) which is equivalent to the equation (1): FAF = a·FAF0 - b·FAF00 + c·Δλ - d.Δλ0 + e·Δλ00 where, FAF is the feedback air-fuel ratio dependent correction coefficient derived per calculation cycle of 20msec., FAF0 is FAF derived in a last calculation cycle, FAF00 is FAF derived in a before-last calculation cycle, Δλ is a deviation derived per calculation cycle of 20msec., Δλ0 is the deviation Δλ derived in the last calculation cycle, and Δλ00 is the deviation Δλ derived in the before-last calculation cycle. The coefficients a, b, c, d and e of the respective terms in the equation (2) are derived based on the following equations (3) to (7): a= 1+ 2k·Kd Δt 1+ k·Kd Δt b= k·Kd Δt 1+ k·Kd Δt c= Kp·(1+ Kd Ki + Kd Δt + Δt Ki ) 1+ k·Kd Δt d= Kp·(1+ Kd Ki + 2Kd Δt ) 1+ k·Kd Δt e= Kp·Kd 1+ k·Kd Δt where, Δt is a calculation cycle. The step 170 of the first air-fuel ratio feedback control routine in Fig. 3 derives the calculation parameters, i.e. the coefficients a, b, c, d and e based on the foregoing equations (3) to (7). The PID control executed by the PID controller 59 will be explained with reference to Fig. 11. Fig. 11 (A) shows variations in the output of the oxygen sensor 19. As described before, in general, a response time of the oxygen sensor 19 is longer when changing from RICH to LEAN than from LEAN to RICH as identified by a solid line. Fig. 11(B) shows a signal derived by differentiating the oxygen sensor output of Fig. 11(A). Fig. 11(C) shows a signal after executing the PID control of the oxygen sensor output of Fig. 11(A) based on the foregoing equation (1). Accordingly, the PID controller 59 outputs the signal identified by a solid line in Fig. 11(C). As seen from the signal of Fig. 16(C), the above-mentioned difference in the response time of the oxygen sensor 19 due to its dynamic characteristic is substantially eliminated by the differential action, i.e. the response times from LEAN to RICH and from RICH to LEAN are substantially equal to each other. Accordingly, the PID control performed by the PID controller 59 effectively eliminates the conventional problem that the center of the air-fuel ratio control is deviated toward the LEAN side due to the dynamic characteristic of the oxygen sensor 19. As a result, the center of the air-fuel ratio control is stably controlled at the target value so that the exhaust emission is controlled properly. As described before, the differential factor represents the approximate expression, which is for suppressing the influence of ripples contained in the oxygen sensor output voltage. On the other hand, the PI controller 61 performs the feedback control identified by the following transfer function Gc(S): Gc S =Kp·(1+ 1 KiS ) where, Kp is a proportional constant and Ki is an integral constant. The equation (8) does not include the differential factor (1 + Kd·S)/(1 + k·Kd·S) which is included in the equation (1). In practice, the step 220 in Fig. 3 derives the feedback air-fuel ratio dependent correction coefficient FAF for the immediate acceleration condition based on the following equation (9) which is equivalent to the equation (8): FAF = a·FAF0 - b·FAF00 + c·Δλ - d·Δλ0 + e·Δλ00 where, FAF is the feedback air-fuel ratio dependent correction coefficient derived per calculation cycle of 20msec., FAF0 is FAF derived in a last calculation cycle, FAF00 is FAF derived in a before-last calculation cycle, Δλ is a deviation derived per calculation cycle of 20msec., Δλ0 is the deviation Δλ derived in the last calculation cycle, and Δλ00 is the deviation Δλ derived in the before-last calculation cycle. The coefficients a, b, c, d and e of the respective terms in the equation (9) are derived based on the following equations (10) to (14): a = 1 , b = 0 , d = Kp e = 0 c= Kp·(1+ Ki Δt )·Δt Ki where, Δt is a calculation cycle. The step 180 in Fig. 3 derives the calculation parameters, i.e. the coefficients a, b. c. d and e based on the equations (10) to (14). The PI control is performed under the immediate acceleration due to the following reason: In the foregoing PID control, the oxygen sensor output signal is corrected by the differential action to substantially eliminate the influence of the dynamic characteristic of the oxygen sensor 19. However, the differential action also works to deteriorate the follow-up characteristic of the control. Since the transitional condition such as the immediate acceleration condition requires the high follow-up controllability of the air-fuel ratio, the air-fuel ratio control under such a condition is performed based on the PI control which includes no differential factor. As a result, the center of the air-fuel ratio control quickly follows the target air-fuel ratio. The feedback air-fuel ratio dependent correction coefficients FAF output from the PID controller 59 and the PI controller 61 are fed to a first selection circuit 63. The first selection circuit 63 is also fed with a pressure variation ΔPm from the intake vacuum sensor 13 and corresponds to the step 160 in Fig. 3. The first selection circuit 63 determines based on the input pressure variation ΔPm whether the engine is under the steady condition or the immediate acceleration. When the steady condition is determined, then the first selection circuit 63 outputs the correction coefficient FAF fed from the PID controller 59 to a second selection circuit 67, on the other hand, when the immediate acceleration is determined, then the first selection circuit 63 outputs the correction coefficient FAF fed from the PI controller 61 to the second selection circuit 67. Now, explanation will be made to a calculation of the feed back air-fuel ratio dependent correction coefficient FAF for the engine idling condition. The deviation Δλ output from the deviation calculation circuit 57 is fed to a PI controller 65. The PI controller 65 performs the feedback control identified by the following transfer function Gc(S): Gc S =Kp·(1+ 1 KiS ) where, Kp is a proportional constant and Ki is an integral constant. As the foregoing transfer function Gc(S) for the immediate acceleration condition, the equation (15) does not include the differential factor (1 + Kd·S)/(1 + k·Kd·S) which is included in the equation (1) for the engine non-idling steady condition. In practice, the step 220 in Fig. 3 calculates the feedback air-fuel ratio dependent correction coefficient FAF based on the following equation (16) which is equivalent to the equation (15): FAF = a·FAF0 - b·FAF00 + c·Δλ - d·Δλ0 + e·Δλ00 where, FAF is the feedback air-fuel ratio dependent correction coefficient derived per calculation cycle of 20msec., FAF0 is FAF derived in a last calculation cycle, FAF00 is FAF derived in a before-last calculation cycle, Δλ is a deviation derived per calculation cycle of 20msec., Δλ0 is the deviation Δλ derived in the last calculation cycle, and Δλ00 is the deviation Δλ derived in the before-last calculation cycle. The coefficients a, b, c, d and e of the respective terms in the equation (16) are derived based on the following equations (17) to (21): a = 1 , b = 0 , d = Kp e = 0 c= Kp·(1+ Ki Δt )·Δt Ki where, Δt is a calculation cycle. The proportional constant Kp in the equation (19) and the integral constant Ki in the equation (21) are respectively set to values which are different from the proportional constant Kp in the equation (12) and the integral constant Ki in the equation (14) for the immediate acceleration condition. The step 210 in Fig. 3 derives the calculation parameters, i.e. the coefficients a, b, c, d and e based on the equations (17) to (21). The feedback air-fuel ratio dependent correction coefficient FAF output from the PI controller 65 is fed to the second selection circuit 67. The second selection circuit 67 is also fed with a signal from the idle switch 15b indicative of idling data of the engine and corresponds to the step 130 in Fig. 3. The second selection circuit 67 determines based on the input idling data indicative signal whether the engine is idling or not. When the engine non-idling is determined, the second selection circuit 67 outputs the correction coefficient FAF fed from the PID controller 59 or the PI controller 61 to the engine 1, on the other hand, when the engine idling is determined, the second selection circuit 67 outputs the correction coefficient FAF fed from the PI controller 65 to the engine 1. The engine 1 performs the air-fuel ratio feedback control based on the input correction coefficient FAF in a known manner. As appreciated from the foregoing description, the first preferred embodiment has the following advantages: As shown in Fig. 8, when the standard excess air ratio λ1 derived based on the output signal from the oxygen sensor 19 is within the given air-fuel ratio range, the for-control excess air ratio λ2 varies according to variations in the standard excess air ratio λ1, on the other hand, when the standard excess air ratio λ1 is outside the given air-fuel ratio range, the for-control excess air ratio λ2 is held constant. Accordingly, not only the high follow-up characteristic of the control is realized, but the unexpected unevenness or shift in level of the oxygen sensor output is effectively excluded from the air-fuel ratio feedback control. As a result, the highly reliable control performance is ensured to improve the exhaust emission. Further, since the PID control is executed during the engine non-idling steady condition, the dynamic characteristic of the oxygen sensor 19 as shown in Fig. 11(A) is effectively compensated to substantially equalize the response times from LEAN to RICH and from RICH to LEAN as shown in Fig. 11(C). Accordingly, the deviation or bias of the center of the air-fuel ratio control toward the LEAN side is prevented as opposed to the prior art so that the exhaust emission is improved. Further, as shown in Fig. 7, the variation of the for-control excess air ratio λ2 for the engine idling condition is set smaller within the given air-fuel ratio range of the standard excess air ratio λ1 except for at the LEAN and RICH side ends thereof. Since the air-fuel ratio feedback control is performed based on the deviation Δλ between the for-control excess air ratio λ2 and the target excess air ratio λ0, the improved follow-up controllability of the air-fuel ratio as well as the high engine stability are ensured during the engine idling. Further, since the for-control excess air ratio λ2 is set biased or shifted toward the RICH or LEAN side in comparison with the actual excess air ratio as shown in Fig. 6 (A) or (B), the center of the air-fuel ratio control is shifted toward the LEAN or RICH side respectively to compensate for such a bias of the for-control excess air ratio λ2. Accordingly, by adjusting a magnitude and a direction of the bias, the center of the air-fuel ratio control is delicately adjusted to the optimum air-fuel ratio depending on the individual characteristic of the engine so as to improve the exhaust emission. Further, the PID control is executed during the engine non-idling steady condition to put more weight on the stability of the air-fuel ratio control, on the other hand, the PI control which includes no differential action is executed during the immediate acceleration to put more weight on the follow-up characteristic of the control. Accordingly, the desirable control characteristic is provided depending on the vehicular running condition. The linear characteristics of the correction linearlizers 51 and 53 defined by the respective linear functions may be replaced by proper curved characteristics defined by a quadratic function. Further, the characteristics of the correction linearlizers 51 and 53 may be given in the form of conversion table data or matrix data. Obviously, the detection of the engine idling condition and the immediate acceleration condition etc. may also be performed by known means other than those disclosed in the first preferred embodiment. Now, a second preferred embodiment of the air-fuel ratio control system according to the present invention will be described with reference to Figs. 13 to 21. In these figures, the same or like members or components are designated by the same reference numerals as in the first preferred embodiment to omit explanation thereof so as to avoid a redundant disclosure. In the second preferred embodiment, the foregoing biased characteristic of the correction linearlizer 51 identified by the dotted line in Fig. 6 and by the solid line in Fig. 9 is further corrected by an output from a downstream oxygen sensor 119. Specifically, the characteristic of the correction linearlizer 51 that the for-control excess air ratio λ2 is biased or shifted toward the RICH or LEAN side is further corrected based on the output of the downstream oxygen sensor 119 toward the RICH or LEAN side. As schematically shown in Fig. 13, the downstream oxygen sensor 119 is provided in the exhaust system 7 downstream of a catalytic converter 118 which is provided downstream of the oxygen sensor 19 (hereinafter referred to as "the upstream oxygen sensor 19" or "the oxygen sensor 19"). The output of the downstream oxygen sensor 119 is also fed into the ECU 30. As shown in a block diagram of Fig. 14, a mean excess air ratio λ 1x is derived based on an output voltage V2 of the downstream oxygen sensor 119 using a map in Fig. 16 or in a block 120 which defines a relation between the output voltage V2 and the mean excess air ratio λ 1x which represents an estimated excess air ratio contained in the actual mixture gas in view of the output voltage V2. Then, a correction amount dλ y is derived using a map in Fig. 17 or in a block 122 which defines a relation between a deviation Δλ x derived by subtracting the mean excess air ratio λ 1x from a target excess air ratio λ0 and the correction amount dλ y . Based on the derived correction amount dλ y , the foregoing biased for-control excess air ratio λ2 in the correction linearlizer 51 is further corrected toward the RICH or LEAN side within the foregoing given air-fuel ratio range of the standard excess air ratio λ1. Subsequently, based on the further corrected for-control excess air ratio λ2, the air-fuel ratio control is performed in substantially the same manner as in the first preferred embodiment. The output of the downstream oxygen sensor 119 is more reliable than that of the upstream oxygen sensor 19 in view of the following reasons: Downstream of the catalytic converter where the downstream oxygen sensor 119 is provided: (1) An oxygen concentration in the exhaust gas is substantially equalized. Accordingly, a variation in the output characteristic of the oxygen sensor due to its individual characteristic is suppressed to be small. (2) Since an exhaust gas temperature is relatively low, a heat based influence to the oxygen sensor is small. Further, since harmful substances in the exhaust gas are caught in the catalytic converter, the oxygen sensor is subject to less harmful substances. Accordingly, time dependent variations in the output characteristic of the oxygen sensor is suppressed to be small. In the foregoing first preferred embodiment, there is a possibility that the output of the oxygen sensor 19 becomes unreliable due to such as uneven air-fuel ratios distributed in the exhaust gas discharged from a plurality of the engine cylinders or due to a time dependent deterioration of the oxygen sensor 19. As a result, the center of the air-fuel ratio control is deviated from the target air-fuel ratio to spoil the exhaust emission. Accordingly, in the second preferred embodiment, the foregoing biased for-control excess air ratio λ2 is further corrected toward the RICH or LEAN side within the given air-fuel ratio range of the standard excess air ratio λ1, depending on the more reliable output voltage V2 of the downstream oxygen sensor 119. This leads to the more reliable air-fuel ratio control which enables the center of the air-fuel ratio control to be delicately adjusted to the target air-fuel ratio so as to improve the exhaust emission. In the second preferred embodiment, the output voltage V2 of the downstream oxygen sensor 119 is used to derive the mean excess air ratio λ 1x which is pre-stored as map data accessible in terms of the output voltage V2, but not used for determining RICH or LEAN in an on-off manner. Since the foregoing biased for-control excess air ratio λ2 is further corrected within the above-noted given air-fuel range toward the RICH or LEAN side based on the deviation Δλ x between the mean excess air ratio λ 1x and the target excess air ratio λ0, the center of the air-fuel ratio control is more delicately adjusted to the target air-fuel ratio depending on a degree of RICH or LEAN of the actual air-fuel ratio detected by the downstream oxygen sensor 119. Fig. 15 shows a first linearlize characteristic correction routine executed by the CPU 31a in the ECU 30 as a timer interrupt per cycle which is longer than that of the first air-fuel ratio feedback control routine in Fig. 3. In the second preferred embodiment, the microcomputer 31 in Fig. 2 is also fed with the output signal from the downstream oxygen sensor 119 via the A/D converter 41. In Fig. 15, at a first step 210, the output voltage V2 of the downstream oxygen sensor 119 is read out via the A/D converter 41. The downstream oxygen sensor 119 is of the same type as the oxygen sensor 19, i.e. of the electromotive-force-type and monitors the oxygen concentration in the exhaust gas. The steps 220 to 270 correspond to a block 124 in Fig. 14, wherein the correction amount dλ y is derived based on the read-out output voltage V2 using the maps of Figs. 16 and 17 or of the blocks 120 and 122 and the biased characteristic of the correction linearlizer 51 is further corrected based on the derived correction amount dλ y . Specifically, at the step 220, the mean excess air ratio λ 1x is derived based on the read-out output voltage V2 using the map in the block 120. Subsequently, at the step 240, the deviation Δλ x is derived by subtracting the mean excess air ratio λ 1x from the target excess air ratio λ0 and stored in the RAM 31c. Since the downstream oxygen sensor 119 is of the same type as the oxygen sensor 19, the map in the block 120 represents substantially the same characteristic as that of the foregoing linearlizer 50 in the first preferred embodiment. Accordingly, when the actual air-fuel ratio becomes larger (LEAN) than the target air-fuel ratio to increase the oxygen concentration in the exhaust gas, the output voltage V2 decreases so that the deviation Δλ x becomes negative. On the other hand, when the actual air-fuel ratio becomes smaller (RICH) than the target air-fuel ratio, the output voltage V2 increases so that the deviation Δλ x becomes positive. At the subsequent step 250, the correction amount dλ y is derived based on the derived deviation Δλ x using the map in the block 122. As shown in Fig. 17, in the map of the block 122, the correction amount dλ y is directly proportional to the deviation Δλ x within a given range across a zero value of the deviation Δλ x . Specifically, the given range of the deviation Δλ x comprises the same given width on the positive and negative sides with respect to the zero value of the deviation Δλ x . On the other hand, the correction amount dλ y is held constant outside the given range of the deviation Δλ x irrespective of variations in the deviation Δλ x . Subsequently, the steps 260 and 270 correct the biased characteristic of the correction linearlizer 51 as identified by the solid line in Fig. 9 based on the correction amount dλ y derived at the step 250. In Fig. 18, a dotted line corresponds to the solid line in Fig. 9, that is, the characteristic of the correction linearlizer 51 before this correction routine, on the other hand, a solid line represents the characteristic of the correction linearlizer 51 corrected by this correction routine. An intersection between a dotted line extending from a RICH side end point A of the given air-fuel ratio range and a dotted line extending from a LEAN side end point B thereof is defined as an X-Y coordinate position (λ1, λ2) = (1.0, λ 2B ). The Y-coordinate λ 2B will be hereinafter referred to as "the before-correction base value". At the step 260, the correction amount dλ y is added to the before-correction base value λ 2B to derive a corrected Y-coordinate λ 2m which is stored in the RAM 31c. The Y-coordinate λ 2m will be hereinafter referred to as "the corrected base value". At the step 270, the X-Y coordinate position (1.0, λ 2B ) is shifted to a corrected X-Y coordinate position (1.0, λ 2m ) as indicated by an arrow in Fig. 18. Further, at the step 270, the corrected X-Y coordinate position (1.0, λ 2m ) is connected to the point A and the point B respectively so as to attain the corrected linearlize characteristic of the correction linearlizer 51. In the corrected linearlize characteristic, the linearlize characteristic identified by the dotted line in Fig. 18 is biased further toward the LEAN side by the correction amount dλ y . Obviously, a magnitude and a direction of the correction of the X-Y coordinate position (1.0, λ 2B ),i.e. the linearlize characteristic identified by the dotted line in Fig. 18 depend on the correction amount dλ y derived at the step 250. The corrected characteristic of the correction linearlizer 51 is stored in a RAM energized by a special power source which is constantly charged by the vehicular battery, and this correction routine is ended. Subsequently, based on the linearlize characteristic corrected by this correction routine, the air-fuel feedback control is performed as in the first preferred embodiment and as shown in Fig. 14. Further explanation will be made hereinbelow to the correction routine of Fig. 15. As shown by an arrow in Fig. 16, when the oxygen concentration in the exhaust gas downstream of the catalystic converter 118 becomes higher (LEAN) than the target excess air ratio λ0, the output voltage V2 of the downstream oxygen sensor 119 decreases to increase the mean excess air ratio λ 1x so that the deviation Δλ x becomes a negative value. As shown by an arrow in Fig. 17, since the deviation Δλ x is the negative value, the correction amount dλ y also becomes a negative value so that, as shown by the solid line in Fig. 18, the biased characteristic of the correction linearlizer 51 toward the LEAN side is further corrected toward the LEAN side. Accordingly, the for-control excess air ratio λ2 is largely deviated toward the LEAN side so that the deviation Δλ between the for-control excess air ratio λ2 and the target excess air ratio λ0 becomes a larger negative value in comparison with that derived before the first correction routine of Fig. 15 is performed. The air-fuel ratio feedback control is performed based on the feedback air-fuel ratio dependent correction coefficient FAF which is derived using this deviation Δλ having the larger negative value. As a result, the center of the air-fuel ratio control which is deviated to the LEAN side is delicately adjusted toward the RICH side to bring the actual excess air ratio to the target excess air ratio λ 0, which can be seen from Fig. 10. In the first linearlize characteristic correction routine as described above, the correction amount dλ y is directly proportional to the deviation Δλ x within the predetermined range of the deviation Δλ x . Since the deviation Δλ x is derived by subtracting the mean excess air ratio λ 1x derived based on the output voltage V2 of the downstream oxygen sensor 119 from the target excess air ratio λ0, the corrected base value λ 2m derived by adding the correction amount dλ y to the before-correction base value λ 2B represents a degree of bias or shift of the corrected characteristic of the correction linearlizer 51 toward the RICH or LEAN side. As shown in a timechart of Fig. 19, time-domain variations of the corrected base value λ 2m corresponds to time-domain variations of the output voltage V2 of the downstream oxygen sensor 119. As appreciated from the foregoing description, according to the second preferred embodiment, the for-control excess air ratio λ2 derived by the biased characteristic of the correction linearlizer 51 is further corrected toward the RICH or LEAN side within the given air-fuel ratio of the standard excess air ratio λ1 according to the reliable output voltage V2 of the downstream oxygen sensor 119. Accordingly, the center of the air-fuel ratio feedback control is delicately adjusted to the target air fuel ratio as much as possible to improve the exhaust emission. In the second preferred embodiment, the biased characteristic of the correction linearlizer 51 identified by the solid line in Fig. 9 is further corrected by the first linearlize characteristic correction routine of Fig. 15. Instead of this, the non-biased characteristic of the correction linearlizer 51 identified by the dotted line in Fig. 9 may be corrected by the first correction routine of Fig. 15. In this case, the before-correction base value λ 2B may be a Y-coordinate corresponding to a predetermined X-coordinate such as the X-coordinate 1.0. Further, when the characteristic of the correction linearlizer 51 is biased toward the LEAN side as identified by the lower dotted line in Fig. 6(B), such a biased characteristic of the correction linearlizer 51 may be further corrected toward the RICH or LEAN side based on the correction amount dλ y as indicated by an arrow in Fig. 20 where the before-correction characteristic is shown by a dotted line and the after-correction characteristic is shown by a solid line. Further, the two maps of Figs. 16 and 17 may be replaced by one map as shown in Fig. 21. In Fig. 21, a relation between the output voltage V2 of the downstream oxygen sensor 119 and the correction amount dλ y is defined. When the map of Fig. 21 is used, a data volume to be pre-stored is reduced and a processing speed gets faster. In Fig. 21, V0 represents a value of the output voltage V2 of the downstream oxygen sensor 119 which corresponds to an oxygen concentration of the target air-fuel ratio. Now, a third preferred embodiment of the air-fuel ratio control according to the present invention will be described with reference to Figs. 22 and 23. In the second preferred embodiment, the output voltage V2 of the downstream oxygen sensor 119 is reflected on the correction amount dλ y using the maps of Figs. 16 and 17. On the other hand, in the third preferred embodiment, the output voltage V2 of the downstream oxygen sensor 119 is compared with a reference voltage VO corresponding to the target excess air ratio λ0 to determine whether the air-fuel ratio is RICH or LEAN relative to the target air-fuel ratio. At the time of an inversion between RICH and LEAN, the before-correction base value λ 2B is changed in a skipped or stepped manner, and then the before-correction base value λ 2B is changed by a small amount, i.e. bit by bit until a next occurrence of inversion between RICH and LEAN. Specifically, the output voltage V2 of the downstream oxygen sensor 119 is first compared with the output voltage V0 representing the target excess air ratio λ0 to determine whether the air-fuel ratio is RICH or LEAN. At the time of an inversion from RICH to LEAN, a given amount dλ R is subtracted as shown in the following equation (22): λ 2m = λ 2B - dλ R Subsequently, a correction amount Δλ R is subtracted per given time until an inversion from LEAN to RICH, as shown in the following equation (23): λ 2m = λ 2B - dλ R - Δλ R ·t On the other hand, at the time of an inversion from LEAN to RICH, a given amount dλ L is added as shown in the following equation (24): λ 2m = λ 2B + dλ L Subsequently, a correction amount Δλ L is added per given time until an inversion from RICH to LEAN, as shown in the following equation (25): λ 2m = λ 2B + dλ L + Δλ L ·t The correction process represented by the equations (22) to (25) will be described in detail hereinbelow with reference to a flowchart of Fig. 22 which shows a second linearlize characteristic correction routine. The second linearlize characteristic correction routine is for correcting the characteristic of the correction linearlizer 51 represented by the solid line in Fig. 9 and is executed by the CPU 31a in ECU 30 as a timer interrupt per cycle of 1sec. Through steps 301 to 305, it is checked whether a condition for executing the second linearlize characteristic correction routine is established. Specifically, the first step checks whether a condition for the air-fuel ratio feedback control is established. The step 301 corresponds to the step 100 in Fig. 3. If answer at the step 301 is NO, then the routine ends. If answer at the step 301 is YES, i.e. the condition for the air-fuel ratio feedback control is established, then the routine goes to the step 303 where an engine coolant temperature is compared with a given value such as 70°C. If answer at the step 303 is NO, i.e. the engine coolant temperature is no more than the given value (THW ≦ 70°C ), then the routine ends. If answer at the step 303 is YES (THW > 70°C), then the step 305 checks whether the idle switch 15b is OFF, i.e. whether the throttle valve 9 is not fully closed. If answer at the step 305 is NO, i.e. the idle switch is ON (LL = 1), then the routine ends. When answer at the step 301, 303 or 305 is NO to end the routine, the characteristic of the correction linearlizer 51 is held unchanged. If answer at the step 305 is YES, i.e. the idle switch is OFF (LL = 0), then the characteristic of the correction linearlizer 51 is corrected through steps 307 to 337 based on the output voltage V2 of the downstream oxygen sensor 119. Specifically, through the steps 307 to 313, it is determined based on the output voltage V2 of the downstream oxygen sensor 119 whether the air-fuel ratio is RICH or LEAN. Subsequently, through the steps 315 to 319, a correction amount ΔRS is derived. Through the steps 321 to 333, a coordinate value λC of the for-control excess air ratio λ2 is corrected based on the derived correction amount ΔRS. The coordinate value λC corresponds to the standard excess air ratio λ1 being 1.0, i.e. the stoichiometric air-fuel ratio in the characteristic map of Fig. 9. Subsequently, at the step 335 or 337, the characteristic of the correction linearlizer 51 is corrected based on the corrected value λC. Referring back to the step 307, the CPU 31a reads out the output voltage V2 of the downstream oxygen sensor 119 via the A/D converter 41. Subsequently, the step 309 compares the read-out output voltage V2 with a reference voltage V0 to determine whether the monitored air-fuel ratio is RICH or LEAN. If V2 ≦ V0 (LEAN), a flag F2 is reset to 0, on the other hand, if V2 > V0, then the flag F2 is set to 1. Subsequently, the routine goes to the step 315 which determines whether the flag F2 has been inverted at the step 311 or 313. If answer at the step 315 is YES, i.e. the flag F2 has been inverted, then the step 317 derives an engine speed N based on an output signal from the engine speed sensor 25 and further derives by interpolation the correction amount ΔRS based on the derived engine speed N using a pre-stored one dimensional map. The engine speed N represents an engine parameter indicative of a transfer delay of the exhaust gas. Accordingly, in the characteristic of the pre-stored one dimensional map, the correction amount ΔRS decreases corresponding to increasing of the engine speed N. Specifically, when the engine speed N increases to reduce the exhaust gas transfer delay at the engine high load driving, the correction amount ΔRS is set to a small value. On the other hand, when the engine speed N decreases to increase the exhaust gas transfer delay at the engine low load driving, the correction amount ΔRS is set to a large value. If answer at the step 315 is NO, i.e. no inversion of the flag F2 has been occurred at the step 311 or 313, then the routine goes to the step 319 where the correction amount ΔRS is set to a fixed amount ΔRSj which is far smaller than the correction amount ΔRS at the step 317. Subsequently, the routine goes to the step 321 which checks whether the flag F2 is 0, i.e. whether the monitored air-fuel ratio is LEAN. If answer at the step 321 is YES, a new value of λC is derived by subtracting the correction value ΔRS derived at the step 317 or 319 from a current value of λC which was derived in the last cycle of this routine. At the subsequent step 327, the new value λC is compared with a preset minimum value. If answer at the step 327 is YES, i.e. the new value λC is less the preset minimum value, the new value λC is set to the preset minimum value at the step 329. Subsequently, the routine goes to the step 335. On the other hand, if answer at the step 327 is NO, i.e. the new value λC is no less than the preset minimum value, the routine goes to the step 335. At the step 335, the characteristic map of the correction linearlizer 51 is updated based on the new value λC derived at the step 323 or 329. Specifically, as in the second preferred embodiment, the X-Y coordinate position (λ1, λ2) = (1.0, λ C) is updated by the new λC, and subsequently a new X-Y coordinate position (1.0, new λC) is connected to the RICH side end point A and the LEAN side end point B by respective lines. Referring back to the step 321, if answer at the step 321 is NO, i.e. the monitored air-fuel ratio is RICH, then the routine goes to the step 325 where a new λC is derived by adding the correction value ΔRS to the value λC which was derived in the last cycle of this routine. Subsequently, at the step 331, the new λC is compared with a preset maximum value. If answer at the step 331 is YES, i.e. the new λC is larger than the preset maximum value, the new λC is set to the preset maximum value at the step 333. Thereafter, the routine goes to the step 337. On the other hand, if answer at the step 331 is NO, i.e. the new λC is no larger than the preset maximum value, the routine goes to the step 337. At the step 337, the characteristic map of the correction linearlizer 51 is updated in the same manner as at the step 335. The preset minimum value at the step 327 is determined not to spoil the follow-up characteristic of the control under the engine transitional condition. On the other hand, the preset maximum value is determined not to deteriorate the driving performance due to variations in the air-fuel ratio. After the characteristic of the correction linearlizer 51 is updated at the step 335 or 337, the second linearlize characteristic correction routine is ended and the air-fuel ratio feedback control is performed based on the updated characteristic of the correction linearlizer 51 as in the foregoing first and second preferred embodiments. As shown in Fig. 23, time-domain variations of the value λC corrected by the second linearlize characteristic correction routine of Fig. 22 substantially correspond to time-domain variations of the output voltage V2 of the downstream oxygen sensor 119. Accordingly, the third preferred embodiment enables the center of the air-fuel ratio feedback control to follow the target air-fuel ratio as in the second preferred embodiment. Further, in the third preferred embodiment, since the correction amount ΔRS is derived based on the monitored engine speed N which is indicative of the exhaust gas transfer delay, the response characteristic of the downstream oxygen sensor 119 is improved on a practical basis. The engine speed N may be replaced by another engine load indicative parameter such as a monitored intake air amount or a monitored intake vacuum pressure for deriving the correction amount ΔRS. Further, the pre-stored one dimensional map used at the step 317 may be replaced by a two dimensional map which defines the correction amount ΔRS in terms of the engine speed and the intake air amount or the intake vacuum pressure. Fig. 24 shows a third linearlize characteristic correction routine which is a modification of the third preferred embodiment. In the second linearlize characteristic correction routine of Fig. 22, the value λC is changed in the skipped manner at the inversion between RICH and LEAN and is thereafter changed per fixed small amount until a next occurrence of the inversion between RICH and LEAN. On the other hand, in the third correction routine of Fig. 24, a correction amount ΔRSi is derived based on an engine parameter such as the engine speed N which is indicative of the exhaust gas transfer delay, and the value λC is corrected by subtracting the correction amount ΔRSi therefrom per execution cycle of the correction routine when the monitored air-fuel ratio is LEAN and by adding the correction amount ΔRSi thereto per execution cycle of the correction routine when the monitored air-fuel ratio is RICH. Steps 401 to 407 correspond to the steps 301 to 307 in Fig. 22. At a subsequent step 409, the correction amount ΔRSi is derived by interpolation based on the engine speed N using a pre-stored one dimensional map which defines a relation between the engine speed N and the correction amount ΔRSi. In the map at the step 409, the correction amount ΔRSi is set to decrease corresponding to increasing of the engine speed N as in the map at the step 317 in Fig. 22. The step 411 corresponds to the step 309 in Fig. 22 and determines whether the monitored air-fuel ratio is RICH or LEAN. If LEAN is determined at the step 411, the characteristic map of the correction linearlizer 51 is corrected through steps 413, 417, 419 and 425 which respectively correspond to the steps 323, 327, 329 and 335 in Fig. 22. On the other hand, if RICH is determined at the step 411, the characteristic map of the correction linearlizer 51 is corrected through steps 415, 421, 423 and 427 which respectively correspond to the steps 325, 331, 333 and 337 in Fig. 22. As shown in Fig. 23, time-domain variations of the value λC corrected by the third correction routine of Fig. 24 correspond to time-domain variations of the output voltage V2 of the downstream oxygen sensor 119 as in the case of the second correction routine of Fig. 22. Accordingly, in this modification of the third preferred embodiment, the center of the air-fuel ratio feedback control is delicately adjusted to follow the target air-fuel ratio with simpler process. Since the correction amount ΔRSi is derived based on the monitored engine speed N, the response characteristic of the downstream oxygen sensor 119 is improved on a practical basis also in the third correction routine of Fig. 24. Further, as in the second correction routine of Fig. 22, the one dimensional map at the step 409 may be replaced by a two dimensional map which defines the correction amount ΔRSi in terms of the engine speed and the intake vacuum pressure or the intake air amount. Further, in the first preferred embodiment and in the first to third linearlize characteristic correction routines, the oxygen sensors 19 and 119 may be replaced by any sensor such as a CO sensor and a lean mixture sensor as long as it detects a concentration of a particular component contained in the exhaust gas so as to monitor the air-fuel ratio of the exhaust gas. Further, though the biased characteristic of the correction linearlizer 51 of the first preferred embodiment is further corrected in the first to third correction routines of Figs. 15, 22 and 24, such a further corrected characteristic of the correction linearlizer 51 is prepared beforehand based on the output voltage V2 of the downstream oxygen sensor 119 and pre-stored in the foregoing backed RAM. Specifically, when finally setting the characteristic of the correction linearlizer 51, the engine is operated under a non-idling condition so as to correct and bias the characteristic of the correction linearlizer 51 identified by the solid line in Fig. 6(A) or (B) toward the RICH or LEAN side within the given air-fuel ratio range of the standard excess air ratio λ1 based on the detected output voltage V2 of the downstream oxygen sensor 119. This biased characteristic of the correction linearlizer 51 is pre-stored in the foregoing backed RAM. This biasing correction of the characteristic of the correction linearlizer 51 is easily performed by using one of the foregoing first to third correction routines. For example, when the first correction routine of Fig. 15 is used, the for-control excess air ratio λ2 corresponding to a value 1.0 of the standard excess air ratio λ1 in the non-biased characteristic of the correction linearlizer 51 as identified by the solid line in Fig. 6(A) is set as the before-correction base value λ 2B . Subsequently, the after-correction base value λ 2m is derived by adding the correction amount dλ y derived based on the output voltage V2 to the before-correction base value λ 2B . Thereafter, the lines are drawn from the new X-Y coordinate position (1.0, λ 2m ) to the RICH and LEAN side end points A and B respectively so as to bias or shift the non-biased characteristic of the correction linearlizer 51 toward the RICH or LEAN side as shown by one of the dotted lines in Fig. 6(A). Explanation will be further made to biasing the non-biased characteristic of the correction linearlizer 51 with reference to Fig. 6(B), using the first correction routine of Fig. 15. In the non-biased characteristic of the correction linearlizer 51 identified by the solid line in Fig. 6(B), one of the points A and B is held fixed and the other of the points A and B is displaced along the X-axis, i.e. the axis for the standard excess air ratio λ 1. For example, when biasing the characteristic toward the LEAN side, the point A is held fixed and only an X-coordinate of the point B is displaced toward the Y-axis by an amount corresponding to the correction amount dλ y so as to obtain a point B1. The biased characteristic of the correction linearlizer 51 is attained by connecting the point B1 to the point B and to the point A respectively. When biasing the characteristic of the correction linearlizer 51 toward the RICH side, the point B is held fixed and only an X-coordinate of the point A is displaced away from the Y-axis by an amount corresponding to the correction amount dλ y so as to obtain a point A1. The biased characteristic of the correction linearlizer 51 is attained by connecting the point A1 to the point A and to the point B respectively. Obviously, the displacement may also be made in a B1-to-B direction or in a A1-to-A direction. Still further, when the second or third correction routine of Fig. 22 or 24 is used, a negative value of the correction amount ΔRS or ΔRSi is used instead of the correction amount dλ y when the monitored air-fuel ratio is LEAN and a positive value of the correction amount ΔRS or ΔRSi is used instead of the correction amount dλ y when the monitored air-fuel ratio is RICH. The subsequent process is the same as in the foregoing case where the first correction routine is used. Further, though the value λC represents a Y-coordinate corresponding to an X-coordinate 1.0 of the standard excess air ratio λ1, i.e. the stoichiometric air-fuel ratio in the first to third correction routines, the value λC may represent a Y-coordinate corresponding to an X-coordinate other than 1.0, i.e. other than a standard excess air ratio λ1 corresponding to the stoichiometric air-fuel ratio. In other words, the value λC may correspond to the standard excess air ratio λ1 which corresponds to a target excess air ratio λ0 other than the stoichiometric air-fuel ratio. Now, a fourth preferred embodiment of the air-fuel ratio control system according to the present invention will be described with reference to Figs. 25 to 32. In the fourth preferred embodiment, an output voltage VOX of the upstream oxygen sensor 19 is compared with a reference voltage VR to determine whether a monitored air-fuel ratio is RICH or LEAN. Based on this determination, a feedback air-fuel ratio dependent correction coefficient FAF is calculated using given control constants such as delay times, skip amounts and integral constants. The air-fuel ratio feedback control is performed based on this calculated FAF, wherein preselected control constants are corrected using a correction amount ΔRSy which is derived depending on a a magnitude of the output voltage V2 of the downstream oxygen sensor 119. Fig. 25 shows a second air-fuel ratio feedback control routine for calculating the air-fuel ratio dependent correction coefficient FAF based on the given control constants, i.e. delay times TDR, TDL, skip amounts RSR, RSL, integral constants KIR, KIL, using a RICH/LEAN determination based on the output voltage VOX of the upstream oxygen sensor 19. This feedback routine is executed by the CPU 31a in the ECU 30 as a timer interrupt per cycle of 4msec. Specifically, at a first step 501, it is determined whether a predetermined condition for executing the air-fuel ratio feedback control is established. If answer at the step 501 is YES, i.e. the condition for the air-fuel ratio feedback control is established, the routine goes to a step 505 where an output voltage VOX of the upstream oxygen sensor 19 is read out. Subsequently, at a step 507, the read-out output voltage VOX is compared with a reference voltage VR to determine whether a monitored actual air-fuel ratio is RICH or LEAN with respect to a target air-fuel ratio. If answer at the step 507 is YES, i.e. LEAN is determined, then the routine goes through steps 509 to 519. Through the steps 509 to 519, a delay counter CDLY is counted down by one (step 513), and when a value of the delay counter CDLY becomes less than a preset minimum value TDL, a flag F1 is set to zero which represents that the air fuel ratio is LEAN. On the other hand, if answer at the step 507 is NO, i.e. RICH is determined, then the routine goes through steps 521 to 531. Through the steps 521 to 531, the delay counter CDLY is counted up by one (step 525), and when the value of the delay counter CDLY becomes larger than a preset maximum value TDR, the flag F1 is set to 1 which represents that the air fuel ratio is RICH. Accordingly, through the steps 509 to 531, a detection of inversion from RICH to LEAN is delayed by a delay time determined by the preset minimum value TDL, and a detection of inversion from LEAN to RICH is delayed by a delay time determined by the preset maximum value TDR, in comparison with the detection thereof at the step 507. As a result, the RICH/LEAN determination as well as the detection of the inversion between RICH and LEAN based on the condition of the flag F1 becomes more reliable. In addition, by adjusting the preset maximum and minimum values TDR and TDL, the center of the air-fuel ratio feedback control is delicately adjusted toward the RICH side or the LEAN side. Subsequently, at a step 533, it is checked whether the flag F1 is inverted between RICH and LEAN. If the step 533 determines the inversion of the flag F1, a step 535 determines whether the flag F1 is set to zero. If answer at the step 535 is YES, i.e. LEAN is determined, then a rich skip amount RSR is added to the feedback air-fuel ratio dependent correction coefficient FAF in a skipped manner at a step 539. On the other hand, if RICH is determined at the step 535, a lean skip amount RSL is subtracted from the coefficient FAF in a skipped manner at a step 541. If no inversion between RICH and LEAN is determined at the step 533, a step 537 checks whether the flag F1 is set to zero. If answer at the step 537 is YES, i.e. LEAN is determined, then a rich integral constant KIR is added to the coefficient FAF at a step 543. On the other hand, if RICH is determined at the step 537, then a lean integral constant KIL is subtracted from the coefficient FAF at a step 545. Through steps 547 to 553, the coefficient FAF is controlled to a value between a maximum value of 1.2 and a minimum value of 0.8. Referring back to the step 501, if answer at the step 501 is NO, i.e. the condition for the air-fuel ratio feedback control is not established, the routine goes to a step 503 where the coefficient FAF is set to 1.0, and is ended. Fig. 26 shows a control constant correction routine for correcting the rich and lean skip amounts RSR and RSL based on the output voltage V2 of the downstream oxygen sensor 119. This correction routine is executed as a timer interrupt per cycle longer than that of the second air-fuel ratio feedback control routine in Fig. 25, for example, per 150msec. Steps 601 to 607 respectively correspond to the steps 301 to 307 in the second linearlize characteristic correction routine in Fig. 22. At a subsequent step 609, an actual excess air ratio λx is derived based on the read-out output voltage V2 using a pre-stored map. At a step 611, a deviation Δλ2 is calculated by subtracting the derived actual excess air ratio λx from a target excess air ratio λ0 and stored in the RAM 31c. Subsequently, at a step 613, a correction amount ΔRSy is derived based on the stored deviation Δλ2 using a pre-stored map which defines a relation between the deviation Δλ2 and the correction amount ΔRSy. As shown in Fig. 27, in this pre-stored map, the correction amount ΔRSy is in inverse proportion to the deviation Δλ2 within a given range across the deviation Δλ2 being a value of zero. Specifically, this given range comprises the same width range on each side with respect to the deviation Δλ2 being zero. On the other hand, the correction amount ΔRSy is held constant outside the above-noted given range. Accordingly, for example, when an oxygen concentration in the exhaust gas downstream of the catalystic converter 118 becomes higher (LEAN) than that of the target excess air ratio λ0, the output voltage V2 of the downstream oxygen sensor 119 decreases to increase the excess air ratio λx so that the deviation Δλ2 becomes a negative value. As a result, the correction amount ΔRSy becomes a positive value as seen from Fig. 27. On the other hand, when the oxygen concentration in the exhaust gas downstream of the catalytic converter 118 becomes less (RICH) than that of the target excess air ratio λ0, then the correction amount ΔRSy becomes a negative value. Subsequently, a step 615 determines whether the correction amount ΔRSy is larger than zero. If answer at the step 615 is YES (LEAN), the routine goes to a step 617 where the rich skip amount RSR is corrected by adding the correction amount ΔRSy thereto. Through steps 619 to 625, the corrected rich skip amount RSR is controlled to a value between preset maximum and minimum values. On the other hand, if answer at the step 615 is NO (RICH), then the routine goes to a step 627 where the lean skip amount RSL is corrected by subtracting the correction amount ΔRSy therefrom. Through steps 629 to 635, the corrected lean skip amount RSL is controlled to a value between preset maximum and minimum values. When the step 625 or 635 is executed, this interrupt routine is ended. Based on the corrected skip amount RSR or RSL, the second air-fuel ratio feedback control routine of Fig. 25 is performed. Since the correction amount ΔRSy is variable depending on a magnitude of the output voltage V2 of the downstream oxygen sensor 119, not only a timing of an inversion between RICH and LEAN determined by the output voltage V2 but also a degree of RICH or LEAN relative to the reference voltage, i.e. the deviation Δλ2 are reflected on the time-domain characteristic of the correction amount ΔRSy as shown in Fig. 28. Accordingly, as shown in Fig. 29, since the skip amounts RSR and RSL are corrected by the correction amount ΔRSy, the deviation Δλ2, i.e. the deviation of the actual excess air ratio relative to the target excess air ratio is also reflected on the time-domain characteristics of the skip amounts RSR and RSL so that the deviation Δλ2 is further reflected on the feedback correction coefficient FAF which is derived based on the skip amount RSR or RSL. As a result, for example, even if the nature of the fuel is significantly changed by refueling to largely deviate the center of the air-fuel ratio feedback control, the deviation Δλ2 which corresponds to such a sudden deviation of the control center is reflected on the feedback correction coefficient FAF. Accordingly, the air fuel ratio feedback control based on such a correction coefficient FAF enables the center of the air-fuel ratio control to follow up the target air-fuel ratio immediately. It is to be noted that reference values for the skip amounts RSR and RSL in Fig. 29 respectively represent values of the skip amounts RSR and RSL before the correction by the correction amount ΔRSy. Instead of the skip amounts RSR and RSL, the integral constants KIR and KIL or the delay times TDR and TDL may be corrected based on the correction amount ΔRSy as in the same manner for the correction of the skip amounts RSR and RSL. In this case, as shown in Figs. 30 and 31, the deviation of the output voltage V2 relative to the reference voltage, i.e. the deviation Δλ2 is also reflected on the time-domain characteristics of the integral constants KIR, KIL and the delay times TDR, TDL. As a result, the deviation Δλ2 is finally reflected on the correction coefficient FAF as in the case of the correction of the skip amounts RSR and RSL. When the skip amounts RSR, RSL are corrected based on the correction amount ΔRSy, the high follow-up controllability of the air-fuel ratio is ensured. When the integral constants KIR, KIL are corrected based on the correction amount ΔRSy, the simple process is resulted. When the delay times TDR, TDL are corrected based on the correction amount ΔRSy, the delicate adjustments of the air-fuel ratio is ensured. Further, more than one of the corrected skip amounts, the corrected integral constants and the corrected delay times may be used for calculating the feedback correction coefficients FAF. Still further, one of the skip amounts RSR and RSL may be held fixed and only the other thereof may be corrected. Similarly, one of the integral constants KIR and KIL or one of the delay times TDR and TDL may be held fixed and only the other thereof may be corrected. The two maps respectively used at the steps 609 and 613 may be replaced by one map as shown in Fig. 32 which directly defines a relation between the output voltage V2 and the correction amount ARSy. This reduces a volume of the data to be stored, and increases the processing speed. Further, the oxygen sensors 19 and 119 may be replaced by the C0 sensor and the lean mixture sensor as in the foregoing preferred embodiments.

Claims: Air-fuel ratio control system for an internal combustion engine, comprising: a first sensor (19) for monitoring a preselected component contained in an exhaust gas to produce an air-fuel ratio indicative signal; first storing means (31b) for pre-storing a standard relation between said first sensor signal and a standard air-fuel ratio indicative value; first deriving means (50) responsive to said first sensor signal to derive said standard air-fuel ratio indicative value according to said pre-stored standard relation; second storing means (31b) for pre-storing a first modified relation between said standard air-fuel ratio indicative value and a for-control air-fuel ratio indicative value, said first modified relation defining said for-control air-fuel ratio indicative value to vary corresponding to a variation of said standard air-fuel ratio indicative value within a given range across said standard air-fuel ratio indicative value representing a stoichiometric air-fuel ratio, while, defining said for-control air-fuel ratio indicative value to be held constant outside said given range; second deriving means (51, 53) responsive to said standard air-fuel ratio indicative value derived by said first deriving means (50) to derive said for-control air-fuel ratio indicative value according to said first modified relation; and control means (55, 57, 59, 61, 65) for performing a feedback control of an air-fuel ratio of a mixture gas to be fed into an engine cylinder, said control means (59, 61, 65) performing said feedback control based on said for-control air-fuel ratio indicative value derived by said second deriving means (51, 53). System as set forth in claim 1, characterized in that said control means (55, 57, 59, 61, 65) includes third deriving means (55, 57) for deriving a deviation between said for-control air-fuel ratio indicative value derived by said second deriving means (51, 53) and a target air-fuel ratio indicative value; System as set forth in claim 1 or 2, characterized in that said first sensor (19) is an oxygen sensor which presents a sudden change in its output across said stoichiometric air-fuel ratio. System as set forth in one of the claims 1 to 3, characterized in that said given range includes substantially the same width on each of RICH and LEAN sides with respect to said standard air-fuel ratio indicative value representing the stoichiometric air-fuel ratio. System as set forth in one of the claims 1 to 4, characterized in that said control means (59) performs a PID control of said air-fuel ratio based on said deviation derived by said third deriving means (55, 57). System as set forth in claim 1 or 2, characterized by including third storing means (31c) for pre-storing a second modified relation between said standard air-fuel ratio indicative value and another for-control air-fuel ratio indicative value, said second modified relation defining said another for-control air-fuel ratio indicative value to have a variation rate smaller than that of said for-control air-fuel ratio indicative value within said given range except for preset ranges adjacent to RICH and LEAN side ends of said given range, while, defining said another for-control air-fuel ratio indicative value to have a variation rate larger than that of the for-control air-fuel ratio indicative value within said preset ranges, said second modified relation further defining said another for-control air-fuel ratio indicative value to be held constant outside said given range, said system further including idling detect means (15b) for detecting an idling condition of the engine, and relation select means (67) for selecting said first modified relation when a nonidling condition of the engine is detected by said idling detect means (15b), while, selecting said second modified relation when the idling condition of the engine is detected by said idling detect means (15b). System as set forth in one of the claims 1 to 6, characterized in that said first modified relation defines said for-control air-fuel ratio indicative value to be biased toward a RICH or LEAN side relative to the standard air-fuel ratio indicative value. System as set forth in one of the claims 1 to 7, characterized in that said control means (59, 61, 65) includes PI control means (61) for performing a PI control of the air-fuel ratio based on said deviation and PID control means (59) for performing a PID control of the air-fuel ratio based on said deviation, and wherein said control means (59, 61, 65) performs said PI control when the engine is under an immediate acceleration, while, said control means (59, 61, 65) performs said PID control when the engine is under a non-immediate acceleration. System as set forth in one of the claims 1 to 8, characterized in that said first sensor (19) is provided upstream of a catalystic converter (118) and a second sensor (119) is further provided downstream of the catalystic converter (118), said second sensor (119) monitoring a preselected component contained in the exhaust gas downstream of the catalystic converter (118) to produce an air-fuel ratio indicative signal, and wherein said system further includes relation correcting means (124) for correcting said first modified relation to bias said for-control air-fuel ratlo indicative value toward a RICH or LEAN side relative to the standard air-fuel ratio indicative value based on a value of said second sensor signal, said bias of the for-control air-fuel ratio indicative value being defined within said given range. System as set forth in claim 9, characterized in that a magnitude and a direction of said bias are determined based on the value of the second sensor signal. System as set forth in claim 9 or 10, characterized in that a correction amount is derived based on the second sensor signal and the target air-fuel ratio indicative value, said correction amount changing its sign when the second sensor signal changes between a RICH value and a LEAN value relative to the target air-fuel ratio indicative value, and wherein the magnitude of said bias is determined by an absolute value of said correction amount and the direction of said bias is determined by a sign of said correction amount. System as set forth in claim 9, characterized in that a direction of said bias is determined by comparing said second sensor signal with a reference value to determine whether said air-fuel ratio is RICH or LEAN, and a magnitude of said bias is determined by a correction amount which is derived based on a preselected engine operation parameter indicative of a transfer delay of the exhaust gas. System as set forth in claim 12, characterized in that said preselected engine operation parameter is a monitored engine speed. System as set forth in claim 12 or 13, characterized in that said correction amount is fixed to a small amount during a period between inversions of the second sensor signal between RICH and LEAN values relative to the target air-fuel ratio indicative value. System as set forth in one of the claims 9 to 14, characterized in that said first and second sensors (19, 119) are oxygen sensors each of which presents a sudden change in its output across the stoichiometric air-fuel ratio. System as set forth in claim 1, characterized in that said first sensor (119) is provided downstream of a catalystic converter for monitoring a preselected component contained in an exhaust gas downstream of the catalystic converter to produce an air-fuel ratio indicative signal, wherein said system includes: a second sensor (19) provided upstream of the catalystic converter for monitoring a preselected component contained in the exhaust gas upstream of the catalystic converter to produce an air-fuel ratio indicative signal; and detection means for comparing said second sensor signal with a reference value to determine whether an air-fuel ratio of a mixture gas to be fed into an engine cylinder is RICH or LEAN relative to a target air-fuel ratio, wherein said control means performs said feedback control of the air-fuel ratio of the mixture gas based on a feedback control constant and said determination of RICH or LEAN by said detection means, and wherein said control means includes correction means for correcting said feedback control constant based on said for-control air-fuel ratio indicative value derived by said second deriving means. System as set forth in claim 16, characterized in that said control constant is limited by preset maximum and minimum values. System as set forth in claim 16 or 17, characterized in that said first and second sensors are oxygen sensors each of which presents a sudden change in its output across the stoichiometric air-fuel ratio. System as set forth in one of the claims 16 to 18, characterized in that said correction amount changes its sign between a first sign and a second sign opposite to the first sign when the second sensor signal changes between a RICH value and a LEAN value relative to the target air-fuel ratio indicative value, and wherein said feedback control constant is a first or second feedback control constant, and wherein said first feedback control constant is corrected by said correction amount when said correction amount has the first sign and used by said control means for the feedback control to make the air-fuel ratio richer, while, said second feedback control constant is corrected by said correction amount when said correction amount has the second sign and used by said control means for the feedback control to make the air-fuel ratio leaner. System as set forth in claim 1, characterized in that said first sensor (119) is provided downstream of a catalystic converter for monitoring a preselected component contained in an exhaust gas downstream of the catalystic converter to produce an air-fuel ratio indicative signal, wherein the system includes: a second sensor (19) provided upstream of the catalystic converter for monitoring a preselected component contained in the exhaust gas upstream of the catalystic converter to produce an air-fuel ratio indicative signal; and storing means for storing a feedback control constant, wherein said control means includes correction means for correcting said feedback control constant based on said for-control air-fuel ratio indicative value derived by said second deriving means, and wherein said control means performs said feedback control of the air-fuel ratio of the mixture gas based on said corrected feedback control constant and said second sensor signal.

Inventors: DOUTA HISAYO, KINUGAWA MASUMI, SUZUKI ATSUSHI, DOUTA, HISAYO, KINUGAWA, MASUMI, SUZUKI, ATSUSHI
Applicants: NIPPON DENSO CO, NIPPONDENSO CO., LTD.
Application year: 1992
Main classification: F02D41
IPC codes: F02D41