Method for identification of a threshold-level catalyst

Systems and methods for estimating catalyst transfer function gain are disclosed. In one example, an air-fuel ratio forcing function is applied to a catalyst. Air-fuel ratios upstream and downstream of the catalyst are manipulated to determine a transfer function gain of the catalyst. The transfer function gain may be a basis for indicating the presence or absence of catalyst degradation.

BACKGROUND AND SUMMARY

A vehicle may include a three-way catalyst (TWC) for treating exhaust gases of an internal combustion engine. Feedback control may be applied to regulate an engine's air-fuel ratio so that engine exhaust constituents may be adjusted in a way that improves catalyst efficiency. Some vehicles may include a universal exhaust gas oxygen (UEGO) sensor positioned upstream of the TWC and a heated exhaust gas oxygen (HEGO) sensor positioned downstream of the TWC to control the AFR near stoichiometry. The UEGO sensor provides feedback to adjust engine out gases about stoichiometry. The HEGO sensor provides feedback to bias the engine air-fuel ratio richer or leaner to improve catalyst efficiency.

Precise engine air-fuel ratio control may improve catalyst conversion efficiency; however, if the catalyst is in a degraded state, vehicle emissions may be above regulated levels even if the engine air-fuel ratio is precisely controlled. Therefore, it may be desirable to determine whether or not a catalyst is degraded so that remedial measures may be taken to bring the vehicle back within a regulated emissions level or to alert the driver to take the vehicle to a dealership for repair.

One way to judge whether or not a catalyst is degraded is to make a one-time change to the engine's air fuel ratio from lean to rich or vise-versa and measure the time it takes to observe a corresponding change in exhaust gas oxygen concentration downstream of a catalyst. The time it takes to observe a change in oxygen concentration may provide an indication as to a level of catalyst degradation. However, engine exhaust emissions may be degraded if rich or lean exhaust gases break through the catalyst due to intrusive changes in the engine's air-fuel ratio. Further, opportunities to monitor a step change may be limited and noise in the system may make the estimated results based on only a few observations less certain.

The inventors have recognized the above-mentioned disadvantages and have developed a method, comprising: during feedback engine air-fuel ratio control responsive to a downstream of a catalyst exhaust gas sensor: indicating degradation of the catalyst in response to a catalyst transfer function determined only within a specified frequency range based on the exhaust gas sensor output.

By determining a catalyst's transfer function only within a specified frequency range, it may be possible to provide the technical result of assessing catalyst degradation via engine air-fuel ratio modulation used to improve catalyst efficiency. In other words, a catalyst degradation assessment may be provided based on small air-fuel ratio variations routinely used to improve catalyst efficiency rather that via a specialized perturbation that may result in emission breakthrough. As a result, an assessment of catalyst degradation may be possible in a way that does not degrade vehicle emissions and may be more robust to many sources of noise.

The present description may provide several advantages. In particular, the approach may improve vehicle catalyst diagnostics. Additionally, the approach may provide improved vehicle emissions by providing an indication of a condition of catalyst degradation. Further, the approach may provide a catalyst diagnostic that is not intrusive or noticeable by a driver.

DETAILED DESCRIPTION

The present description is related to diagnosing the presence or absence of catalyst degradation. Specifically, methods and systems for determining a catalyst transfer function and its gain are described. The systems and methods may be implemented in a vehicle that includes an engine such as the engine system depicted inFIG. 1. The engine system may include an air-fuel control system as is shown inFIG. 2. A method for determining a catalyst transfer function gain is provided inFIG. 3. Example performance results for the method and system are shown inFIGS. 4-7.

FIG. 1illustrates a schematic diagram showing one cylinder of multi-cylinder engine10, which may be included in a propulsion system of an automobile. Engine10may be controlled at least partially by a control system including controller12and by input from a vehicle operator132via an input device130. In this example, input device130is an accelerator pedal and it includes a pedal position sensor134for generating a proportional pedal position signal PP. Combustion chamber (e.g., cylinder)30of engine10may include combustion chamber walls32with piston36positioned therein. Piston36may be coupled to crankshaft40so that reciprocating motion of the piston is translated into rotational motion of the crankshaft. Crankshaft40may be coupled to at least one drive wheel of a vehicle via an intermediate transmission system. Further, a starter motor may engage crankshaft40via a flywheel to enable a starting operation of engine10.

Combustion chamber30may receive intake air from intake manifold44via intake passage42and may exhaust combustion gases via exhaust passage48. Intake manifold44and exhaust passage48can selectively communicate with combustion chamber30via respective intake valve52and exhaust valve54. In some examples, combustion chamber30may include two or more intake valves and/or two or more exhaust valves. In this example, intake valve52and exhaust valve54may be controlled by cam actuation via one or more cams and may utilize one or more of cam profile switching (CPS), variable cam timing (VCT), variable valve timing (VVT), and/or variable valve lift (VVL) systems that may be operated by controller12to vary valve operation. The position of intake valve52and exhaust valve54may be determined by position sensors55and57, respectively. In alternative examples, intake valve52and/or exhaust valve54may be controlled by electric valve actuation. For example, cylinder30may alternatively include an intake valve controlled via electric valve actuation and an exhaust valve controlled via cam actuation including CPS and/or VCT systems.

In some examples, each cylinder of engine10may be configured with one or more fuel injectors for providing fuel thereto. As a non-limiting example, cylinder30is shown including one fuel injector66, which is supplied fuel from fuel system172. Fuel injector66is shown coupled directly to cylinder30for injecting fuel directly therein in proportion to the pulse width of signal FPW received from controller12via electronic driver68. In this manner, fuel injector66provides what is known as direct injection (hereafter also referred to as “DI”) of fuel into combustion cylinder30.

It will be appreciated that in an alternate example, injector66may be a port injector providing fuel into the intake port upstream of cylinder30. It will also be appreciated that cylinder30may receive fuel from a plurality of injectors, such as a plurality of port injectors, a plurality of direct injectors, or a combination thereof.

Continuing withFIG. 1, intake passage42may include a throttle62having a throttle plate64. In this particular example, the position of throttle plate64may be varied by controller12via a signal provided to an electric motor or actuator included with throttle62, a configuration that is commonly referred to as electronic throttle control (ETC). In this manner, throttle62may be operated to vary the intake air provided to combustion chamber30among other engine cylinders. The position of throttle plate64may be provided to controller12by throttle position signal TP. Intake passage42may include a mass air flow sensor120and a manifold air pressure sensor122for providing respective signals MAF and MAP to controller12.

Ignition system88can provide an ignition spark to combustion chamber30via spark plug92in response to spark advance signal SA from controller12, under select operating modes. Though spark ignition components are shown, in some examples, combustion chamber30or one or more other combustion chambers of engine10may be operated in a compression ignition mode, with or without an ignition spark.

An upstream exhaust gas sensor126is shown coupled to exhaust passage48upstream of emission control device70. Upstream sensor126may be any suitable sensor for providing an indication of exhaust gas air-fuel ratio such as a linear wideband oxygen sensor or UEGO (universal or wide-range exhaust gas oxygen), a two-state narrowband oxygen sensor or EGO, a HEGO (heated EGO), a NOx, HC, or CO sensor. In one example, upstream exhaust gas sensor126is a UEGO configured to provide output, such as a voltage signal, that is proportional to the amount of oxygen present in the exhaust. Controller12uses the output to determine the exhaust gas air-fuel ratio.

Emission control device70is shown arranged along exhaust passage48downstream of exhaust gas sensor126. Device70may be a three-way catalyst (TWC), configured to reduce NOx and oxidize CO and unburnt hydrocarbons. In some examples, device70may be a NOx trap, various other emission control devices, or combinations thereof.

A second, downstream exhaust gas sensor129is shown coupled to exhaust passage48downstream of emissions control device70. Downstream sensor129may be any suitable sensor for providing an indication of exhaust gas air-fuel ratio such as a UEGO, EGO, HEGO, etc. In one example, downstream sensor129is a HEGO configured to indicate the relative enrichment or leanness of the exhaust gas after passing through the catalyst. As such, the HEGO may provide output in the form of a switch point, or the voltage signal at the point at which the exhaust gas switches from lean to rich.

Further, in the disclosed examples, an exhaust gas recirculation (EGR) system may route a desired portion of exhaust gas from exhaust passage48to intake passage42via EGR passage140. The amount of EGR provided to intake passage42may be varied by controller12via EGR valve142. Further, an EGR sensor144may be arranged within the EGR passage and may provide an indication of one or more of pressure, temperature, and concentration of the exhaust gas. Under some conditions, the EGR system may be used to regulate the temperature of the air and fuel mixture within the combustion chamber.

Controller12is shown inFIG. 1as a microcomputer, including microprocessor unit102, input/output ports104, an electronic storage medium for executable programs and calibration values shown as read only memory chip106in this particular example, random access memory108, keep alive memory110, and a data bus. Controller12may receive various signals from sensors coupled to engine10, in addition to those signals previously discussed, including measurement of inducted mass air flow (MAF) from mass air flow sensor120; engine coolant temperature (ECT) from temperature sensor112coupled to cooling sleeve114; a profile ignition pickup signal (PIP) from Hall effect sensor118(or other type) coupled to crankshaft40; throttle position (TP) from a throttle position sensor; and absolute manifold pressure (MAP) signal from sensor122. Engine speed, RPM, may be generated by controller12from signal PIP.

Storage medium read-only memory106can be programmed with computer readable data representing non-transitory instructions executable by processor102for performing the methods described below as well as other variants that are anticipated but not specifically listed.

In some examples, controller12may output an indication of system degradation to a light or display panel131. The indication may be a visual alert such as an illuminated light or a message. The message may include a diagnostic code that indicates the nature of the degraded condition. For example, controller12may indicate a degraded catalyst via light or display panel131. The indication may be an alpha-numeric code representing catalyst or other component degradation.

As described above,FIG. 1shows only one cylinder of a multi-cylinder engine, and each cylinder may similarly include its own set of intake/exhaust valves, fuel injector, spark plug, etc.

FIG. 2shows a schematic illustration of inner and outer feedback control loops for a catalyst control architecture200. Catalyst control architecture200includes an engine system206and a catalyst control system214, where the engine10includes an exhaust system225.

The engine system208may include an engine10having a plurality of cylinders230. The engine10includes an engine intake42and an engine exhaust48. The engine intake42includes a throttle62in fluidic communication with engine intake manifold44. The engine exhaust system225includes an exhaust manifold48leading to an exhaust passage235that routes exhaust gas to the atmosphere. The engine exhaust system225may include one or more emission control devices70, which may be mounted in a close-coupled position in the exhaust. One or more emission control devices may include a three-way catalyst, lean NOx trap, particulate filter, oxidation catalyst, etc. It will be appreciated that other components may be included in the engine such as a variety of valves and sensors, as depicted, for example, inFIG. 1.

The vehicle system206may further include a catalyst control system214. Catalyst control system214is shown receiving information from exhaust gas oxygen sensors126and129and sending control signals to fuel injectors66. As one example, exhaust gas oxygen sensors may include exhaust gas sensor126located upstream of the emission control device70, and exhaust gas sensor129located downstream of the emission control device70. Other sensors such as pressure, temperature, air-fuel ratio, and composition sensors may be coupled to various locations in the vehicle system206. The catalyst control system214may receive input data from the various sensors, process the input data, and apply the actuators in response to the processed input data based on instructions or code programmed therein corresponding to one or more routines. Catalyst control system214may be configured with instructions stored in non-transitory memory that cause catalyst control system214to perform control routines via one or more actuators based on information received via one or more sensors. Example control routines are described herein with reference toFIG. 3.

In one example, emission control device70is a three-way catalyst, exhaust gas sensor126is a UEGO sensor, and exhaust gas sensor129is a HEGO sensor.

Catalyst control system214regulates the air-to-fuel ratio (AFR) to a desired air-fuel ratio near stoichiometry and fine-tunes this regulation based on the deviation of a HEGO voltage from a pre-determined HEGO-voltage set point Inner-loop controller207uses the upstream UEGO sensor126for higher-bandwidth feedback control while outer-loop controller205uses the HEGO sensor129for lower-bandwidth control. Catalyst control system214may be implemented by an engine controller, such as controller12.

Inner-loop controller207may comprise a proportional-integral-derivative (PID) controller that regulates the engine AFR by generating an appropriate fuel command (e.g., fuel pulse width). Summing junction222combines the fuel command from inner-loop controller207with commands from feed-forward controller220. This combined set of commands is delivered to the fuel injectors66of engine10. UEGO sensor126provides a feedback signal to the inner-loop controller207, the UEGO feedback signal proportional to the oxygen content of the feedgas or engine exhaust between the engine10and TWC70. Outer-loop controller205generates a UEGO reference signal (e.g., a desired air-fuel ratio) provided to the inner-loop controller207. The UEGO reference signal is combined with the UEGO feedback signal at junction216. The error or difference signal provided by junction216is then used by inner-loop controller207to adjust the fuel command so that the actual AFR within engine10approaches the desired AFR. HEGO sensor129provides feedback to the outer loop controller205. The HEGO feedback signal may be used to adjust the UEGO reference signal, or air-fuel ratio reference signal, provided to inner-loop controller207via junction216. Additionally, outer loop controller205works to improve catalyst efficiency by imposing a low amplitude air-fuel ratio square wave at the catalyst input. The square wave allows exhaust gas constituents entering the catalyst to vary so as to replenish oxygen and CO in the catalyst, thereby improving hydrocarbon oxidation and NOx reduction.

Thus, the system ofFIGS. 1 and 2provides for a system, comprising: an engine including an exhaust system, the exhaust system including a catalyst and oxygen sensors positioned upstream and downstream of the catalyst; and a controller including instructions stored in non-transitory memory for adjusting an actuator in response to a catalyst transfer function gain determined only within a specified frequency range of a predetermined square wave forcing function plus and minus an offset. The system includes where the specified frequency range of the predetermined forcing function is 1.5 Hz. The example system includes where the offset is 1 Hz. Thus, the example pass band may be between 0.5 Hz and 2.5 Hz. The example system further comprises additional instructions to band-pass filter output of the upstream and downstream oxygen sensors. The system further comprises additional instructions to determine an error from a difference between the band-pass filtered output of the upstream and downstream oxygen sensors. The system further comprises supplying an air-fuel ratio varying at a first frequency to estimate a first catalyst transfer function gain.

FIG. 3is a high-level flow chart illustrating an example method300for identifying a threshold catalyst in accordance with the current disclosure. In particular, method300relates to determining the magnitude of a catalyst's frequency-domain transfer function in a specific range of frequencies corresponding to a commanded square-wave input. Method300will be described herein with reference to the components and systems depicted inFIGS. 1 and 2, though it should be understood that the method may be applied to other systems without departing from the scope of this disclosure. Method300may be carried out by controller12, and may be stored as executable instructions in non-transitory memory.

At302, method300evaluates engine operating conditions. Operating conditions may include but are not limited to engine temperature, ambient temperature, engine speed, engine load, time since engine stop, engine air-fuel ratio, and HEGO sensor voltage. Method300proceeds to304after engine operating conditions are determined.

At304, method300applies an air-fuel modulation to the engine air-fuel ratio. The amplitude of the modulation is centered about stoichiometry or a small bias may be applied. The air-fuel modulation frequency may be based on the volume and location of the catalyst for which the transfer function is being estimated or other factors such as engine speed and load. In one example, the frequency may be 1.5 Hz. Method300proceeds to306after beginning to modulate the engine's air-fuel ratio. In some example systems, step304is already active when outer loop control is enabled.

At306, method300judges if the engine's outer air-fuel ratio control loop has been activated. In one example, the outer air-fuel control ratio may be activated after the engine's inner air-fuel ratio control loop has activated and controlling to a desired air-fuel ratio near stoichiometry, after the rear HEGO sensor reaches a threshold temperature, and in response to a threshold amount of time since engine start. In this way, method300may avoid determining the magnitude of the catalyst's transfer function if the vehicle is operating in a fuel cut-out mode, cold start, or other condition where post catalyst air-fuel ratio may not be reliable for catalyst transfer function determination. If method300judges that the outer air-fuel control loop is active, the answer is yes and method300proceeds to308. Otherwise, the answer is no and method300proceeds to310.

At310, method300deactivates the catalyst monitor. The catalyst monitor is deactivated since the HEGO output may not be reliable under the present conditions. Method300returns to306after the catalyst monitor is deactivated and will not attempt to run until the next program loop.

At308, method300activates and increments a timer. The timer allows the system to avoid determining the catalyst transfer function magnitude during mode transients after the outer air-fuel ratio control loop is activated. Method300proceeds to309after the timer is incremented.

At309, method300judges if a value of the timer is greater than a threshold value. If so, the answer is yes and method300proceeds to312. Otherwise, the answer is no and method300returns to308where the timer is incremented.

At312, method300prepares the monitored catalyst's input and output for processing. In particular, the output voltage of the upstream UEGO is converted into an air-fuel ratio. Likewise, the HEGO sensor output is converted into an air-fuel ratio. The voltage output from the sensors is representative of an oxygen concentration in the exhausts. The voltages are converted into air-fuel ratios via passing the voltages through transfer functions having air-fuel ratio as output.

Additionally, the tail pipe air-fuel ratio as estimated from the HEGO sensor output is operated on by a high pass filter with an adjustable time constant tc(e.g., a typical safeguard against signal noise introduced near the sampling frequency) to estimate the derivative of the output as shown in the following equation:

y.f=stc⁢s+1⁢y
where {dot over (y)}fis the estimated derivative of the catalyst output gas air-fuel ratio y, s is the Laplace operator, and tcis an adjustable time constant. The catalyst air-fuel ratio input determined from the UEGO is converted into a modeled output of the subject catalyst. In particular, the UEGO determined air-fuel ratio, the input u, is operated on by a system delay τd, a low-pass filter with time constant tc, and a system gain k0to provide the modeled derivative of the catalyst output gas air-fuel ratio as described in the following equation:

y.m,f=k0tc⁢s+1⁢u⁡(t-τd)
where {dot over (y)}m,fis the modeled estimated derivative of the catalyst output gas air-fuel ratio y, s is the Laplace operator, and tcis an adjustable time constant, u is the catalyst input air-fuel ratio, and τdis a time delay. The koand τdare representative of a nominal catalyst system and are typically functions of engine variables such as mass flow through the engine system. Method300proceeds to314after the sensor outputs are converted into air-fuel ratios and filtered as described above.

At314, method300the derivative of the measured downstream or post catalyst air-fuel ratio {dot over (y)}fand the derivative of the modeled downstream air-fuel ratio {dot over (y)}m,fare band-passed filtered. The filtering may be expressed by the following equation:
{{dot over (y)}bp,{dot over (y)}m,bp}=Gbp(s){{dot over (y)}f,{dot over (y)}m,f,tcl,tch}
where Gbpdesignates the transfer function of the band-pass filter, {dot over (y)}bpis the band-pass filtered version of {dot over (y)}f, {dot over (y)}m,bpis the band-passed filtered version of {dot over (y)}m,f, and tcland tchare low and high cut off frequencies of the band pass filter. Method300proceeds to316after the signals have been band-pass filtered.

At316, method300applies a low-pass or moving average filter to {dot over (y)}bpand {dot over (y)}m,bp. The low-pass filtering may be expressed by the following equation:
{{dot over (y)}lp,{dot over (y)}m,lp}=Glp(s){|{dot over (y)}bp|,|{dot over (y)}m,bp|}
where Glpdesignates the transfer function of the low-pass filter, {dot over (y)}lpis the low-pass filtered version of {dot over (y)}bp, and {dot over (y)}m,lpis the low-passed filtered version of {dot over (y)}m,bp. The low pass filter is applied so that the input/output phasing does not affect the estimation result of the catalyst's transfer function gain. Method300proceeds to318after the signals have been low-pass filtered.

At318, method300determines a model error ε is determined. The modeling error is determined according to the following equation:
ε={dot over (y)}lp−kscl×{dot over (y)}m,lp
where ε is the model error and ksclis the catalyst transfer function gain magnitude estimate that is given a starting value (e.g., 1), which the algorithm adjusts as the method iterates after each program loop. Method300proceeds to320after the catalyst transfer function gain magnitude estimate is determined.

At320, method300determines an updated catalyst transfer function gain magnitude estimate. In particular, method300applies an integrator and a calibrated (e.g. adjustable) gain γ to update the catalyst transfer function gain magnitude as indicated in the following equation.
{dot over (k)}scl=γ·ε
Method300proceeds to321after the catalyst transfer function gain magnitude has been updated.

At321, method300judges if the estimation has met a maturity metric. In one example, the maturity metric is an amount of time has been exceeded (e.g., ten minutes). In other examples, the maturity metric may be a distance traveled by the vehicle. More sophisticated methods that evaluate engine variables in terms of persistent change are yet another effective way to evaluate maturity. If method300judges that the maturity metric has been met, the answer is yes and method300proceeds to322. Otherwise, the answer is no and method300returns to318.

At322, method300judges if the estimated catalyst transfer function gain magnitude is greater than a threshold magnitude. If so, the answer is yes and method300proceeds to326. Otherwise, the answer is no and method300proceeds to324.

At324, method300indicates that the catalyst is a nominal or within specification catalyst. Method300may provide no indication of catalyst degradation if the catalyst is determined to be a nominal catalyst. Method300proceeds to328.

At328, method300outputs an estimated catalyst age in response to the estimated catalyst transfer function gain magnitude. In one example, a table or function of empirically determined catalyst age values are indexed using the estimated catalyst transfer function gain magnitude and the catalyst age is output. Additionally, if it is determined that the catalyst is a threshold catalyst, or degraded, method300adjusts actuators to attempt to reduce engine emissions in response to the catalyst transfer function gain magnitude. In one example, the engine fuel injectors are adjusted so as to reduce the amplitude of the square wave air-fuel ratio provided to the catalyst being diagnosed for possible degradation. A higher amplitude square wave may be desirable when the catalyst is operating as desired since it may require additional gases to penetrate and refresh catalyst reaction cites near the downstream side of the catalyst because the front reaction cites are operating efficiently. However, if the catalyst is degraded, a square wave of the same amplitude may result in lean or rich breakthrough. Therefore, the square wave amplitude may be reduced via adjusting fuel injector on time. Method300proceeds to exit after the catalyst age estimate is output and actuators are adjusted responsive to catalyst age.

At326, method300indicates that the catalyst is a threshold or degraded catalyst. Method300may provide an indication of catalyst degradation if the catalyst is determined to be a threshold catalyst. In one example, method300provides an indication of degradation via changing an operating state of a light or display panel. Method300proceeds to328after the catalyst has been identified as a threshold catalyst.

Thus, the method ofFIG. 3provides for a method, comprising: during feedback engine air-fuel ratio control responsive to a downstream of a catalyst exhaust gas sensor: indicating degradation of the catalyst in response to a catalyst transfer function determined only within a specified frequency range based on the exhaust gas sensor output; and adjusting an actuator in response to the indicated degradation. The method includes wherein the catalyst transfer function is further based on a modeled output compared with the exhaust gas sensor output. The method includes wherein the degradation is based on a gain of the catalyst transfer function within the specified frequency range above a threshold. The method also includes wherein the specified example frequency range is from 1 to 2 Hz.

In some examples, the method includes wherein the feedback engine air-fuel control is an outer loop feedback control, the method further comprising during the outer loop feedback control, further performing inner loop feedback engine air-fuel ratio control responsive to an oxygen sensor located upstream of the catalyst, wherein the outer loop includes a superimposed square wave added to the feedback control. The method also includes wherein the specified frequency range bounds a frequency of the superimposed square wave from above and below with an upper and lower frequency limit, respectfully, the lower frequency limit greater than zero. The method includes wherein during the feedback control the engine experiences transient and steady state operating conditions while the catalyst transfer function is determined. The method includes wherein air-fuel ratio control includes adjusting fuel injection pulse width.

The method ofFIG. 3also provides for a method, comprising: perturbing a catalyst via supplying the catalyst exhaust gases resulting from a varying air-fuel ratio supplied to an engine; routing data from an upstream oxygen sensor through a model to provide a model output and data from a downstream oxygen sensor through a high pass filter to provide a tailpipe air-fuel ratio derivative estimate; band-pass filtering the model output to provide a band-passed model output and band-pass filtering the tailpipe air-fuel ratio derivative estimate to provide a band-passed tailpipe air-fuel ratio; estimating a catalyst transfer function gain magnitude from a difference between the band-passed tailpipe air-fuel ratio and the band-passed model output. The method further comprises low pass filtering the band-passed model output and the band-passed tailpipe air-fuel ratio before estimating the catalyst transfer function gain magnitude.

In some examples, the method further comprises determining an error between the low pass filtered band-passed model output and the low pass filtered band-passed tailpipe air-fuel ratio. The method further comprises adjusting an estimate of a catalyst transfer function gain magnitude in response to the error.

Referring now toFIG. 4, a plot of magnitude versus frequency for the band-pass filter applied at314is shown. The band-pass filter attenuates or reduces the magnitude of signal frequencies that are not in the pass band of the filter. In this example, the pass band is at 1.5 Hz. The magnitude at 1.5 Hz for the output of the filter is 0 dB, or unfiltered at the pass frequency. Frequencies greater than and less than the pass frequency are attenuated. The width of the pass band is determined by the choices of step314inFIG. 3, tcland tch. Thus, the band-pass filter allows the catalyst transfer function to be determined only within a specified frequency range from the exhaust gas sensor output. By band-pass filtering the exhaust air-fuel ratio, it may be possible to reduce influence from air-fuel variations that are not related to the forcing function (e.g., air-fuel ratio square wave) applied to the catalyst.

Referring now toFIG. 5, a plot of magnitude versus frequency for the low-pass filter applied at316is shown. The low-pass filter attenuates or reduces the magnitude of signal frequencies that are greater than a cut-off frequency of the low band of the filter. In this example, the pass band is less than 1 Hz. Frequencies greater than the upper cut-off frequency are attenuated. By low-pass filtering the band-pass filtered exhaust air-fuel ratio, it may be possible to reduce signal phasing influences on the estimate of the catalyst's transfer function gain magnitude.

Referring now toFIG. 6, a plot of adapted catalyst transfer function scaling factor gains for green, full-useful life, and threshold catalysts is shown. The method ofFIG. 3was conducted seventy six times using the three types of catalysts staring with an initial gain estimate of one. The gains were allowed to update continuously when the outer air-fuel control loop was activated. Labels602,610, and620represent the mean gain values for the respective green, full-useful life, and threshold catalysts. Likewise, labels604,612, and622represent the maximum gains for the respective green, full-useful life, and threshold catalysts. Similarly, labels606,614, and624represent the minimum gains for the respective green, full-useful life, and threshold catalysts. It may be observed that the gains for the threshold catalyst are substantially greater than for the green and useful life catalyst. As such, the gains are a useful way of estimating catalyst age and degradation. Further, the gains for the green and full-useful life catalysts are quite similar.

Referring now toFIG. 7, an example plot of catalyst transfer function adaptation of gains that begin at different initial conditions for a full useful life catalyst is shown. The method ofFIG. 3is applied to a single catalyst with different initial conditions of kscl(from step320inFIG. 3) during three separate evaluations. The gain values start out spread widely apart and converge toward each other by time1200. The gains were each allowed to adapt over a federal test procedure 74 cycle. Although the gains do not converge to the exact same number, they are grouped tightly enough to fall within the range of values shown inFIG. 6for a full useful life catalyst. Thus, the method ofFIG. 3is shown to be robust for determining catalyst degradation even in the presence of induced error in the system.