CN1877105B - Automobile longitudinal acceleration tracking control method - Google Patents

Abstract

The invention relates to a method for tracking and controlling the longitudinal acceleration of vehicle, belonging to the vehicle longitudinal dynamics control technique. It is characterized in that: it utilizes the estimator of multiplicative deterministic model of controlled object formed by reversed and positive dynamic models, to estimate the system increment of present input signal on the model difference between each model and real object, and uses the estimated system increment as the switch index function, to on-line select relative controller from the controller, to control the opening degree of throttle valve of engine and realize the track and control of longitudinal acceleration, with high stability and track ability.

Description

A kind of automobile longitudinal acceleration tracking control method

Technical field:

A kind of automobile longitudinal acceleration tracking control method belongs to automobile longitudinal dynamics Controlling technical field.

Background technique:

The automobile longitudinal kinetic control system is designed to hierarchy usually: the upper strata controller is mainly considered problems such as driver characteristics, formation stability and traffic flow according to relative spacing and the speed of a motor vehicle output expectation acceleration during design; Lower floor's acceleration tracking control unit makes the automobile actual acceleration follow the tracks of expected value through the control to actuator, mainly considers the dynamics of vehicle problem during design.The automobile longitudinal acceleration tracking Control is one of key technology of automobile longitudinal motion control.Document 1 (Mikael Persson; Etc. take up the adaptive cruise control system design of Controller of stopping function; Proceedings of the 1999 IEEEInternational Conference on Control Application; 1999) the longitudinal direction of car dynamics is approximately linear system, adopts PI method design acceleration tracking control unit.Because it is non-linear that the longitudinal direction of car dynamics has, the method that is approximately linear system is difficult in all working point and all obtains effect preferably.Document 2 (R.Mayr; Automobile function cruise control system design based on feedback linearization method; Proceedings of the American Control Conference; 1994) at first adopt the exact linearization method method that nonlinear model is converted into linear model, designed the automobile longitudinal acceleration controller based on linearized model then.Document 3 (J.K.Hedrick; Gamma controller design towards automatic driving vehicle; UKACC International Conference on Control; 1998) setting up on the non-linear longitudinal direction of car dynamic model basis, adopting sliding-mode control to design the automobile longitudinal acceleration FOLLOWING SLIDING MODE CONTROLLER.Document 4 (Kyongsu Yi, etc. is based on the following distance and the vehicle speed control system design of electric control vacuum booster, JSAE Review; 22,2001), (YangBin, etc. take up the cruise control system acceleration Tracking Control Design of stopping function to document 5; Proceedings of the 2004IEEE International Conference on Networking, Sensing Control, 2004) and document 6 (Hou Dezao etc.; Based on level controlling system under the automobile active collision avoidance of Model Matching method; Automotive engineering, 25 (4), 2003) all at first eliminate the non-linear of transmission system through inverse dynamics model; To be approximately linear system by the new system that reverse and forward longitudinal direction of car dynamic model are formed and the linear system characteristic will be carried out on the identification basis; Document 4 adopts the PI method, and document 5 adopts sliding-mode method, and document 6 adopts feedforward to be fed back to H for the Model Matching controller _∞The two degrees of freedom structure of controller has designed the relevant acceleration tracking control unit respectively.

Above-mentioned controlling method needs auto model more accurately, even H _∞Can not handle very big model uncertainty Deng robust control method.But under the actual travel condition; Because the model error that inevitable not modeling dynamic characteristic and parameter variation cause in the modeling process can make the longitudinal direction of car dynamics change in a scope very greatly, feasible controller through a preset parameter is difficult in and obtains acceleration tracking performance preferably when guaranteeing closed loop stability.

Summary of the invention:

The objective of the invention is to, propose a kind of automobile longitudinal acceleration tracking control method.This method is according to selecting the appropriate control device in the slave controller set online of certain switching law; Through the control of throttle opening being realized the tracking Control of automobile longitudinal acceleration; Make when the automobile longitudinal dynamics in very large range changes, can guarantee closed-loop system stability and tracking performance preferably simultaneously.

The invention is characterized in; It is the estimator that utilizes the property the taken advantage of ambiguous model of the controlled device of being made up of the reverse of automobile and the positive power model element in gathering to design; Model error between each model and the practical object is estimated the system gain of current input signal; And with this system gain of estimating to obtain as switching target function; From the controller set that designs according to the element the said property the taken advantage of ambiguous model set, select corresponding controller online, the engine air throttle aperture is controlled, realize the tracking Control of automobile longitudinal acceleration;

This method contains the following steps of in entire car controller, carrying out:

1) initialization:

The parameter of vehicle parameter and automobile running environment;

δ: the exponential decay coefficient, its scope is: 0.1～1;

U: Acceleration Control amount, its initial value are 0;

With the corresponding estimator set of element in the set of the controlled device property taken advantage of ambiguous model be:

${\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">E</figure-callout>}1}=A_{E1}{x}_{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">E</figure-callout>}1}+B_{E1}u,{\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}=A_{E2}{x}_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}+B_{E2}u,$

e _i＝a _i-a＝C _E1ix _E1+D _E1iu-a，z _i＝C _E2ix _E2+D _E2iu，i＝1…N，

In the formula (13), x _E1And x _E2For with the controlled device property taken advantage of ambiguous model set in the corresponding estimator state of element, its initial value is 0; N is the controller number, A _E1, B _E1, A _E2, B _E2, C _E1i, D _E1i, C _E2i, D _E2iIt is the state matrix of estimator;

With the corresponding controller set C of element in the set of the controlled device property taken advantage of ambiguous model be:

$C=\{K_i:\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ci}}{x}_C+B_{\mathrm{Ci}}(a_{\mathrm{des}}-a)\\ u=C_{\mathrm{Ci}}{x}_C+D_{\mathrm{Ci}}(a_{\mathrm{des}}-a)\end{array},i=1\&CenterDot;\&CenterDot;\&CenterDot;N\}$

In the formula (19), K _iBe i the controller of controller set C, x _cBe the state of controller set, its initial value is 0; N is the controller number, A _Ci, B _Ci, C _Ci, D _CiIt is state matrix; Element satisfies among the controller set C:

${\left|\right|\mathrm{\&Sigma;}(A_i,B_i,C_{1i},D_{1i})\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&eta;}<\frac{1}{\mathrm{\&gamma;}},{\left|\right|W_{\mathrm{per}}\left(s\right)\mathrm{\&Sigma;}(A_i,B_i{C}_{2i},D_{2i})\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&beta;},i=1\&CenterDot;\&CenterDot;\&CenterDot;N,$

$A_{\mathrm{\&sigma;}}=\left[\begin{array}{ccc}{A}_{E1}-{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E1}{D}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="C\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_E& 0& {\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E1}{C}_{\mathrm{C\&sigma;}}\\ -{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E2}{D}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="C\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_E& A_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}& {\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E2}{C}_{\mathrm{C\&sigma;}}\\ -{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="C\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_E& 0& A_{\mathrm{C\&sigma;}}-{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="D\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">D</figure-callout>}}_E{C}_{\mathrm{C\&sigma;}}\end{array}\right],B_{\mathrm{\&sigma;}}={\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}\left[\begin{array}{c}{B}_{E1}{D}_{\mathrm{C\&sigma;}}\\ B_{E2}{D}_{\mathrm{C\&sigma;}}\\ B_{\mathrm{C\&sigma;}}\end{array}\right],$

C _1σ＝[-Φ _σD _E2σD _CσC _E1σ?C _E2σ?Φ _σD _E2σC _Cσ]，D _1σ＝Φ _σD _E2σD _Cσ，

D _2σ＝Φ _σ，C _2σ＝-Φ _σ[C _E1σ?0?D _E1σC _Cσ]；

W wherein _Per(s) be the performance index weighting function, the symbol ∑ (A, B, C, D) expression is satisfied by the state-space model that A, B, C, D do matrix of the coefficients:

$\frac{{\left|\right|W_{\mathrm{per}}\left(s\right)q\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|a_{\mathrm{des}}\left|\right|}_2^{\mathrm{\&delta;}}}<\frac{\mathrm{\&beta;}}{1-\mathrm{\&eta;\&gamma;}};$

2) gather pickup a, expectation pickup a _Des

3) matrix of the coefficients according to the estimator of the property the taken advantage of ambiguous model of controlled device set design calculates evaluated error e _iWith uncertain part input z _i:

${\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">E</figure-callout>}1}=A_{E1}{x}_{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">E</figure-callout>}1}+B_{E1}u,{\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}=A_{E2}{x}_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}+B_{E2}u,$

e _i＝C _E1ix _E1+D _E1iu-a，z _i＝C _E2ix _E2+D _E2iu，i＝1…N， (1)

Wherein N is the number of element in the set of the controlled device property taken advantage of ambiguous model;

4) the switching index of N model in the set of the employing computes property taken advantage of ambiguous model:

$J_i\left(t\right)=\frac{{\left|\right|e_i\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|z_i\left|\right|}_2^{\mathrm{\&delta;}}},i=1\&CenterDot;\&CenterDot;\&CenterDot;N---\left(2\right)$

5) above-mentioned N switches index and controller set $C=\{K_i:\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ci}}{x}_C+B_{\mathrm{Ci}}(a_{\mathrm{Des}}-a)\\ u=C_{\mathrm{Ci}}{x}_C+D_{\mathrm{Ci}}(a_{\mathrm{Des}}-a)\end{array},i=1\&CenterDot;\&CenterDot;\&CenterDot;N\}$ In N element corresponding one by one according to the order of i, select above-mentioned N switching index J that switches minimum in the index _k(t) the controller compute control amount u of correspondence:

$C=\{K_{\mathrm{\&sigma;}}:\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ck}}{x}_C+B_{\mathrm{Ck}}(a_{\mathrm{des}}-a)\\ u=C_{\mathrm{Ck}}{x}_C+D_{\mathrm{Ck}}(a_{\mathrm{des}}-a)\end{array}\}$

6) calculate throttle according to contrary automobile longitudinal dynamic model:

$T_{\mathrm{edes}}=\frac{r}{R_{\mathrm{<figure-callout\; id="0"\; label="d\; R\; g"\; filenames="S06189496X20060717E000013.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">d</figure-callout>}}{R}_g{0}_{}{\mathrm{\&eta;}}_0}(M_{0}u+{\mathrm{<figure-callout\; id="2"\; label="C\; D\; Av"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">C</figure-callout>}}_D{\mathrm{Av}}^{}{}^2+{\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="S06189496X20060717E000013.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">M</figure-callout>}}_0{\mathrm{gf}}_0)$

θ＝MAP ^-1(T _edes，ω _e) (3)

The parameter that wherein comprises following vehicle parameter and automobile running environment:

V is the speed of a motor vehicle, T _EdesBe the Engine torque of expectation, ω _eBe engine speed, θ is a throttle opening, and r is a radius of wheel, R _dBe main reducing gear speed ratio, R _G0Be the nominal value of transmission gear ratio, η ₀Be the nominal value of transmission system mechanical efficiency, M ₀Be the nominal value of complete vehicle quality, C _DBe coefficient of air resistance, g is a gravity constant, f ₀Be the nominal value of coefficient of rolling resistance, A is a wind-exposuring area; MAP ^-1(■) be the contrary torque characteristics figure of motor;

7) throttle that obtains according to aforementioned calculation is controlled the motor of automobile, and controlled quentity controlled variable u value is returned the 2nd) go on foot and proceed to calculate and control.

The constitution step of the property the taken advantage of ambiguous model set of said controlled device is:

The first step: the possible excursion of vehicle and enviromental parameter is separated into limited parameter point, is made as M; Utilize the method for process identification to utilize the inputoutput data identification to obtain the model of controlled device at each parameter point, can obtain M transfer function so altogether, H _i(s), i=1...M;

Second step: adopt M transfer function on frequency domain, to cover certain zone, the number according to intending the nominal model that adopts is made as N, and this zone leveling is divided into the N piece, is expressed as Ω _i, i=1...N, the transfer function of selecting every regional center obtains N nominal model G as the nominal model _i(s), i=1...N;

The 3rd step: to each zone that obtains in the first step, utilize computes should the zone in the model error of all transfer functions nominal model corresponding with this zone:

${\mathrm{\&Delta;H}}_i\left(s\right)=\frac{H_i\left(s\right)-G_i\left(s\right)}{G_i\left(s\right)},{\&ForAll;H}_i\left(s\right)\&Element;{\mathrm{\&Omega;}}_j,---\left(3\right)$

According to the model error that calculates, choose model error weighting function W _j(s) on all frequencies, satisfy

$\left|W_j(s-0.5\mathrm{\&delta;})\right|>\frac{1}{\mathrm{\&gamma;}}\left|{\mathrm{\&Delta;H}}_i(s-0.5\mathrm{\&delta;})\right|,\&ForAll;H_i\left(s\right)\&Element;{\mathrm{\&Omega;}}_j,---\left(4\right)$

Wherein δ is the exponential decay coefficient, is a constant; Symbol | | the amplitude of expression transfer function so just obtains describing regional Ω _jThe property taken advantage of uncertainty models:

$P=\{P_i\left(s\right)=[1+{\mathrm{\&Delta;}}_i{W}_i\left(s\right)]G_i\left(s\right),{\left|\right|{\mathrm{\&Delta;}}_i\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&gamma;},i=1,\&CenterDot;\&CenterDot;\&CenterDot;,N\}---\left(5\right)$

Wherein γ is the upper limit of plant model error; W _i(s) be to have the polynomial model error weighting function of same characteristic features; G _i(s) be to have the polynomial nominal model of same characteristic features; Δ _iBe the uncertain part of the model of controlled device; Its size is guaranteed by (4); N is the number of model in the model set; Symbol ‖ ‖ _∞ ^δThe L of expression system _{2 δ}Gain.

Evidence: have greatlyyer when uncertain in automobile and enviromental parameter, the method among the present invention can effectively be controlled automobile longitudinal acceleration, has stability and tracking performance preferably.

Description of drawings:

Fig. 1, the overall structure figure of automobile longitudinal acceleration tracking control method;

Fig. 2, the controlled device structural drawing;

Fig. 3, the switch logic flow chart;

Fig. 4, the automobile longitudinal acceleration tracking control method flow chart;

Fig. 5, the contrary torque characteristics figure of domestic Jetta AT type motorcar engine;

Fig. 6, controlled device frequency domain response characteristic coverage area, wherein (a) is amplitude versus frequency characte figure, (b) is phase-frequency characteristic figure;

Fig. 7, automobile longitudinal acceleration tracking control method simulation result, (a) automobile longitudinal acceleration response curve wherein, (b) switching signal response curve, (c) car speed response curve, (d) throttle opening response curve;

Fig. 8, automobile longitudinal acceleration tracking control method empirical curve, (a) automobile longitudinal acceleration response curve wherein, (b) switching signal response, (c) car speed response curve, (d) throttle opening response.

Embodiment:

As shown in Figure 1, be the overall structure of automobile longitudinal acceleration tracking control method of the present invention.a _DesPickup for expectation; A is actual pickup; Q=a _Des-a is the tracking error that actual pickup is followed the tracks of the expectation acceleration; J _i(t), i=1...N is that the model error between each element and the controlled device is to the system gain of current demand signal in the model set, and N is the number of element in the set of the controlled device property taken advantage of ambiguous model; σ is a switching signal, numbers the controller consistent with σ and will be connected in the control loop; The controlled quentity controlled variable of u for calculating according to controller.The whole control system comprises that controlled device, estimator, switch logic and controller gather four parts.Estimator is estimated the switching index that each controller is corresponding in real time according to controlled quentity controlled variable u and pickup; Switch logic selects to switch the corresponding numbering of the minimum controller of index as output according to the switching index of estimator output; Select corresponding controller compute control amount u in the controller numbering slave controller set according to switch logic output; Can obtain accelerator open degree according to u by the contrary vertically dynamic model of automobile, thereby motor is controlled.

To introduce the principle and the structure of each several part below respectively.

(A) controlled device and the property taken advantage of uncertainty models set description thereof

Because the motor in the automobile etc. has comparison severe nonlinear characteristic, reference 4, document 5 and document 6 also adopt a contrary automobile longitudinal dynamic model to eliminate nonlinear characteristics among the present invention.Obtain the controlled device of forming by contrary automobile longitudinal dynamics and automobile as shown in Figure 2.

Among Fig. 2, v is the speed of a motor vehicle, T _EdesBe the Engine torque of expectation, ω _eBe engine speed, θ is a throttle opening.For given acceleration u, according to automobile resistance driving force equation of equilibrium (Yu Zhisheng, automobile theory, Beijing: China Machine Press, 2000 the 3rd edition) can calculate the engine output torque of expectation:

$T_{\mathrm{edes}}=\frac{r}{R_d{R}_{\mathrm{<figure-callout\; id="0"\; label="g"\; filenames="S06189496X20060717E000013.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">g</figure-callout>}0}{\mathrm{\&eta;}}_0}(M_{0}u+{\mathrm{<figure-callout\; id="2"\; label="C\; D\; Av"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">C</figure-callout>}}_D{\mathrm{Av}}^{}{}^2+M_{0}g{f}_0),---\left(1\right)$

Wherein r is a radius of wheel, R _dBe main reducing gear speed ratio, R _G0Be the nominal value of transmission gear ratio, η ₀Be the nominal value of transmission system mechanical efficiency, M ₀Be the nominal value of complete vehicle quality, C _DBe coefficient of air resistance, g is a gravity constant, f ₀Be the nominal value of coefficient of rolling resistance, A is a wind-exposuring area.Because in the actual travel process; Gear, transmission system mechanical efficiency, complete vehicle quality, rolling resistance are with environmental change; And be difficult to these parameter values are carried out real-time detection, so in control procedure, can only utilize (1) that the Engine torque of expecting is calculated according to its nominal value.Based on expectation engine torque and engine speed, utilize the contrary torque characteristics figure of engine can obtain the throttle opening of engine:

θ＝MAP ^-1(T _edes，ω _e)， (2)

MAP wherein ^-1Be the contrary torque characteristics figure of motor (■), the figure shows the relation between the same engine speed of engine air throttle aperture, the expectation Engine torque, this figure can obtain from motor supplier.(1) and (2) be the contrary vertically dynamic model of automobile.

Under the actual travel condition, because the not modeling dynamic characteristic that exists in the variation of vehicle and enviromental parameter and the modeling process can make the dynamic characteristic of controlled device in very large range change.Only adopt a model that controlled device is described and to cause very big modeling error, describe controlled device so adopt a plurality of property taken advantage of ambiguous model composition models to gather among the present invention.The establishment method of the property taken advantage of ambiguous model set has multiple, introduces document 7 (X.Rong Li, the model set design conventional method that etc. controls towards multi-model below; IEEE Transactions on Automatic Control; 2005,50 (9)) and document 8 (initiatively anti-collision system research [Doctor's Degree paper] of Hou Dezao, automobile; 2004, Department of Automobile Engineering of Tsing-Hua University) the middle method of introducing:

The first step: the possible excursion of vehicle and enviromental parameter (like the speed ratio of the time constant of the quality of automobile, motor, gear, the gradient, wind speed etc.) is separated into limited parameter point, is made as M.Utilize the method (like Fang Chongzhi, etc., process identification, Beijing: publishing house of Tsing-Hua University, 1988) of process identification to utilize the inputoutput data identification to obtain the model of controlled device at each parameter point, can obtain M transfer function so altogether, H _i(s), i=1...M.

Second step: M transfer function can cover certain zone on frequency domain, the number according to intending the nominal model that adopts is made as N, and this zone leveling is divided into the N piece, is expressed as Ω _i, i=1...N, the transfer function of selecting every regional center is as the nominal model, thereby obtains N nominal model G _i(s), i=1...N.

The 3rd step: to each zone that obtains in second step, with Ω _jBe example, utilize computes should the zone in the model error of all transfer functions nominal model corresponding with this zone:

${\mathrm{\&Delta;H}}_i\left(s\right)=\frac{H_i\left(s\right)-G_j\left(s\right)}{G_j\left(s\right)},{\&ForAll;H}_i\left(s\right)\&Element;{\mathrm{\&Omega;}}_j,---\left(3\right)$

According to the model error that calculates, choose model error weighting function W _j(s) on all frequencies, satisfy

$\left|W_j(s-0.5\mathrm{\&delta;})\right|>\frac{1}{\mathrm{\&gamma;}}\left|{\mathrm{\&Delta;H}}_i(s-0.5\mathrm{\&delta;})\right|,\&ForAll;H_i\left(s\right)\&Element;{\mathrm{\&Omega;}}_j,---\left(4\right)$

Wherein δ is the exponential decay coefficient, is a constant, and its physical significance is set forth in the back; γ is a constant, has reacted the probabilistic size of the property taken advantage of, and is taken as 1 usually; Symbol | | the amplitude of expression transfer function.So just, obtain describing regional Ω _jThe property taken advantage of uncertainty models:

$P_j\left(s\right)=[1+{\mathrm{\&Delta;}}_j{W}_j\left(s\right)]G_j\left(s\right),{\left|\right|{\mathrm{\&Delta;}}_j\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&gamma;},---\left(5\right)$

Δ wherein _jBe the uncertain part of model, its size is guaranteed by (4); Symbol ‖ ‖ _∞ ^δThe L of expression system _{2 δ}Gain is when adopting L _{2 δ}When norm was come the gauge signal size, it had reacted the magnification factor of system to input signal, L _{2 δ}Norm ‖ ‖ ₂ ^δBe defined as:

${\left|\right|u\left|\right|}_2^{\mathrm{\&delta;}}=\sqrt{{\&Integral;}_0^t{e}^{-\mathrm{\&delta;}(t-\mathrm{\&tau;})}{u}^2\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;}},---\left(6\right)$

Wherein u is a time-domain signal, and consistent in δ meaning and (4) formula can find out that from (6) δ has reacted in the past constantly data by the speed of exponential decay.Directly calculate L with (6) formula of employing _{2 δ}The norm more complicated is according to defining the L that can know signal _{2 δ}Norm be signal u square and e ^{-δ t}The square root of convolution, then can adopt the L of computes signal _{2 δ}Norm:

${\left|\right|u\left|\right|}_2^{\mathrm{\&delta;}}=\sqrt{\frac{1}{s+\mathrm{\&delta;}}{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">u</figure-callout>}}^2}.---\left(7\right)$

Because the plant characteristic region covered is divided into the N piece, all can obtains the corresponding property taken advantage of ambiguous model to every through top computing, thereby obtain describing the property the taken advantage of uncertainty models set of controlled device characteristic:

$P=\{P_i\left(s\right)=[1+{\mathrm{\&Delta;}}_i{W}_i\left(s\right)]G_i\left(s\right),{\left|\right|{\mathrm{\&Delta;}}_i\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&gamma;},i=1,\&CenterDot;\&CenterDot;\&CenterDot;,N\}.---\left(8\right)$

When the transfer function of carrying out N nominal model and N model error weighting function selection, make: N nominal model G above _i(s) has identical proper polynomial, N model error weighting function W _i(s) has identical proper polynomial.

(B) estimator

The effect of estimator is the input/output information according to controlled device, and the size of the uncertain part of model of each element and object in the model set is estimated.Suppose that controlled device is by describing like inferior property ambiguous model:

a＝[1+ΔW(s)]G(s)u。(9)

If G(s) stable, then can adopt following formula that the output of controlled device is estimated:

$\hat{a}=G\left(s\right)u.---\left(10\right)$

(9) subtract (10) and can obtain controlled device output evaluated error:

$e=\hat{a}-a=-\mathrm{\&Delta;W}\left(s\right)G\left(s\right)u.---\left(11\right)$

Can find out that by (10) the uncertain part of model is output as evaluated error e, is input as

z＝W(s)G(s)u。(12)

Utilization (11) and (12) can be to the L of the uncertain part of model to current input signal _{2 δ}Gain is estimated.

Based on above-mentioned consideration; Reference literature 7 (Wu Lin; Automatic Control Theory (volume two); Beijing: publishing house of Tsing-Hua University, 1992 the 1st edition) in the method for transformation of controllable canonical form obtain the corresponding controllable canonical form form of each element in the property the taken advantage of ambiguous model set of (A) partial design, and with it as estimator:

${\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">E</figure-callout>}1}=A_{E1}{\mathrm{<figure-callout\; id="1"\; label="x\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">x</figure-callout>}}_E+B_{E1}u,{\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}=A_{E2}{\mathrm{<figure-callout\; id="2"\; label="x\; E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">x</figure-callout>}}_E+B_{E2}u,$

e _i＝a _i-a＝C _E1ix _E1+D _E1iu-a，z _i＝C _E2ix _E2+D _E2iu，i＝1…N， (13)

A wherein _iFor based on model P _i(s) design object output estimator is to the estimated value of controlled device output, e _iBe correspondence output evaluated error, z _iFor based on model P _i(s) estimated value that model uncertainty is partly exported between the nominal model of design and the object.According to document 7, can know that the matrix of the coefficients of the equation of state in (13) will satisfy:

C _E1i(sI-A _E1) ^-1B _E1+D _E1i＝G _i(s)，

C _E2i(sI-A _E2) ^-1B _E2+D _E2i＝W _i(s)G _i(s)，i＝1…N。(14)

By the analysis of (13) and front, can adopt the L of following formula to the uncertain part of model between each element and the object in the model set _{2 δ}Gain is the switching index, calculates:

$J_i\left(t\right)=\frac{{\left|\right|e_i\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|z_i\left|\right|}_2^{\mathrm{\&delta;}}},i=1\&CenterDot;\&CenterDot;\&CenterDot;N.---\left(15\right)$

J _i(t) reacted model P _i(s) the uncertain part of model is to the L of current input signal and between the controlled device _{2 δ}Gain.

(C) switch logic

The effect of switch logic is according to the switching index J of estimator output _i(t), selection control is controlled controlled device in the set of i=1...N slave controller, and its output is the numbering of the controller of selection.And the minimum model of the uncertain part of model should be the most approaching with object between the controlled device, and the controller based on this model design should be able to obtain to control preferably effect so.Based on above-mentioned consideration, adopt switch logic shown in Figure 3, among the figure, J _{σ (t)}Be the switching index that current controller is corresponding, if the corresponding switching index of current controller continues to adopt current controller to control for hour; If the switching index that current controller is corresponding is not minimum, then select the corresponding controller of minimum switching index to control.K representes that t switches the minimum pattern number of index constantly.

(D) controller set

Definition according to evaluated error has

a＝a _σ-e _σ。(16)

(16) substitution (13) can be obtained

${\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">E</figure-callout>}1}=A_{E1}{\mathrm{<figure-callout\; id="1"\; label="x\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">x</figure-callout>}}_E+B_{E1}u,{\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}=A_{E2}{\mathrm{<figure-callout\; id="2"\; label="x\; E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">x</figure-callout>}}_E+B_{E2}u,$

a＝C _E1σx _E1+D _E1σu-e _σ，z _σ＝C _E2σx _E2+D _E2σu。(17)

In the system that (17) are described, with e _σAs the disturbance that the uncertain part of model causes, z _σAs the input of the uncertain part of model, the switching law of design can guarantee the following formula establishment.

$\frac{\left|\right|e_{\mathrm{\&sigma;}}\left|\right|}{\left|\right|z_{\mathrm{\&sigma;}}\left|\right|}<\mathrm{\&gamma;}.---\left(18\right)$

If the controller set is:

$C=\{K_i:\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ci}}{x}_C+B_{\mathrm{Ci}}(a_{\mathrm{des}}-a)\\ u=C_{\mathrm{Ci}}{x}_C+D_{\mathrm{Ci}}(a_{\mathrm{des}}-a)\end{array},i=1\&CenterDot;\&CenterDot;\&CenterDot;N\}.---\left(19\right)$

Then by the controller K of current selection _σThe closed-loop system of forming with system (17) is:

$\stackrel{\&CenterDot;}{x}=A_{\mathrm{\&sigma;}}x+B_{\mathrm{\&sigma;}}(a_{\mathrm{des}}+e_{\mathrm{\&sigma;}}),$ z _σ＝C _1σx+D _1σ(a _des+e _σ)，q＝C _2σx+D _2σ(a _des+e _σ)， (20)

Wherein $x=\left[\begin{array}{c}{x}_{E1}\\ x_{E2}\\ x_C\end{array}\right],$ $A_{\mathrm{\&sigma;}}=\left[\begin{array}{ccc}{A}_{E1}-{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E1}{D}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="C\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_E& 0& {\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E1}{C}_{\mathrm{C\&sigma;}}\\ -{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E2}{D}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="C\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_E& A_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}& {\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E2}{C}_{\mathrm{C\&sigma;}}\\ -{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="C\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_E& 0& A_{\mathrm{C\&sigma;}}-{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{\mathrm{C\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="D\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">D</figure-callout>}}_E{C}_{\mathrm{C\&sigma;}}\end{array}\right],$ $B_{\mathrm{\&sigma;}}={\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}\left[\begin{array}{c}{B}_{E1}{D}_{\mathrm{C\&sigma;}}\\ B_{E2}{D}_{\mathrm{C\&sigma;}}\\ B_{\mathrm{C\&sigma;}}\end{array}\right],$

C _1σ＝[-Φ _σD _E2σD _CσC _E1σ?C _E2σ?Φ _σD _E2σC _Cσ]，D _1σ＝Φ _σD _E2σD _Cσ，D _2σ＝Φ _σ，C _2σ＝-Φ _σ[C _E1σ?0?D _E1σC _Cσ]。

If element satisfies among the controller set C

${\left|\right|\mathrm{\&Sigma;}(A_i,B_i,C_{1i},D_{1i})\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&eta;}<\frac{1}{\mathrm{\&gamma;}},{\left|\right|W_{\mathrm{per}}\left(s\right)\mathrm{\&Sigma;}(A_i,B_i{C}_{2i},D_{2i})\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&beta;},i=1\&CenterDot;\&CenterDot;\&CenterDot;N,---\left(21\right)$

W wherein _Per(s) be the performance index weighting function, the symbol ∑ (A, B, C, D) expression is made the state-space model of matrix of the coefficients by A, B, C, D, so:

$\frac{{\left|\right|W_{\mathrm{per}}\left(s\right)q\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|a_{\mathrm{des}}\left|\right|}_2^{\mathrm{\&delta;}}}<\frac{\mathrm{\&beta;}}{1-\mathrm{\&eta;\&gamma;}},---\left(22\right)$

The acceleration tracking error q that is the acceleration control system among the present invention is to expectation acceleration a _DesThe disturbance that causes has certain inhibition ability, thereby guarantees certain tracking performance.In addition, if signal a _DesBounded can be known also bounded of acceleration tracking error q according to (22), thus also bounded (Feng Chunbai is etc. the design of, robust control system, Nanjing: Southeast China University, nineteen ninety-five the 1st edition) of the acceleration signal a of automobile.

Based on the switching signal of switch logic output, select the coefficient matrix of element in the numbering controller set consistent that controlled quentity controlled variable is calculated with σ.

The flow chart of this method is as shown in Figure 4; Need to prove; In this method; Only used controller set and estimator that the model set according to controlled device designs, and need be, needed only according to design result the matrix of the coefficients of controller and estimator is carried out initialization at plant model and the CONTROLLER DESIGN and the estimator all set up in service of each flow process.Method flow is following:

2) initialization:

The parameter of vehicle parameter and automobile running environment;

δ: the exponential decay coefficient, its scope is: 0.1～1;

U: Acceleration Control amount, its initial value are 0;

With the corresponding controller state matrix A of element in the set of the controlled device property taken advantage of ambiguous model _Ci, B _Ci, C _Ci, D _Ci

With the corresponding estimator state matrix A of element in the set of the controlled device property taken advantage of ambiguous model _E1, B _E1, A _E2, B _E2, C _E1i, D _E1i, C _E2i, D _E2i

x _E1And x _E2For with the controlled device property taken advantage of ambiguous model set in the corresponding estimator state of element, its initial value is 0;

x _CFor with the controlled device property taken advantage of ambiguous model set in the corresponding controller state of element, its initial value is 0;

2) gather pickup a, expectation pickup a _Des

3) matrix of the coefficients according to the estimator of the property the taken advantage of ambiguous model of controlled device set design calculates evaluated error e _iWith uncertain part input z _i:

${\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">E</figure-callout>}1}=A_{E1}{\mathrm{<figure-callout\; id="1"\; label="x\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">x</figure-callout>}}_E+B_{E1}u,{\stackrel{\&CenterDot;}{x}}_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}=A_{E2}{\mathrm{<figure-callout\; id="2"\; label="x\; E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">x</figure-callout>}}_E+B_{E2}u,$

e _i＝C _E1ix _E1+D _E1iu-a，z _i＝C _E2ix _E2+D _E2iu，i＝1…N，

Wherein N is the number of element in the set of the controlled device property taken advantage of ambiguous model;

4) employing formula $J_i\left(t\right)=\frac{{\left|\right|e_i\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|z_i\left|\right|}_2^{\mathrm{\&delta;}}},$ I=1 ... N calculates the switching index of N model in the set of the property taken advantage of ambiguous model:

Can adopt the L of the method signal calculated shown in (15) formula during Practical Calculation _{2 δ}Norm.

5) above-mentioned N switches index and controller set $C=\{K_i:\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ci}}{x}_C+B_{\mathrm{Ci}}(a_{\mathrm{Des}}-a)\\ u=C_{\mathrm{Ci}}{x}_C+D_{\mathrm{Ci}}(a_{\mathrm{Des}}-a)\end{array},i=1\&CenterDot;\&CenterDot;\&CenterDot;N\}$ In N element corresponding one by one according to the order of i, select above-mentioned N switching index J that switches minimum in the index _k(t) the controller compute control amount u of correspondence:

$C=\{K_{\mathrm{\&sigma;}}:\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ck}}{x}_C+B_{\mathrm{Ck}}(a_{\mathrm{des}}-a)\\ u=C_{\mathrm{Ck}}{x}_C+D_{\mathrm{Ck}}(a_{\mathrm{des}}-a)\end{array}\}$

6) calculate throttle according to contrary automobile longitudinal dynamic model:

$T_{\mathrm{edes}}=\frac{r}{R_d{R}_{\mathrm{<figure-callout\; id="0"\; label="g"\; filenames="S06189496X20060717E000013.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">g</figure-callout>}0}{\mathrm{\&eta;}}_0}(M_{0}u+{\mathrm{<figure-callout\; id="2"\; label="C\; D\; Av"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">C</figure-callout>}}_D{\mathrm{Av}}^{}{}^2+M_{0}g{f}_0)$

θ＝MAP ^-1(T _edes，ω _e)

The parameter that wherein comprises following vehicle parameter and automobile running environment:

V is the speed of a motor vehicle, T _EdesBe the Engine torque of expectation, ω _eBe engine speed, θ is a throttle opening, and r is a radius of wheel, R _dBe main reducing gear speed ratio, R _G0Be the nominal value of transmission gear ratio, η ₀Be the nominal value of transmission system mechanical efficiency, M ₀Be the nominal value of complete vehicle quality, C _DBe coefficient of air resistance, g is a gravity constant, f ₀Be the nominal value of coefficient of rolling resistance, A is a wind-exposuring area; MAP ^-1(■) be the contrary torque characteristics figure of motor;

7) according to the throttle that calculates the motor of automobile is controlled, and controlled quentity controlled variable u value is returned the 2nd) go on foot and proceed to calculate and control.

Specific embodiment:

To domestic Jetta AT type car, the excursion and the nominal value of its relevant parameter are as shown in table 1.

Table 1, the excursion of automobile and enviromental parameter and corresponding nominal value

The contrary torque factor of motor is as shown in Figure 5.

The frequency domain characteristic coverage area that obtains controlled device according to (A) method partly is as shown in Figure 6.Controlled device frequency domain response characteristic coverage area is divided into four parts, obtains the following property taken advantage of ambiguous model set:

$P=\{P_i\left(s\right)=[1+{\mathrm{\&Delta;}}_i{W}_i\left(s\right)]G_i\left(s\right),{\left|\right|{\mathrm{\&Delta;}}_i\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<1,i=1,\&CenterDot;\&CenterDot;\&CenterDot;,4\},---\left(23\right)$

Model error weighting function wherein $W\left(s\right)=\frac{2.1s+2.478}{s+5.1},$ Exponential decay coefficient δ=0.4, the nominal model is as shown in table 2.

Table 2, nominal Model Transfer function

According to model set, the matrix of the coefficients that obtains estimator is:

A _E1＝-3.33， $A_{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">E</figure-callout>}2}=\left[\begin{array}{cc}0& -17\\ 1& -8.43\end{array}\right],$ ${\mathrm{<figure-callout\; id="1"\; label="B\; E"\; filenames="S06189496X20060717E000011.png,S06189496X20060717E000031.png"\; state="\{\{state\}\}">B</figure-callout>}}_E=1,{\mathrm{<figure-callout\; id="2"\; label="B\; E"\; filenames="S06189496X20060717E000031.png,S06189496X20060717E000042.png"\; state="\{\{state\}\}">B</figure-callout>}}_E=\left[\begin{array}{c}1\\ 0\end{array}\right],$ C _E11＝6.2367，C _E12＝3.314，C _E13＝2.3013，C _E14＝1.703，C _E21＝[13.097-94.997]，C _E22＝[6.959-50.479]，C _E23＝[4.833-35.054]，C _E24＝[3.576-25.94]。

(24)

Utilize the element of the controller set C that the LMI toolbox of Matlab calculates to be according to model set P:

$K_1\left(s\right)=\frac{137.14(s+4.9)(s+3.133)}{s(s+41.85)(s+45.7)},$ $K_2\left(s\right)=\frac{233.41(s+4.9)(s+3.133)}{s(s+80.06)(s+21.42)},$

${\mathrm{<figure-callout\; id="3"\; label="K"\; filenames="S06189496X20060717E000031.png"\; state="\{\{state\}\}">K</figure-callout>}}_3=\frac{572.97(s+4.9)(s+3.133)}{s(s+29.63)(s+99.3)},$ $K_4\left(s\right)=\frac{283.35(s+4.9)(s+3.133)}{s(s+54.15)(s+19.89)},---\left(25\right)$

Get the performance index weighting function in the controller set design process $W_{\mathrm{Per}}\left(s\right)=\frac{0.1s+1.1}{s},$ Constant η=β=0.7.The simulation result of automobile longitudinal acceleration tracking control method is as shown in Figure 7.Can find out the whole process that from Fig. 7 (a) except that about 25s and 75s because the impact that car gear shifting causes, actual pickup can be followed the tracks of the expectation acceleration preferably.Wherein dotted line is represented actual pickup a, and solid line is represented the pickup a that expects _DesCan find out that from Fig. 7 (b) along with the variation of automobile longitudinal characteristic, the Different control device can be switched in the feedback loop, explain that the switching target function among the present invention can be estimated the potential performance of controller.(c) and (d) be respectively car speed and throttle opening response curve.

Shown in real vehicle experimental result Fig. 8 of automobile longitudinal acceleration tracking control method.The result shows the variation along with the automobile longitudinal dynamics, and corresponding controller can be switched in the feedback loop.In the whole control process, actual acceleration can be followed the tracks of the expectation acceleration well.

Appendix 1

Explanation by the satisfied controlled system performance index of condition (formula 21) (formula 22) of controller:

Be without loss of generality, suppose that current object can use P _j(s) describe, and the controller that is connected in the feedback loop is K _k(s).Obtain according to object model (5) and estimator equation (13):

e _j＝-Δ _jW _j(s)G _j(s)u，z _j＝W _j(s)G _j(s)u。(26)

Because ${\left|\right|{\mathrm{\&Delta;}}_j\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&gamma;},$ Can obtain:

$J_j\left(t\right)={\left|\right|e_j\left|\right|}_2^{\mathrm{\&delta;}}/{\left|\right|z_j\left|\right|}_2^{\mathrm{\&delta;}}<\mathrm{\&gamma;}.---\left(27\right)$

Switch logic S selects to switch the corresponding controller of the minimum model of index, and according to the front hypothesis, current controller is K _k(s), then have:

$J_k\left(t\right)={\left|\right|e_k\left|\right|}_2^{\mathrm{\&delta;}}/{\left|\right|z_k\left|\right|}_2^{\mathrm{\&delta;}}\&le;J_j\left(t\right)<\mathrm{\&gamma;}.---\left(28\right)$

According to closed-loop system equation (20), can obtain:

z _k＝∑(A _k，B _k，C _1k，D _1k)(a _des+e _k)。(29)

The condition (21) that is satisfied by (28) and controller set has

$\left|\right|e_k\left|\right|<\mathrm{\&gamma;}{\left|\right|z_k\left|\right|}_2^{\mathrm{\&delta;}}\&le;\mathrm{\&gamma;\&eta;}\left|\right|a_{\mathrm{des}}+e_k\left|\right|.---\left(30\right)$

By e _k=a _Des+ e _k-a _Des, utilize triangle inequality to obtain again:

$\left|\right|a_{\mathrm{des}}+e_k\left|\right|<\frac{1}{1-\mathrm{\&gamma;\&eta;}}{\left|\right|a_{\mathrm{des}}\left|\right|}_2^{\mathrm{\&delta;}}.---\left(31\right)$

On the other hand, can obtain by closed-loop system equation (20):

W _per(s)q＝W _per(s)∑(A _k，B _k，C _2k，D _2k)(a _des+e _k)。(32)

The condition (21) that is satisfied by the controller set has

${\left|\right|W_{\mathrm{per}}\left(s\right)q\left|\right|}_2^{\mathrm{\&delta;}}\&le;\mathrm{\&beta;}{\left|\right|a_{\mathrm{des}}+e_k\left|\right|}_2^{\mathrm{\&delta;}}.---\left(33\right)$

(31) substitution (33) can be obtained inequality:

$\frac{{\left|\right|W_{\mathrm{per}}\left(s\right)q\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|a_{\mathrm{des}}\left|\right|}_2^{\mathrm{\&delta;}}}\&le;\frac{\mathrm{\&beta;}}{1-\mathrm{\&gamma;\&eta;}}.---\left(34\right)$

Claims (2)

1. automobile longitudinal acceleration tracking control method; It is characterized in that; It is the estimator that utilizes the property the taken advantage of ambiguous model of the controlled device of being made up of the reverse of automobile and the positive power model element in gathering to design; Model error between each model and the practical object is estimated the system gain of current input signal, and with this system gain of estimating to obtain as switching target function, from the controller set that designs according to the element the said property the taken advantage of ambiguous model set, select corresponding controller online; The engine air throttle aperture is controlled, realized the tracking Control of automobile longitudinal acceleration;

This method contains the following steps of in entire car controller, carrying out:

1) initialization:

The parameter of vehicle parameter and automobile running environment;

δ: the exponential decay coefficient, its scope is: 0.1～1;

U: Acceleration Control amount, its initial value are 0;

With the corresponding estimator set of element in the set of the controlled device property taken advantage of ambiguous model be:

${\stackrel{\&CenterDot;}{x}}_{E1}=A_{E1}{x}_{E1}+B_{E1}u,$ ${\stackrel{\&CenterDot;}{x}}_{E2}=A_{E2}{x}_{E2}+B_{E2}u,$

e _i＝a _i-a＝C _E1ix _E1+D _E1iu-a，z _i＝C _E2ix _E2+D _E2iu，i＝1…N，

In the formula (13), x _E1And x _E2For with the controlled device property taken advantage of ambiguous model set in the corresponding estimator state of element, its initial value is 0; N is the controller number, A _E1, B _E1, A _E2, B _E2, C _E1i, D _Eli, C _E2i, D _E2iIt is the state matrix of estimator;

With the corresponding controller set C of element in the set of the controlled device property taken advantage of ambiguous model be:

$C=\left\{\begin{array}{c}{K}_i:\end{array}\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ci}}{x}_C+B_{\mathrm{Ci}}(a_{\mathrm{des}}-a)\\ u=C_{\mathrm{Ci}}{x}_C+D_{\mathrm{Ci}}(a_{\mathrm{des}}-a)\end{array},i=1\&CenterDot;\&CenterDot;\&CenterDot;N\right\}$

In the formula (19), K _iBe i the controller of controller set C, x _cBe the state of controller set, its initial value is 0; N is the controller number, A _Ci, B _Ci, C _Ci, D _CiIt is state matrix; Element satisfies among the controller set C:

${\left|\right|\mathrm{\&Sigma;}(A_i,B_i,C_{1i},D_{1i})\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&eta;}<\frac{1}{\mathrm{\&gamma;}},$ ${\left|\right|W_{\mathrm{per}}\left(s\right)\mathrm{\&Sigma;}(A_i,B_i,C_{2i},D_{2i})\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&beta;},$ i＝1…N，

$A_{\mathrm{\&sigma;}}=\left[\begin{array}{ccc}{A}_{E1}-{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E1}{D}_{\mathrm{C\&sigma;}}{C}_{E1\mathrm{\&sigma;}}& 0& {\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E1}{C}_{\mathrm{C\&sigma;}}\\ -{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E2}{D}_{\mathrm{C\&sigma;}}{C}_{E1\mathrm{\&sigma;}}& A_{E2}& {\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{E2}{C}_{\mathrm{C\&sigma;}}\\ -{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{\mathrm{C\&sigma;}}{C}_{E1\mathrm{\&sigma;}}& 0& A_{\mathrm{C\&sigma;}}-{\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}{B}_{\mathrm{C\&sigma;}}{D}_{E1\mathrm{\&sigma;}}{C}_{\mathrm{C\&sigma;}}\end{array}\right],$ $B_{\mathrm{\&sigma;}}={\mathrm{\&Phi;}}_{\mathrm{\&sigma;}}\left[\begin{array}{c}{B}_{E1}{D}_{\mathrm{C\&sigma;}}\\ B_{E2}{D}_{\mathrm{C\&sigma;}}\\ B_{\mathrm{C\&sigma;}}\end{array}\right],$

C _1σ＝[-Φ _σD _E2σD _CσC _E1σ?C _E2σ?Φ _σD _E2σC _Cσ]，D _1σ＝Φ _σD _E2σD _Cσ，

D _2σ＝Φ _σ，C _2σ＝-Φ _σ[C _E1σ?0?D _E1σC _Cσ]；

W wherein _Per(s) be the performance index weighting function, the symbol ∑ (A, B, C, D) expression is satisfied by the state-space model that A, B, C, D do matrix of the coefficients:

$\frac{{\left|\right|W_{\mathrm{per}}\left(s\right)q\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|a_{\mathrm{des}}\left|\right|}_2^{\mathrm{\&delta;}}}<\frac{\mathrm{\&beta;}}{1-\mathrm{\&eta;\&gamma;}};$

2) gather pickup a, expectation pickup a _Des

3) matrix of the coefficients according to the estimator of the property the taken advantage of ambiguous model of controlled device set design calculates evaluated error e _iReally part is not imported z _i

${\stackrel{\&CenterDot;}{x}}_{E1}=A_{E1}{x}_{E1}+B_{E1}u,$ ${\stackrel{\&CenterDot;}{x}}_{E2}=A_{E2}{x}_{E2}+B_{E2}u,$

e _i＝C _E1ix _E1+D _E1iu-a，z _i＝C _E2ix _E2+D _E2iu，i＝1…N， (1)

Wherein N is the number of element in the set of the controlled device property taken advantage of ambiguous model;

4) the switching index of N model in the set of the employing computes property taken advantage of ambiguous model:

$J_i\left(t\right)=\frac{{\left|\right|e_i\left|\right|}_2^{\mathrm{\&delta;}}}{{\left|\right|z_i\left|\right|}_2^{\mathrm{\&delta;}}},i=1\&CenterDot;\&CenterDot;\&CenterDot;N---\left(2\right)$

5) above-mentioned N switches index and controller set $C=\left\{\begin{array}{c}{K}_i:\end{array}\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ci}}{x}_C+B_{\mathrm{Ci}}(a_{\mathrm{Des}}-a)\\ u=C_{\mathrm{Ci}}{x}_C+D_{\mathrm{Ci}}(a_{\mathrm{Des}}-a)\end{array},i=1\&CenterDot;\&CenterDot;\&CenterDot;N\right\}$ In N element

Order according to i is corresponding one by one, selects above-mentioned N to switch switching index J minimum in the index _k(t) the controller compute control amount u of correspondence:

$C=\left\{\begin{array}{c}{K}_{\mathrm{\&sigma;}}\end{array}:\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_C=A_{\mathrm{Ck}}{x}_C+B_{\mathrm{Ck}}(a_{\mathrm{des}}-a)\\ u=C_{\mathrm{Ck}}{x}_C+D_{\mathrm{Ck}}(a_{\mathrm{des}}-a)\end{array}\right\}$

6) calculate throttle according to contrary automobile longitudinal dynamic model:

$T_{\mathrm{edes}}=\frac{r}{R_d{R}_{g0}{\mathrm{\&eta;}}_0}(M_{0}u+C_D{\mathrm{Av}}^2+M_0{\mathrm{gf}}_0)$

θ＝MAP ^-1(T _edes，ω _e) (3)

The parameter that wherein comprises following vehicle parameter and automobile running environment:

V is the speed of a motor vehicle, T _EdesBe the Engine torque of expectation, ω _eBe engine speed, θ is a throttle opening, and r is a radius of wheel, R _dBe main reducing gear speed ratio, R _G0Be the nominal value of transmission gear ratio, η ₀Be the nominal value of transmission system mechanical efficiency, M ₀Be the nominal value of complete vehicle quality, C _DBe coefficient of air resistance, g is a gravity constant, f ₀Be the nominal value of coefficient of rolling resistance, A is a wind-exposuring area; MAP ^-1(■) be the contrary torque characteristics figure of motor;

7) throttle that obtains according to aforementioned calculation is controlled the motor of automobile, and controlled quentity controlled variable u value is returned the 2nd) go on foot and proceed to calculate and control.

2. automobile longitudinal acceleration tracking control method as claimed in claim 1 is characterized in that, the constitution step of the property the taken advantage of ambiguous model set of said controlled device is:

The first step: the possible excursion of vehicle and enviromental parameter is separated into limited parameter point, is made as M; Utilize the method for process identification to utilize the inputoutput data identification to obtain the model of controlled device at each parameter point, can obtain M transfer function so altogether, H _i(s), i=1...M;

Second step: adopt M transfer function on frequency domain, to cover certain zone, the number according to intending the nominal model that adopts is made as N, and this zone leveling is divided into the N piece, is expressed as Ω _i, i=1...N, the transfer function of selecting every regional center obtains N nominal model G as the nominal model _i(s), i=1...N;

The 3rd step: to each zone that obtains in the first step, utilize computes should the zone in the model error of all transfer functions nominal model corresponding with this zone:

$\mathrm{\&Delta;}{H}_i\left(s\right)=\frac{H_i\left(s\right)-G_j\left(s\right)}{G_j\left(s\right)},\&ForAll;H_i\left(s\right)\&Element;{\mathrm{\&Omega;}}_j,---\left(3\right)$

According to the model error that calculates, choose model error weighting function W _i(s) on all frequencies, satisfy

$\left|W_j(s-0.5\mathrm{\&delta;})\right|>\frac{1}{\mathrm{\&gamma;}}\left|{\mathrm{\&Delta;H}}_i(s-0.5\mathrm{\&delta;})\right|,\&ForAll;H_i\left(s\right)\&Element;{\mathrm{\&Omega;}}_j,---\left(4\right)$

Wherein δ is the exponential decay coefficient, is a constant; Symbol | | the amplitude of expression transfer function so just obtains describing regional Ω _jThe property taken advantage of uncertainty models:

$P=\{P_i\left(s\right)=[1+{\mathrm{\&Delta;}}_i{W}_i\left(s\right)]G_i\left(s\right),{\left|\right|{\mathrm{\&Delta;}}_i\left|\right|}_{\&infin;}^{\mathrm{\&delta;}}<\mathrm{\&gamma;},i=1,\&CenterDot;\&CenterDot;\&CenterDot;,N\}---\left(5\right)$

Wherein γ is the upper limit of plant model error; W _i(s) be to have the polynomial model error weighting function of same characteristic features; G _i(s) be to have the polynomial nominal model of same characteristic features; Δ _iBe the uncertain part of the model of controlled device; Its size is guaranteed by (4); N is the number of model in the model set; Symbol || || _∞ ^δThe L of expression system _{2 δ}Gain.

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