Abstract:
A slip control system for a torque converter with a lockup clutch comprises a controller that outputs a slip control signal to a slip control actuator of the lockup clutch to adjust an actual slip rotation speed of the torque converter at a target slip rotation speed. The controller is coupled to sensors for detecting information indicative of a condition of a drive system including the torque converter. The controller decides an operating state of the torque converter at time when the slip control is started, and selects one of initial valves for a slip command signal corresponding to the slip control signal according to the decided operating state of the torque converter at the start of the slip control. This arrangement functions to prevent troubles including shocks due to shortage of slippage in the torque converter and generation of radial slippage of the torque convert from generating at a time staring the slip control.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to improvements in a slip control system which converges a slip rotation speed between input and output elements of a torque converter at a target value, and more particularly to a slip control system which suitably functions even during a transient period from the non slip-control range to a slip control range. 
     Generally, a torque converter has merits such as a torque fluctuation absorbing function and a torque multiplying function due to a fluid power transmission, although a transmission efficiency of the fluid power transmission is lower than that of a power transmission by a direct mechanical connection. In order to improve the transmission efficiency of the torque converter, most torque converters employ lockup clutches for directly connecting input and output elements of the torque converter when the vehicle is put in a running condition where the torque fluctuation absorbing function or the torque multiplying function are not required. Further, some of lockup torque converters have been proposed to execute a slip control of a lockup clutch. Such a slip control for a torque converter is generally arranged to determine a target slip rotation speed according to a vehicle running condition and to control an engagement force of the lockup clutch so as to adjust an actual slip rotation speed to the target slip rotation speed. 
     SUMMARY OF THE INVENTION 
     However, such a slip control system, which is arranged to estimate an output torque of the torque converter on the basis of a modeled torque converter and a modeled engine, is required to be further improved. More specifically, the slip control system is required to suitably operate even if the correspondence between the modeled objects and the controlled objects is degraded by errors in modeling, aging of the controlled objects, or deviation among controlled objects. Inventers of this invention have executed various simulations upon taking account of the degradation of this correspondence, and found that such degradation of the correspondence in some cases degrades the operational performance of the torque converter during a starting period of the slip control. 
     It is therefore an object of the present invention to provide an improved slip control system that solves the degradation of operational performance of a torque converter. 
     According to the present invention, a slip control system for a torque converter with a lockup clutch is arranged to control an actual slip rotation speed between input and output elements of the torque converter at a target slip rotation speed. The torque converter is connected to an engine and a transmission of a vehicle. The slip control system comprises a vehicle operation condition detector detecting operating condition of the vehicle, an actuator controlling a lockup clutch engagement pressure of the lockup clutch according to a control signal to adjust the actual slip rotation speed at the target slip rotation speed and a controller connected to the vehicle operating condition detector and the actuator. The controller is arranged to decide an operating state of the torque converter when the slip control is started, to decide an initial value of a slip rotation speed command value according to the operating state of the torque converter at the start of the slip control, to calculate the slip rotation speed command value on the basis of the detected vehicle operating condition, and to output the control signal corresponding to the slip rotation speed command value to the actuator. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic view of a slip control system of a torque converter of an embodiment according to the present invention. 
     FIG. 2 is a schematic view of a drive system of a vehicle provided with the slip control system of FIG.  1 . 
     FIG. 3 is a graph showing a relationship between a signal pressure outputted from a lockup solenoid and a lockup clutch engagement pressure. 
     FIG. 4 is a block diagram showing the slip control executed by a controller of the slip control system according to the present invention. 
     FIG. 5 is a detailed block diagram of a slip rotation speed control section of FIG.  4 . 
     FIG. 6 is a further detailed block diagram showing a slip rotation speed command value calculating section of FIG.  5 . 
     FIG. 7A is a detailed block diagram of a slip rotation speed initial command value calculating section of FIG.  5 . 
     FIGS. 7B and 7C are block diagrams showing other modifications of the slip rotation speed initial command value calculating section of FIG.  5 . 
     FIG. 8 is a flowchart showing a program for deciding a transmission operating range deciding program executed at a slip control range deciding section of a controller of FIG.  4 . 
     FIG. 9 is a flowchart showing a slip control program executed at the slip rotation speed control section of the controller of FIG.  4 . 
     FIG. 10 is a graph showing boundaries among a converter range, a slip control range and a lockup range of the torque converter. 
     FIG. 11 is a graph showing a predetermined map of a target slip rotation speed with respect to a turbine runner rotation speed and a throttle opening. 
     FIG. 12 is a graph showing a relationship between a turbine rotation speed and a slip rotation speed gain of a torque converter. 
     FIG. 13 is a graph showing a relationship among a throttle opening, a rotation speed and an output torque of an engine coupled to the torque converter. 
     FIG. 14 is a graph showing a relationship between the engagement pressure and an engagement capacity of the lockup clutch. 
     FIG. 15 is a graph showing a relationship between the lockup clutch engagement pressure and a lockup solenoid drive duty. 
     FIGS. 16A to  16 E are time charts showing an operation ensured by the slip control according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIGS. 1 to  16 E, there is shown an embodiment of a slip control system for a torque converter  2  in accordance with the present invention. 
     FIG. 1 shows the slip control system of the torque converter  2  according to the embodiment of the present invention. The slip control system is employed in a drive system for a vehicle shown in FIG.  2 . The drive system is constituted by an engine  1 , the torque converter  2 , a gear transmission mechanism  3  of an automatic transmission, a differential gear unit  4  and wheels  5  which are connected in order of mention. 
     The torque converter  2  is of a lockup type and comprises a pump impeller  2   a  functioning as an input element driven by the engine  1 , a turbine runner  2   b  functioning as an output element connected to an input shaft of the gear transmission mechanism  3 , and a lockup clutch  2   c  directly connecting the pump impeller  2   a  and the turbine runner  2   b.    
     An engagement force of the lockup clutch  2   c  is determined by a difference (lockup clutch engagement pressure) between an apply pressure P A  and a release pressure P R . When the apply pressure P A  is smaller than the release pressure P R , the lockup clutch  2   c  is put in a released condition so as not to directly connect the pump impeller  2   a  and the turbine runner  2   b . That is, under this pressure balance, the torque converter  2  is put in a converter state where the slip between the pump impeller  2   a  and the turbine runner  2   b  is not limited. 
     When the apply pressure P A  is greater than the release pressure P R  and when the difference therebetween is smaller than a predetermined value, the lockup clutch  2   c  is slippingly engaged according to the difference such that the torque converter  2  is operated in a slip control state where the slip speed of the torque converter  2  is controlled according to the engagement force of the lockup clutch  2   b . Further, when the apply pressure P A  is greater than the release pressure P R  and when the difference becomes greater than the predetermined value, the torque converter  2  is put in a lockup state where a relative rotation between the pump impeller  2   a  and the turbine runner  2   b  becomes zero. 
     A slip control valve  11  is arranged to determine the apply pressure P A  and the release pressure P R  according to a signal pressure P S  from a lockup solenoid  13  duty-controlled by a controller  12 . The ship control valve  11  and the lockup solenoid  13  are of conventional types, respectively. That is, the lockup solenoid  13  is arranged to increase the signal pressure P S  according to increase the solenoid drive duty D applied from the controller  12  to employ a pilot pressure P P  as a base pressure. 
     The slip control valve  11  receives the signal pressure P S  and the feedback release pressure P R  in the same direction and receives a spring force of a spring  11   a  and the feedback apply pressure P A  in an opposite direction opposite to the direction of the signal pressure P S , as shown FIG.  1 . The lockup clutch engagement pressure represented by a difference (P A −P R ) between the apply pressure P A  and the release pressure P R  is changed according to the change of the signal pressure P S  as shown in FIG.  3 . 
     When the lockup clutch engagement pressure (P A −P R ) takes a negative value, that is, when P R &gt;P A , the torque converter  2  is put in a converter state. When the lockup clutch engagement pressure (P A −P R ) takes a positive value, that is, when P A &lt;P R , the engagement capacity of the lockup clutch  2   c  is increased according to the increase of the positive value (P A −P R ) so as to increase the limiting of the slip rotation of the torque converter  2 . Then, when the lockup clutch engagement pressure becomes greater than a predetermined value, the torque converter  2  is put in the lockup state. 
     As shown in FIG. 1, the controller  12  receives a plurality of signals, such as a signal TV 0  from a throttle opening sensor  21  for detecting a throttle opening TV 0  of the engine  1 , a signal ω IR  from an impeller rotation speed sensor  22  for detecting a rotation speed ω IR  of the pump impeller  2   a , a signal ω TR  from a turbine rotation speed sensor  23  for detecting a rotation speed ω TR  of the turbine runner  2   b , a signal TEMP from an oil temperature sensor  24  for detecting a working oil temperature TEMP of an automatic transmission, a signal N 0  representative of a transmission output rotation speed corresponding to a vehicle speed from a transmission output rotation speed sensor  25 , a transmission ratio indicative signal i P  from a transmission ration calculating section  26 , and a signal V ig  from an electric source voltage sensor  27 . 
     The controller  12  determines a drive duty ratio D of the lockup solenoid  13  by executing the calculations on the basis of the above-mentioned signals. More specifically, the controller  12  executes the slip control according to the present invention by executing the calculations according to functional block diagrams shown in FIGS. 4 to  6  and  7 A. 
     As shown in FIG. 4, the slip control range determining section  30  receives the throttle opening TV 0 , the transmission output speed N 0  and the fluid temperature TEMP and the transmission ratio i p . The slip control range determining section  30  of the controller  12  decides whether the torque converter  2  is operated in a drive slip control (S/L) range, a converter (C/V) range or a lockup (L/U) range, by executing a range deciding program shown in FIG.  8 . When the torque converter  2  is operating in the drive slip control range, the torque converter  2  is controlled so that the slip rotation speed of the torque converter  2  is adjusted at a target slip rotation speed. When the torque converter  2  is operating in the converter range, the slippage between the pump impeller  2   a  and the turbine runner  2   b  is not restricted. When the torque converter  2  is operating in the lockup range, no slippage between the pump impeller  2   a  and the turbine runner  2   b  is generated. 
     The range deciding operation for deciding the operating range of the torque converter  2  will be explained with reference to the flowchart of FIG. 8, hereinafter. 
     At a step S 31  of FIG. 8, the controller  12  decides whether the hydraulic oil temperature TEMP is within an allowable range in which the slip limiting operation can be executed and which corresponds to a condition after warming up of the engine  1 . When the decision at the step S 31  is negative, the routine proceeds to a step S 36  wherein a slip control flag FLAG is set at 01 (FLAG=01). When the decision at the step S 31  is affirmative, the routine proceeds to a step S 32 . 
     At the step S 32 , the controller  12  decides whether the transmission ratio i p  is within an allowable range in which the slip limiting can be executed. When the decision at the step S 32  is negative, the routine proceeds to the step S 36 . When the decision at the step S 32  is affirmative, the routine proceeds to a step S 33 . 
     At the step S 33 , the controller  12  decides whether the torque converter  3  is operated in the drive slip control range, the converter range or the lockup range, on the basis of a first map corresponding to the graph shown in FIG. 10, the transmission output rotation speed No and the throttle opening TV 0 . The first map has been previously stored in a data storage section of the controller  12  so that the controller  12  can quickly check the state of the torque converter  3 . In FIG. 10, the converter (C/V) range corresponds to a slip unlimited state where the lockup clutch  2   c  is released so that the torque converter  2  is operated in the converter range in that the slip rotation speed between the input and output elements are not limited. The drive slip control (S/L) range corresponds to a slip control range where the lockup clutch  2   c  is set at a sliding state so that the slip rotation speed between the input and output elements  2   a  and  2   b  of the torque converter  2  is adjusted at a target speed to maintain a slip control state. The lockup (L/U) range corresponds to a non slipping state where the lockup clutch  2   c  is fully engaged so as to maintain the slip rotation speed between the input and output elements  2   a  and  2   b  at zero. 
     A dead zone is provided at a boundary among the drive slip control range, the converter range and the lockup range, as shown in FIG.  10 . The dead zone functions to absorb the hysteresis of the operation of the torque converter  2 . That is, the provision of this dead zone functions to prevent hunting as to the decision of the operation range of the torque converter  2  from being generated. 
     When the controller  12  decides at the step S 33  that the torque converter  2  is operating in the driver slip control (S/L) range, the routine proceeds to a step S 34  wherein the slip control flag FLAG is set at 10 (FLAG=10). 
     When the controller  12  decides at the step S 33  that the torque converter  2  is operating in the lockup (L/U) range, the routine proceeds to a step S 35  wherein the slip control flag FLAG is set at 11 (FLAG=11). 
     When the controller  12  decides at the step S 33  that the torque converter  2  is operating in the converter (C/V) range, the routine proceeds to the step S 36  wherein the slip control flag FLAG is set at 01 (FLAG=01). 
     The slip control flag FLAG determined in the range decision program of FIG. 8 is supplied to a slip rotation speed controlling section  40  shown in FIG.  4 . The slip rotation speed controlling section  40  is provided in the controller  12  in the form of a program. 
     The slip rotation speed controlling section  40  is constituted by a slip rotation speed command value calculating section  410 , a slip rotation speed gain calculating section  420 , a target converter torque calculating section  430 , an engine output torque estimating section  440 , a target lockup clutch engagement capacity calculating section  450 , a lockup clutch engagement pressure command value calculating section  460 , a solenoid drive signal calculating section  470  and a slip rotation speed initial command value calculating section  480 , as shown in FIG. 5. A drive duty D for operating the lockup solenoid  13  is determined by the calculations executed in the slip rotation speed controlling section  40  and is employed in the slip control. 
     The slip rotation speed command value calculating section  410  is arranged as shown in FIG.  6 . That is, a target slip rotation speed calculating section  411  shown in FIG. 6 is arranged to calculate a target slip rotation speed ω SLPT  on the basis of a second map corresponding to a graph shown in FIG.  11  and from the transmission ratio i p , the hydraulic oil temperature TEMP, a turbine runner rotation speed ω TR , and the throttle opening TV 0 . The second map has been obtained by each transmission ratio i p  and the hydraulic oil temperature TEMP and has been stored in the controller  12 . The target slip rotation speed ω SLPT  is a smallest value within a range where torque deviation from the torque converter  2  and noises in a passenger compartment are suppressed. Accordingly, for the purpose of preventing the torque deviation and the noises in the passenger compartment, the target slip rotation speed ω SLPT  takes a larger value according to the decrease of the turbine runner rotation speed ω TR . Further, when the throttle opening TV 0  representative of an engine load is large, that is, when the vehicle requires large driving force, the input torque during this period should be sufficiently supplied from the torque converter  2  to a transmission mechanism  3  so as not to generate a shortage of the input torque during the slip control. Therefore, the target slip rotation speed ω SLPT  is set a larger value which is increased according to the increase of the throttle opening TV 0 . 
     The actual slip rotation speed calculating section  412  shown in FIG. 6 is arranged to calculate an actual slip rotation speed ω SLPR  by subtracting the turbine runner rotation speed ω TR  from a pump impeller rotation speed ω IR  (ω SLPR =ω IR ω TR ). 
     The slip rotation speed difference calculating section  413  is arranged to calculate a slip rotation speed difference between the target slip rotation speed ω SLPT  and the actual slip rotation speed ω SLPR  from the following equation (1): 
     
       
         ω SLPER =ω SLPT −ω SLPR   (1) 
       
     
     Further, the feedback compensator  414  of FIG. 6 is arranged to calculate a slip rotation speed command value ω SLPC  at time t on the basis of a transfer function G CNT  (s). More specifically, the slip rotation speed command value ω SLPC  at time t is employed for adjusting the actual slip rotation speed ω SLPR  at the target slip rotation speed ω SLPT  by canceling the slip rotation speed difference ω SLPER  and is calculated from the following equation (2): 
     
       
         ω SLPC ( t )= G   CNT ( S )·ω SLPER ( t ).  (2) 
       
     
     The feedback compensator  414  especially sets the slip rotation speed command value ω SLPC  at an initial value ω SLPC0  (ω SLPC ← SLPC0 ) when the controller  12  decides from the slip control flag FLAG that the slip control has been just started. The detailed function of the feedback compensator  414  will be understood from the explanation of the slip rotation speed control section  40  with reference to FIGS. 5 and 9. 
     The slip rotation speed gain calculating section  420  of FIG. 5 retrieves a slip rotation speed gain g SLP  from a map corresponding to a graph of FIG. 12 on the basis of the turbine runner rotation speed ω TR The slip rotation speed gain g SLP  is defined as a ratio of the slip rotation speed ω SLP  with respect to a converter torque T CNV  and is expressed as follows: 
     
       
           g   SLP =ω SLP   /T   CNV   (3) 
       
     
     The converter torque T CNV  is a transfer torque transferred by means of the fluid transfer of the torque converter  2 . A relationship among the converter torque T CNV , the slip rotation speed ω SLP  and the turbine runner rotation speed ω TR  can be previously obtained from the transfer characteristic of the torque converter  2 . Further, the slip rotation speed gain g SLP  decreases according to the increase of the turbine runner rotation speed ω TR  as shown by a continuous line in the graph of FIG.  12 . Therefore, it is possible to retrieve the slip rotation speed gain g SLP  from the above-mentioned relationships and the turbine runner rotation speed ω TR . 
     The target converter torque calculating section  430  receives the retrieved slip rotation speed gain g SLP  and calculates the converter torque T CNV  necessary for achieving the slip rotation speed command ω SLPC  under the turbine rotation runner rotation speed ω TR . Mere specifically, the converter torque T CNV  is obtained by executing the calculation of the following equation (4): 
     
       
           T   CNV ( t )=ω SLPC ( t )/ g   SLP   (4) 
       
     
     The engine output torque estimating section  440  retrieves a stationary value ω IR  from an engine performance map corresponding to a graph shown in FIG.  13  and from the pump impeller rotation speed ω IR  corresponding to the engine rotation speed and the throttle opening TV 0 . Further, the engine output torque estimating section  440  executes a filter treatment by treating the obtained stationary value T ES  at a filter which has a value corresponding to an engine dynamic delay of the engine  1  to obtain an engine torque T EH  which is further close to an actual value. Practically, the further actual engine output torque T EH  is obtained from the following equation (5): 
     
       
           T   EH ( t )=[1/( t   ED   ·S =1)] T   ES ( t )  (5) 
       
     
     The target lockup clutch engagement capacity calculating section  450  calculates a target lockup engagement capacity T LUC  by subtracting the target converter torque T CNV  from the filtered engine output torque T EH , practically by executing the calculation of the following equation (6): 
     
       
           t   LUC ( t )= T   EH ( t )− T   CNV ( t )  (6) 
       
     
     The lockup clutch engagement pressure command value calculating section  460  retrieves a lockup clutch engagement pressure command value P LUC  for achieving the target lockup clutch engagement T LUC  from a map corresponding to a graph shown in FIG.  14 . A relationship shown FIG. 14 is prepared by each torque converter and has been previously obtained by means of experiments. Therefore, the target lockup clutch engagement capacity T LUC  can be obtained from the map corresponding to the graph of FIG. 14 by each torque converter and the lockup clutch engagement pressure command P LUC . 
     The solenoid drive signal calculating section  470  determines a lockup solenoid drive duty D for adjusting the actual lockup clutch engagement pressure P LU  at the target lockup clutch engagement pressure P LUT  on the basis of a map which has been prepared for each source voltage V ig  as shown in FIG.  15 . The solenoid drive signal calculating section  470  outputs the determined lockup solenoid drive duty D to the lockup solenoid  13 . This enables the slip control system according to the present invention to adjust the actual slip rotation speed ω SLPR  at the slip rotation speed command value ω SLPC  during the transient period of the slip control and to adjust the actual slip rotation speed ω SLPR  at the target slip rotation speed ω SLPT  during the stationary period of the slip control. 
     The slip rotation speed initial command value calculating section  480  employed in the first embodiment is particularly arranged as shown in FIG.  7 A. Before explaining the construction of slip rotation speed initial command value calculating section  480 , the processing executed by the feedback compensator  414  shown in FIG. 6 will be discussed. 
     When the feedback compensator  414  obtains the slip command value and when the equation (2) for obtaining the slip rotation speed command value ω SLPC  is employed in the control system, it is possible to employ the following state equations (7), (8) and (9): 
     
       
         ( d/dt ) x ( t )= A   CNT   x ( t )+ B   CNT ω SLPER ( t )  (7) 
       
     
     
       
         ω SLPC (0)=ω SLPC0   (8) 
       
     
     
       
         ω SLPC ( t )= C   CNT   x ( t )+ D   CNT ω SLPER ( t )  (9) 
       
     
     where x(t) is an n-dimension state vector, A is an n×n dimension matrix, B is an n×1-matrix, C is a 1×n-matrix and D is a 1×1-matrix. 
     The equation (8) represents an equation for setting an initial value ω SLPC0  of the slip rotation speed command value ω SLPC . When the slip control is started from the converter state or the lockup state, an initialization of the lockup command value ω SLPC  is executed by the following manner. 
     The slip rotation speed initial command value calculating section  480  determines the initial value ω SLPC0  by initializing the slip rotation speed command value ω SLPC0 , and outputs the initial value ω SLPC0  to the slip rotation speed command value calculating section  410  of FIG. 5, and more particularly to the feedback compensator  414  of FIG.  6 . 
     As shown in FIG. 7A, the slip rotation speed initial command value calculating section  480  is constituted by a solenoid drive signal inverse calculating section  481 , a lockup clutch engagement pressure command value inverse calculating section  482 , a target lockup clutch engagement capacity inverse calculating section  483  and a target converter torque inverse calculating section  484 . Each of these calculating sections  481  to  484  is an inverse system of each of the calculating sections  430 ,  450 ,  460  and  470  shown in FIG.  5 . 
     The solenoid drive signal inverse calculating section  481  receives the initial value D 0  of the lockup solenoid drive duty and the source voltage V ig , and executes an inverse calculation of the lockup solenoid diver signal calculating section  470  of FIG.  5 . That is, the solenoid drive signal inverse calculating section  481  inversely retrieves the lockup clutch engagement pressure initial command value P LUC0  from the map prepared by each source voltage V ig  as shown in FIG.  15  and the solenoid drive duty initial value D 0 . When the slip control is started from the converter state, the lockup solenoid drive duty initial value D 0  is set at a value by which the actual slip rotation speed ω SLPR  is compensated so as to be greater than the allowable lower limit of the slip rotation speed where the engagement shock of the lockup clutch  2   c  is negligible. On the other hand, when the slip control is started from the lockup state, the lockup solenoid drive duty initial value D 0  is set such that the actual slip ω SLPR  is maintained at zero. 
     The lockup clutch engagement pressure command value inverse calculating section  482  receives the lockup clutch engagement initial command value P SLPO  and executes an inverse calculation of the lockup clutch engagement pressure command value calculating section  460  of FIG.  5 . That is, the lockup clutch engagement pressure command value inverse calculating section  482  inversely retrieves the target lockup clutch engagement capacity initial command value T LUC0  from a map corresponding to the graph shown in FIG.  14  and the lockup clutch engagement pressure initial command value  TLUC0 . 
     The target lockup clutch engagement capacity inverse calculating section  483  receives the target lockup clutch engagement capacity initial value T LUC0  and the engine output torque estimate T EH  and executes an inverse calculation of the calculation executed at the target lockup clutch engagement capacity calculating section  450  of FIG.  5 . That is, the target lockup clutch engagement capacity inverse calculating section  483  calculates the target converter torque initial value T CNV0  from the following equation (10) based on the equation (6): 
     
       
           T   CNV0 ( t )= T   EH ( t )− T   LUC0   (10) 
       
     
     The target converter torque inverse calculating section  484  receives the target converter torque initial value T CNV0  and the slip rotation speed gain g SLP  and executes an inverse calculation of the target converter torque calculating section  430  of FIG.  5 . More specifically, the target lockup clutch engagement capacity inverse calculating section  484  calculates the slip rotation speed initial command value ω SLPC0  from the following equation (11) based on the equation (4): 
     
       
         ω SLPC0 ( t )= g   SLP ( t )· T   CNV0   (11) 
       
     
     The lockup solenoid drive duty initial value D 0  has been set to have two values one of which is set so that the actual slip rotation speed ω SLPR  is adjusted to the allowable lower limit of the slip rotation speed when the slip control is executed from the converter state, and the other of which is set such that the actual slip ω SLPR  is maintained at zero when the slip control is started from the lockup state. Therefore, the slip rotation speed initial command value ω SLPC0  obtained on the basis of the lockup solenoid drive duty initial value D 0  also has two values. Hereinafter, ω SLPC0 (C/V) represents the slip rotation speed initial command value ω SLPC0  based on the duty initial value D 0  obtained when the slip control is started from the converter state, and ω SLPC0 (L/U) represents the slip rotation speed initial command value ω SLPC0  based on the duty initial value D 0  obtained when the slip control is started from the lockup state. 
     The operation for determining the lockup solenoid drive duty D during the slip control executed by the slip rotation speed control section  40  of FIG. 5 will be discussed with reference to the program shown in FIG.  9 . 
     At a step S 41 , the controller  12  decides whether the slip control flag FLAG is 10 or not, that is, whether the torque converter  2  is operated in the slip control (S/L) range or not. When the decision at the step S 41  is affirmative, that is, when the torque converter  2  is operated in the slip control range (FLAG=10), the routine proceeds to a step S 42 . When the decision at the step S 41  is negative (FLAG≠10), the routing proceeds to a step S 48 . 
     At the step S 42 , the controller decides whether FLAG=10 is first time or not, more specifically, whether or not the slip control has been just started from a non slip-control state including the converter state and the lockup state. When the decision at the step S 42  is affirmative, the routine proceeds to a step S 43 . When the decision at the step S 42  is negative, the routine proceeds to a step S 47 . 
     At the step S 43 , the controller  12  decides whether the torque converter  2  is operating under the converter state or the lockup state. That is, the step S 43  is executed to check whether the slip control is started from the converter state or the lockup state. When the controller  12  decides that the slip control is started from the converter state, the routine proceeds to a step S 44  wherein the initial value ω SLPC0 (C/V) for the converter state is employed as the initial value ω SLPC0  (ω SLPC0   77  ω SLPC0 (C/V)). When the controller  12  decides that the slip control is started from the lockup state, the routine proceeds to a step S 45  wherein the initial value ω SLPC0 (L/U) for the lockup state is employed as the initial value ω SLPC0  (ω SLPC0 ←ω SLPC0 (L/U)). 
     At a step  46  following to the step S 44  or S 45 , the controller  12  starts the slip control upon employing the initial value ω SLPC0  decided by the above processing. More specifically, the target converter torque calculating section  430  receives the slip rotation speed command value ω SLPC  which has been initialized, and the lockup solenoid drive duty D is then determined by sequentially executing the calculations of the calculating sections  450 ,  460  and  470 . The slip control is started by this operation. 
     At the step S 47  following to the negative decision of the step S 42 , the controller  12  executes an operation for continuing the slip control for adjusting the actual slip rotation speed ω SLPR  to the target slip rotation speed ω SLPT  by a predetermined response. Practically, this continuation of the slip control is executed by inputting the slip rotation speed command value ω SLPC , which corresponds to the slip rotation speed difference and is obtained by the equation (2), to the target converter torque calculating section  430 . 
     At the step  48  following to the negative decision at the step S 41 , the controller  12  decides whether the slip control flag FLAG is set at 11 or not. When the decision at the step S 48  is affirmative (FLAG=11), that is, when the torque converter  2  is put in the lockup range, the routine proceeds to a step S 49  wherein the controller  12  sets the torque converter  2  to the lockup state by increasing a gradient indicative of the change of the lockup solenoid drive duty D with respect to a time period. When the decision at the step S 48  is negative (FLAG≠11 ), that is, when the torque converter  2  is put in the converter range, the routine proceeds to a step S 50  wherein the controller  12  sets the torque converter  2  to the converter state by decreasing the gradient indicative of the change of the lockup solenoid drive duty D with respect to a time period. 
     In this embodiment, when the slip control is started from the converter state, the initial value ω SLPC0 (C/V) for converter state is employed as the slip rotation speed command value ω SLPC0  (corresponding to the execution of the step S 44 ). This setting compensates the actual slip rotation speed ω SLPC0  so as to be greater than or equal to the allowable lower limit where the engagement shock of the lockup clutch  2  is negligible. Therefore, as is apparent from the simulation result executed on the basis of the slip control maneuver according to the present invention, even when the engine output torque estimate T EH  is offset from an actual engine output torque T E  due to errors of modeling the control system or aging deterioration of the engine as shown in FIG. 16C, the actual slip rotation speed ω SLPR  is controlled so as not to become smaller than the allowable lower limit during a transient period of the start of the slip control from the converter state as shown in FIG. 16E, and the engagement shock or engagement vibrations of the lockup clutch  2  during the transient period is certainly avoided by this arrangement. The simulation result shown in FIG. 16E represents timed variations of the actual slip rotation speed ω SLPC  and the slip rotation speed command value ω SLPC . The simulation result was obtained by executing under a condition where the throttle opening TV 0  was kept at ⅛ to continue the running of a vehicle as shown in FIG. 16A, and the slip control flag FLAG was changed from 01 to 10 at the moment t 1 , as shown in FIG. 16B while the engine output torque T EH  is offset from the actual engine output torque T E  as shown in FIG.  16 D. According to the change of the operating state of the torque converter  2  from the converter state to the slip control state at the moment t 1 , the lockup clutch engagement pressure (P A −P B ) was gradually increased as shown in FIG.  16 D. 
     In this case, if the initial value ω SLPC0 (C/V) for converter state is set so that the actual slip rotation speed corresponds to the allowable lower limit of the slip rotation speed, the initial value of the slip rotation speed command value may be set at the necessary minimum value with reference to the above-mentioned operations. This prevents the initial value from becoming too large, and the degradation of the responsibility of the slip control is also prevented. 
     When the slip control is started from the lockup state, the initial value ω SLPC0 (L/U) for the lockup state is employed as the slip rotation speed command value ω SLPC0 . The operation corresponds to the execution of the step S 45 . Therefore, the actual slip rotation speed ω SLPCR  is compensated so as to be zero when the slip control is started from the lockup state. Accordingly, even if the engine output torque estimate T EH  is largely offset from the actual engine output torque T E  due to the error of modeling the control system or the aging deterioration of the engine, the torque converter  2  is never set so as to largely generate a slip just after the start of the slip control. This certainly prevents racing of the engine  1  during high load state and undesired running of the vehicle during engine braking period when the slip control is started. 
     Further, when the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation command value are obtained, the electronic control signal (solenoid drive duty D) for controlling the engagement pressure of the lockup clutch  2  at the command value P LUC  is determined at one of the first, second and third compensation values. The first compensation value functions to set the actual slip rotation speed at a speed greater than the allowable lower limit. The second compensation value functions to set the actual slip rotation speed at the allowable lower limit. The third compensation value functions to set the actual slip rotation speed at zero. The determined electronic control signal is the solenoid drive duty D, and the initial value of the slip rotation speed command value is obtained on the basis of the determined electronic control signal by means of the inverse calculations in contrast with the procedure for obtaining the electronic control signal D from the slip rotation speed command value. This ensures the following advantages: 
     That is, since the electronic control signal D is nearest to the controlled object (solenoid  13 ), it is possible to minimize a margin with respect to the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U). The margin is determined upon taking account of the error between the engine output torque estimate TEH and the actual engine output torque TE. This certainly ensures the above mentioned advantages while maintaining the responsibility of the slip control. 
     Although the embodiment according to the present invention has been shown and described such that the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation speed command value are obtained from the slip rotation speed initial command value calculating section  480  arranged as shown in FIG. 7A, it will be understood that the arrangement of the slip rotation speed initial command value calculating section  480  is not limited to this and may be arranged as shown in FIGS. 7B and 7C. 
     The slip rotation speed initial command value calculating section  480  of FIG. 7B is constituted by a lockup engagement pressure command value inverse calculating section  482 , a target lockup clutch engagement capacity inverse calculating section  483  and a target converter torque inverse calculating section  484  which are the same as those of FIG.  7 A. The lockup engagement capacity inverse calculating section  482  is arranged to receive the lockup clutch engagement pressure initial command value P LUC0  which is set by the similar manner with that of the lockup solenoid drive duty initial value D 0  employed in FIG.  7 A. Therefore, by inputting the thus arranged lockup clutch engagement pressure initial command value P LUC0  to the slip rotation speed initial command value calculating section  480  of FIG. 7B, the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation speed command value are obtained. If the arrangement shown in FIG. 7B is employed, the margin with respect to the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation speed command value becomes larger than that of the case of FIG. 7A (since it is apart from the controlled object as compared with the distance of FIG.  7 A). However, the increased amount of the margin functions to decrease the load for the calculation of the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation speed command value. 
     The slip rotation speed initial command value calculating section  480  of FIG. 7C is constituted by a target lockup clutch engagement capacity inverse calculating section  483  and a target converter torque inverse calculating section  484  which are the same as those of FIG.  7 A. The target lockup clutch engagement capacity inverse calculating section  483  is arranged to receive the lockup clutch engagement capacity initial value T LUC0  which is set by the similar manner with that of the lockup solenoid drive duty initial value D 0  employed in FIG.  7 A. Therefore, by inputting the thus arranged lockup clutch engagement capacity initial value T LUC0 , the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation speed command value are obtained. If the arrangement shown in FIG. 7C is employed, the margin with respect to the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation speed command value become larger than that of the case of FIG. 7A since it is apart from the controlled object as compared with the distance of FIG.  7 B. However, the increased amount of the margin functions to decrease the load for the calculation of the initial values ω SLPC0 (C/V) and ω SLPC0 (L/U) of the slip rotation speed command value. 
     With the thus arranged slip control system according to the present invention, when the slip control is started and when the torque converter is put in the converter state, the initial value of the slip rotation speed command value is set at a value by which the actual slip rotation speed becomes greater than a lower limit of a range wherein shocks caused by engaging the lockup clutch is negligible. Therefore, even if an error between an actual torque and an estimated torque for the slip control is generated, the actual slip rotation speed ω SLPR  is controlled so as not to become smaller than the allowable lower limit during a transient period of the start of the slip control from the converter state, and the engagement shock or engagement vibrations of the lockup clutch  2  during the transient period is certainly avoided by this arrangement. 
     The entire contents of Japanese Patent Application No. 10-315776 filed on Nov. 6, 1998 in Japan are incorporated herein by reference. 
     Although the invention has been described above by reference to a certain embodiment of the invention, the invention is not limited to the embodiment described above. Modifications and variations of the embodiment described above will occur to those skilled in the art, in light of the above teaching.