CN106438593A - Method for electro-hydraulic servo control under conditions of parameter uncertainty and load disturbance as well as mechanical arm - Google Patents

Abstract

The invention provides a method for electro-hydraulic servo control under conditions of parameter uncertainty and load disturbance as well as a mechanical arm. According to the method, a mathematic model of an asymmetric electro-hydraulic servo actuator is converted into a strict-feedback nonlinear model at first; hydraulic uncertainty parameters in the model are estimated by adopting a parameter adaptive estimation rule; external load dynamic disturbance is online estimated by adopting a high-gain observer; in order to avoid a differential blast effect generated by the virtual control quantity in a backstepping control rule, a first-order dynamic surface design technology is adopted, and then acute changes in the virtual control variable during backstepping iteration are inhibited; and meanwhile, a system energy function is created by adopting a barrier-based Lyapunov function, and the final backstepping control rule is designed, so that an output displacement tracking error as well as pressure in a rodless cavity and a rod cavity of a hydraulic cylinder can be restrained within preset index boundaries, and the dynamic control performance of joint motion of the 2-DOF mechanical arm can be improved.

Description

A kind of electro-hydraulic servo control method that there is parameter uncertainty and load disturbance and machine Tool arm

Technical field

The present invention relates to a kind of control method that can be used for asymmetrical cylinder actuator, especially while there is hydraulic pressure In the case of parameter uncertainty and outer load disturbance, the state constraint of electro-hydraulic servo actuator controls.

Background technology

Consider the uncertain and outer load dynamic disturbance of hydraulic parameter in electrohydraulic servo-controlling system simultaneously, and to electricity Fluid servo system state and system export into row constraint.The interference observer of this patent adoption rate integrated form is adaptive with parameter Should estimate that restrain the method combining estimates unknown hydraulic parameter and outer load disturbance, using based on obstacle Li Yapu love letter simultaneously The backstepping control method of number and dynamic surface control technology realize about asymmetrical cylinder cavity pressure constraint and hydraulic cylinder displacement with , it is ensured that system mode convergence, parameter estimation and outer load estimation convergence simultaneously, dynamic surface is stable, and hydraulic pressure is dynamic for track error constraints Response performance is good, thus driving the joint motions of mechanical arm.

Content of the invention

The purpose of the present invention is to overcome the shortcomings of current electro-hydraulic servo control method not knowing it is adaptable to there is hydraulic parameter Property and outer load disturbance in the case of electro-hydraulic servo actuator state constraint control, can prevent from controlling saturation, and improve electro-hydraulic The performance of dynamic tracking of servo-control system.

The technical scheme is that a kind of electro-hydraulic servo control method that there is parameter uncertainty and load disturbance, should Method includes：

Step 1：Set up Asymmetric Electric hydraulic servo actuator model；

Asymmetric Electric hydraulic servo actuator model is：

Y=x₁

Wherein

Y hydraulic cylinder output displacement,For output displacement rate of change, p_aAnd p_b For asymmetrical cylinder rodless cavity and rod chamber pressure, x_vFor valve core of servo valve displacement, m is load quality, p_sFor charge oil pressure, A_aAnd A_bFor the cross-sectional area of asymmetrical cylinder rodless cavity and rod chamber, C_tlFor the total leadage coefficient of hydraulic cylinder, V_0aAnd V_0bFor asymmetric Hydraulic cylinder rodless cavity and the original volume of rod chamber, β_eFor hydraulic oil effective volume elastic modelling quantity, C_dFor servo valve discharge coefficient, w For servo valve area gradient, ρ is hydraulic oil density, and K is load stiffness coefficient, and b is hydraulic oil damped coefficient, F_LFor outer load pressure Power, K_svFor servo valve amplification coefficient, T_svFor servo valve first-order kernel time constant, sgn () is sign function, and u is servo valve Control voltage.

Because model (1) contains 1 internal dynamic, therefore define 2 new state variables Simultaneously need to it is as follows that model (1) is converted to Strict-feedback model form：

Wherein θ₁=b, θ₂=β_e, θ₃=β_eC_tl,For 4 unknown uncertain hydraulic parameters,

f₂₁(x₁)=- Kx₁/m f₂₂(x₂)=- x₂/m

g₂=A_a/ m d (t)=- F_L(t)/m

f₃₁(x₁,x₂)=- (h₁A_a+h₂A_bυ)x₂/β_e

f₃₂(x₁,x₃,x₄)=- (x₃-x₄)(h₁+h₂)/β_e

g₄=K_sv/T_sv

Wherein υ represents the ratio of hydraulic cylinder rodless cavity and rod chamber area, υ=A_b/A_a.

Step 2：Drive electro-hydraulic servo, obtain the feedback data of electro-hydraulic servo in real time：Hydraulic cylinder output displacement, hydraulic cylinder are defeated Go out pressure, the valve core of servo valve displacement of change in displacement rate, hydraulic cylinder rodless cavity and rod chamber；

Step 3：Estimated using the external load disturbance of high-gain interference observer；

Step 4：Estimate that restraining normal parameter unknown to hydraulic pressure estimates using parameter adaptive；

Step 5：Virtual controlling variable in Reverse Step Control is calculated using dynamic surface control；

Step 6：Based on obstacle Li Yapu love function, and combine feedback data, systematic error and, parameter adaptive estimate Value and load disturbance estimator calculate Reverse Step Control rule；

Step 7：According to Reverse Step Control rule, asymmetric electrohydraudic servomechanism is driven in real time.

Further, in described step 3, the external load disturbance of high-gain interference observer is estimated as follows：

WhereinWithFor load disturbance d and unknown parameter θ₁Estimated value, K_dFor observer gain.

Further, in described step 4, parameter adaptive estimates that rule design is as follows：

First, systematic error z_i(i=1 ..., 4) it is expressed as

Wherein y_dRepresent hydraulic cylinder expectation displacement commands, α_i(i=1,2,3) become for virtual controlling in Reverse Step Control rule design Amount；

Secondly, parameter adaptive estimates that rule is expressed as：

WhereinFor the estimated value of 4 unknown hydraulic parameters,ForInitial value, k_θi(i= 1 ..., 4) rule gain, η are estimated for parameter adaptive_i(i=1 ..., 4) is the normal number setting,

k_a1And k_b1For systematic error z₃Left and right restrained boundary.

Further, in described step 5, Dynamic Surface Design is as follows：

Wherein β_i(i=1 ..., 3) is dynamic surface stability function, τ_i(i=1 ..., 3) it is dynamic surface time constant；

Dynamic surface error is expressed as S_i=α_i-β_i(i=1 ..., 3), virtual controlling amount differential representation isDynamic surface stability function β_i(i=1 ..., 3) it is further represented as：

WhereinRepresent output error z₁Restrained boundary, k_i(i=1,2,3) represents control gain,

Further, in described step 6, the design of Reverse Step Control rule is as follows：

First it is considered to system mode constraints is as follows：

Wherein k_c1For output error z₁Restrained boundary, k_a1And k_b1For systematic error z₃Left and right restrained boundary, be expressed as：

k_a1=(υ+1) p_s-p_r, k_b1=p_s-(υ+1)p_r

Wherein υ represents the ratio of hydraulic cylinder rodless cavity and rod chamber area, p_sExpression system charge oil pressure, p_rExpression system is returned Oil pressure；

Based on obstacle Li Yapu love function, the energy function of constructing system is：

Then state constraint Reverse Step Control rule u is expressed as：

Wherein k₄Represent and control gain,τ_i(i=1 ..., 3) it is dynamic surface time constant.

There is the mechanical arm of the electro-hydraulic servo control method of parameter uncertainty and load disturbance, this mechanical arm in a kind of application Including：3 mechanical linkages, including：First connecting rod, second connecting rod, third connecting rod, 2 electrohydraulic servo valves, 2 double-action hydraulics Cylinder, 1 servomotor, 1 quantitative plunger pump, 1 fuel tank；Wherein hinged between first connecting rod and second connecting rod, at this be called Shoulder joint, second connecting rod is hinged with third connecting rod, is called elbow joint at this；Shoulder joint and elbow joint be respectively provided with one electro-hydraulic Servo valve and double acting hydraulic cylinder；Whole mechanical arm arranges 1 servomotor, 1 quantitative plunger pump and 1 fuel tank；Second even It is respectively provided with a photoelectric encoder, for measuring movement angle and the angular velocity in two joints on bar and third connecting rod；At two Hydraulic cylinder oil inlet and oil-out respectively arrange 1 pressure transducer, and the carrying of measurement hydraulic cylinder, in quantitative plunger pump discharge peace Fill 1 pressure gauge, the charge oil pressure of monitoring system.

The third object of the present invention is to propose state based on obstacle Leah Pu Luofu function and Dynamic Surface Design technology about Beam control method, estimates rule in conjunction with high-gain load disturbance observer and parameter adaptive, can be to 4 uncertain ginsengs of hydraulic pressure Number is estimated, the outer load disturbance of time-varying can also be estimated simultaneously, and evaded to anti-using Dynamic Surface Design Virtual controlling amount in step control law carries out direct differentiation resolving, prevents differential explosion phenomenon, and output displacement is followed the tracks of by mistake The pressure confines of difference and hydraulic cylinder rodless cavity and rod chamber, within predetermined index border, improve the dynamic of electrohydraulic servo system State property energy.

Brief description

Fig. 1 be the present invention using have that hydraulic parameter is uncertain and load disturbance in the case of electro-hydraulic servo actuator shape The two degrees of freedom mechanical arm mechanism schematic diagram of modal constraint control method；

Fig. 2 have that hydraulic parameter is uncertain for one kind of the present invention and load disturbance in the case of electro-hydraulic servo actuator state About beam control method conceptual scheme.

Specific embodiment

There is electro-hydraulic servo actuator in the case of hydraulic parameter uncertainty and load disturbance in one kind of the present invention presented below State constraint controls the concrete real-time mode driving two degrees of freedom mechanical arm.

The model of Asymmetric Electric hydraulic servo actuator is 5 order mode types, does not consider the model of mechanical arm mechanism motion, mechanical arm Joint moment required for motion considers as the load disturbance of electro-hydraulic servo actuator, is summarized as follows：

1) Asymmetric Electric hydraulic servo actuator model electro-hydraulic servo actuator modeling

The electro-hydraulic servo actuator model describing servo valve driving hydraulic cylinder loop using five order mode types is as follows：

Y=x₁

Wherein

x_i(i=1 ..., 4) is model state variable,Y hydraulic cylinder exports Displacement,For output displacement rate of change, p_aAnd p_bFor asymmetrical cylinder rodless cavity and rod chamber pressure, x_vFor valve core of servo valve Displacement, m is load quality, p_sFor charge oil pressure, A_aAnd A_bFor the cross-sectional area of asymmetrical cylinder rodless cavity and rod chamber, C_tlFor liquid The total leadage coefficient of cylinder pressure, V_0aAnd V_0bFor the original volume of asymmetrical cylinder rodless cavity and rod chamber, β_eFor the effective body of hydraulic oil Long-pending elastic modelling quantity, C_dFor servo valve discharge coefficient, w is servo valve area gradient, and ρ is hydraulic oil density, and K is load stiffness system Number, b is hydraulic oil damped coefficient, F_LFor outer load pressure, K_svFor servo valve amplification coefficient, T_svFor the servo valve first-order kernel time Constant, sgn () is sign function, and u is servo valve control voltage.

Because model (1) contains 1 internal dynamic, therefore define 2 new state variables Simultaneously need to it is as follows that model (1) is converted to Strict-feedback model form：

Wherein θ₁=b, θ₂=β_e, θ₃=β_eC_tl,For 4 unknown uncertain hydraulic parameters,

f₃₁(x₁,x₂)=- (h₁A_a+h₂A_bα)x₂/β_e

f₃₂(x₁,x₃,x₄)=- (x₃-x₄)(h₁+h₂)/β_e

2) high-gain load disturbance observer is expressed as：

WhereinWithFor load disturbance d and unknown parameter θ₁Estimated value, K_dFor observer gain.

3) parameter adaptive estimates that rule is expressed as：

WhereinFor the estimated value of 4 unknown hydraulic parameters,ForInitial value, k_θi(i= 1 ..., 4) rule gain, η are estimated for parameter adaptive_i(i=1 ..., 4) is the normal number setting,

Systematic error z_i(i=1 ..., 4) it is expressed as

Wherein y_dRepresent hydraulic cylinder expectation displacement commands, α_i(i=1,2,3) become for virtual controlling in Reverse Step Control rule design Amount.

4) virtual controlling variable α_iThe Dynamic Surface Design of (i=1 ..., 3) is as follows：

Wherein β_i(i=1 ..., 3) is dynamic surface stability function, τ_i(i=1 ..., 3) it is dynamic surface time constant.

Dynamic surface error is expressed as S_i=α_i-β_i(i=1 ..., 3), virtual controlling amount differential representation isDynamic surface stability function β_i(i=1 ..., 3) it is further represented as：

5) the state constraint Reverse Step Control rule u based on obstacle Li Yapu love function is expressed as：

Claims (6)

1. a kind of electro-hydraulic servo control method that there is parameter uncertainty and load disturbance, the method includes：

Step 1：Set up Asymmetric Electric hydraulic servo actuator model；

Asymmetric Electric hydraulic servo actuator model is：

$\begin{array}{c}\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=\left(x_3{A}_a-x_4{A}_b-{\mathrm{Kx}}_1-{\mathrm{bx}}_2-F_L\right)/m\\ {\stackrel{\·}{x}}_3=h_1\left(-A_a{x}_2-C_{tl}\left(x_3-x_4\right)\right)\\ +h_1{C}_d{\mathrm{wx}}_5\sqrt{\frac{2}{\mathrm{\ρ}}}\left(s_1\sqrt{p_s-x_3}+s_2\sqrt{x_3-p_r}\right)\\ {\stackrel{\·}{x}}_4=h_2\left(A_b{x}_2+C_{tl}\left(x_3-x_4\right)\right)\\ -h_2{C}_d{\mathrm{wx}}_5\sqrt{\frac{2}{\mathrm{\ρ}}}\left(s_1\sqrt{x_4-p_r}-s_2\sqrt{p_s-x_4}\right)\\ {\stackrel{\·}{x}}_5=-x_5/T_{sv}+K_{sv}u/T_{sv}\end{array}\right.\\ y=x_1\end{array}---\left(1\right)$

Wherein

$\begin{array}{cc}{h}_1=\frac{{\mathrm{\β}}_e}{V_{0a}+A_a{x}_1}& h_2=\frac{{\mathrm{\β}}_e}{V_{0b}-A_b{x}_1}\\ s_1=\frac{1+\mathrm{sgn}\left(x_5\right)}{2}& s_2=\frac{1-\mathrm{sgn}\left(x_5\right)}{2}\end{array}$

Y hydraulic cylinder output displacement,For output displacement rate of change, p_aAnd p_bFor non- Symmetrical hydraulic cylinder rodless cavity and rod chamber pressure, x_vFor valve core of servo valve displacement, m is load quality, p_sFor charge oil pressure, A_aWith A_bFor the cross-sectional area of asymmetrical cylinder rodless cavity and rod chamber, C_tlFor the total leadage coefficient of hydraulic cylinder, V_0aAnd V_0bFor asymmetric hydraulic pressure Cylinder rodless cavity and the original volume of rod chamber, β_eFor hydraulic oil effective volume elastic modelling quantity, C_dFor servo valve discharge coefficient, w is to watch Take valve face and amass gradient, ρ is hydraulic oil density, K is load stiffness coefficient, b is hydraulic oil damped coefficient, F_LFor outer load pressure, K_svFor servo valve amplification coefficient, T_svFor servo valve first-order kernel time constant, sgn () is sign function, and u is servo valve control Voltage processed.

Because model (1) contains 1 internal dynamic, therefore define 2 new state variables Simultaneously need to it is as follows that model (1) is converted to Strict-feedback model form：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=f_{21}\left(x_1\right)+{\mathrm{\θ}}_1{f}_{22}\left(x_2\right)+g_2{\stackrel{\‾}{x}}_3+d\left(t\right)\\ {\stackrel{\·}{\stackrel{\‾}{x}}}_3={\mathrm{\θ}}_2{f}_{31}(x_1,x_2)+{\mathrm{\θ}}_3{f}_{32}\left(x_1,x_3,x_4\right)+{\mathrm{\θ}}_4{g}_3\left(x_1,x_3,x_4\right){\stackrel{\‾}{x}}_4\\ {\stackrel{\·}{\stackrel{\‾}{x}}}_4=f_4\left({\stackrel{\‾}{x}}_4\right)+g_{4}u\end{array}\right.---\left(2\right)$ Wherein θ₁=b, θ₂= β_e, θ₃=β_eC_tl,For 4 unknown uncertain hydraulic parameters,

f₂₁(x₁)=- Kx₁/m f₂₂(x₂)=- x₂/m

g₂=A_a/ m d (t)=- F_L(t)/m

f₃₁(x₁,x₂)=- (h₁A_a+h₂A_bυ)x₂/β_e

f₃₂(x₁,x₃,x₄)=- (x₃-x₄)(h₁+h₂)/β_e

$g_3(x_1,x_3,x_4)={\stackrel{\‾}{s}}_1(h_1\sqrt{p_s-x_3}+{\mathrm{\υh}}_2\sqrt{x_4-p_r})/{\mathrm{\β}}_e+{\stackrel{\‾}{s}}_2(h_1\sqrt{x_3-p_r}+{\mathrm{\υh}}_2\sqrt{p_s-x_4})/{\mathrm{\β}}_e$

$\begin{array}{cc}{f}_4\left({\stackrel{\‾}{x}}_4\right)=-{\stackrel{\‾}{x}}_4/T_{sv}& g_4=K_{sv}/T_{sv}\end{array}$

$\begin{array}{cc}{\stackrel{\‾}{s}}_1=\frac{1+\tanh \left(k{\stackrel{\‾}{x}}_4\right)}{2}& {\stackrel{\‾}{s}}_2=\frac{1-\tanh \left(k{\stackrel{\‾}{x}}_4\right)}{2}\end{array}$

Wherein υ represents the ratio of hydraulic cylinder rodless cavity and rod chamber area, υ=A_b/A_a.

Step 2：Drive electro-hydraulic servo, obtain the feedback data of electro-hydraulic servo in real time：Hydraulic cylinder output displacement, hydraulic cylinder carry-out bit Move pressure, the valve core of servo valve displacement of rate of change, hydraulic cylinder rodless cavity and rod chamber；

Step 3：Estimated using the external load disturbance of high-gain interference observer；

Step 4：Estimate that restraining normal parameter unknown to hydraulic pressure estimates using parameter adaptive；

Step 5：Virtual controlling variable in Reverse Step Control is calculated using dynamic surface control；

Step 6：Based on obstacle Li Yapu love function, and combine feedback data, systematic error and, parameter adaptive estimated value and Load disturbance estimator calculates Reverse Step Control rule；

Step 7：According to Reverse Step Control rule, asymmetric electrohydraudic servomechanism is driven in real time.

2. a kind of electro-hydraulic servo control method that there is parameter uncertainty and load disturbance as claimed in claim 1, it is special Levy and be that in described step 3, the external load disturbance of high-gain interference observer is estimated as follows：

$\stackrel{\·}{\hat{d}}=K_d({\stackrel{\·}{x}}_2-f_{21}(x_1)-{\widehat{\mathrm{\θ}}}_1{f}_{22}(x_2)-g_2{\stackrel{\‾}{x}}_3-\hat{d})---\left(3\right)$

WhereinWithFor load disturbance d and unknown parameter θ₁Estimated value, K_dFor observer gain.

3. a kind of electro-hydraulic servo control method that there is parameter uncertainty and load disturbance as claimed in claim 1, it is special Levy and be that in described step 4, parameter adaptive estimates that rule design is as follows：

First, systematic error z_i(i=1 ..., 4) it is expressed as

$\left\{\begin{array}{c}{z}_1=x_1-y_d\\ z_2=x_2-{\mathrm{\α}}_1\\ z_i={\stackrel{\‾}{x}}_i-{\mathrm{\α}}_{i-1},i=3,4\end{array}\right.---\left(4\right)$

Wherein y_dRepresent hydraulic cylinder expectation displacement commands, α_i(i=1,2,3) for virtual controlling variable in Reverse Step Control rule design；

Secondly, parameter adaptive estimates that rule is expressed as：

$\left\{\begin{array}{c}{\stackrel{\·}{\widehat{\mathrm{\θ}}}}_1=\[z_2{f}_{22}-{\mathrm{\η}}_1\left({\widehat{\mathrm{\θ}}}_{10}-{\widehat{\mathrm{\θ}}}_1\right)\]/k_{\mathrm{\θ}1}\\ {\stackrel{\·}{\widehat{\mathrm{\θ}}}}_2=\[{\mathrm{\μf}}_{31}{z}_3-{\mathrm{\η}}_2\left({\widehat{\mathrm{\θ}}}_{20}-{\widehat{\mathrm{\θ}}}_2\right)\]/k_{\mathrm{\θ}2}\\ {\stackrel{\·}{\widehat{\mathrm{\θ}}}}_3=\[{\mathrm{\μf}}_{32}{z}_3-{\mathrm{\η}}_3\left({\widehat{\mathrm{\θ}}}_{30}-{\widehat{\mathrm{\θ}}}_3\right)\]/k_{\mathrm{\θ}3}\\ {\stackrel{\·}{\widehat{\mathrm{\θ}}}}_4=\[{\mathrm{\μg}}_3{z}_3{\stackrel{\‾}{x}}_4-{\mathrm{\η}}_4\left({\widehat{\mathrm{\θ}}}_{40}-{\widehat{\mathrm{\θ}}}_4\right)\]/k_{\mathrm{\θ}4}\end{array}\right.,---\left(5\right)$

WhereinFor the estimated value of 4 unknown hydraulic parameters,ForInitial value, k_θi(i=1 ..., 4) rule gain, η are estimated for parameter adaptive_i(i=1 ..., 4) is the normal number setting,

$\mathrm{\μ}=\frac{(1-q(z_3\left)\right)}{k_{a1}^2-z_3^2}+\frac{q\left(z_3\right)}{k_{b1}^2-z_3^2},$

$q\left(z_3\right)=\left\{\begin{array}{cc}1& 0<z_3<k_{b1}\\ 0& -k_{a1}<z_3\&le;0\end{array}\right..$

k_a1And k_b1For systematic error z₃Left and right restrained boundary.

4. a kind of electro-hydraulic servo control method that there is parameter uncertainty and load disturbance as claimed in claim 1, it is special Levy and be that in described step 5, Dynamic Surface Design is as follows：

${\mathrm{\&tau;}}_i{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_i+{\mathrm{\&alpha;}}_i={\mathrm{\&beta;}}_i,{\mathrm{\&alpha;}}_i\left(0\right)={\mathrm{\&beta;}}_i\left(0\right)---\left(6\right)$

Wherein β_i(i=1 ..., 3) is dynamic surface stability function, τ_i(i=1 ..., 3) it is dynamic surface time constant；

Dynamic surface error is expressed as S_i=α_i-β_i(i=1 ..., 3), virtual controlling amount differential representation isDynamic surface stability function β_i(i=1 ..., 3) it is further represented as：

$\left\{\begin{array}{c}{\mathrm{\&beta;}}_1=-(k_{c_1}^2-z_1^2)k_1{z}_1+{\stackrel{\&CenterDot;}{y}}_d\\ {\mathrm{\&beta;}}_2=-\frac{1}{g_2}(k_2{z}_2+\frac{z_1}{k_{c_1}^2-z_1^2}+f_{21}+{\widehat{\mathrm{\&theta;}}}_1{f}_{22}+\hat{d}+S_1/{\mathrm{\&tau;}}_1)\\ {\mathrm{\&beta;}}_3=-\frac{1}{{\widehat{\mathrm{\&theta;}}}_4{g}_3}(\frac{g_2{z}_2}{\mathrm{\&mu;}}+{\widehat{\mathrm{\&theta;}}}_2{f}_{31}+{\widehat{\mathrm{\&theta;}}}_3{f}_{32}+S_2/{\mathrm{\&tau;}}_2+k_3\mathrm{\&phi;}(z_3,k_{a1},k_{b1}\left)\right)z_3\end{array}\right.---\left(7\right)$

WhereinRepresent output error z₁Restrained boundary, k_i(i=1,2,3) represents control gain,

5. a kind of electro-hydraulic servo control method that there is parameter uncertainty and load disturbance as claimed in claim 1, it is special Levy and be that in described step 6, the design of Reverse Step Control rule is as follows：

First it is considered to system mode constraints is as follows：

$\left\{\begin{array}{c}-k_{c1}<z_1=x_1-y_d<k_{c1}\\ -k_{a1}<z_3={\stackrel{\&OverBar;}{x}}_3-{\mathrm{\&alpha;}}_2<k_{b1}\end{array}\right.---\left(8\right)$

Wherein k_c1For output error z₁Restrained boundary, k_a1And k_b1For systematic error z₃Left and right restrained boundary, be expressed as：

k_a1=(υ+1) p_s-p_r, k_b1=p_s-(υ+1)p_r

Wherein υ represents the ratio of hydraulic cylinder rodless cavity and rod chamber area, p_sExpression system charge oil pressure, p_rRepresent system oil return pressure Power；

Based on obstacle Li Yapu love function, the energy function of constructing system is：

$\left\{\begin{array}{c}{V}_1=\frac{1}{2}\ln \frac{k_{c_1}^2}{k_{c_1}^2-z_1^2}+\frac{1}{2}{S}_1^2\\ V_2=V_1+\frac{1}{2}{z}_2^2+\frac{1}{2}{k}_{{\mathrm{\&theta;}}_1}{\widetilde{\mathrm{\&theta;}}}_1^2+\frac{1}{2}{\tilde{d}}^2+\frac{1}{2}{S}_2^2\\ V_3=V_2+\frac{1}{2}\underset{i=2}{\overset{4}{\mathrm{\&Sigma;}}}{k}_{{\mathrm{\&theta;}}_i}{\widetilde{\mathrm{\&theta;}}}_i^2+\frac{1}{2}\left(1-q\left(z_3\right)\right)\ln \frac{k_{a1}^2}{k_{a1}^2-z_3^2}+\frac{1}{2}q\left(z_3\right)\ln \frac{k_{b1}^2}{k_{b1}^2-z_3^2}+\frac{1}{2}{S}_3^2\\ V_4=V_3+\frac{1}{2}{z}_4^2\end{array}\right.---\left(9\right)$

Then state constraint Reverse Step Control rule u is expressed as：

$u=-\frac{1}{g_4}(k_4{z}_4+\mathrm{\&mu;}{\widehat{\mathrm{\&theta;}}}_4{g}_3{z}_3+f_4({\stackrel{\&OverBar;}{x}}_4)+\frac{S_3}{{\mathrm{\&tau;}}_3})---\left(10\right)$

Wherein k₄Represent and control gain,For dynamic surface time constant.

6. there is the mechanical arm of the electro-hydraulic servo control method of parameter uncertainty and load disturbance in a kind of application, this mechanical arm bag Include：3 mechanical linkages, including：First connecting rod, second connecting rod, third connecting rod, 2 electrohydraulic servo valves, 2 double acting hydraulic cylinders, 1 servomotor, 1 quantitative plunger pump, 1 fuel tank；Wherein hinged between first connecting rod and second connecting rod, it is called shoulder joint at this Section, second connecting rod is hinged with third connecting rod, is called elbow joint at this；Shoulder joint and elbow joint are respectively provided with an electro-hydraulic servo Valve and double acting hydraulic cylinder；Whole mechanical arm arranges 1 servomotor, 1 quantitative plunger pump and 1 fuel tank；Second connecting rod with One photoelectric encoder is respectively provided with third connecting rod, for measuring movement angle and the angular velocity in two joints；In two hydraulic pressure Cylinder oil-in and oil-out respectively arrange 1 pressure transducer, the carrying of measurement hydraulic cylinder, install 1 in quantitative plunger pump discharge Individual pressure gauge, the charge oil pressure of monitoring system.