CN105697463A - Self-adaptation control method for output feedback of hydraulic position servo system - Google Patents

Abstract

The invention discloses a self-adaptation control method for the output feedback of a hydraulic position servo system. The self-adaptation control method includes the steps that firstly, a model of the controlled hydraulic position servo system is established, above various variable parameters are obtained through real-time detection of respective detection instruments, friction force is neglected, a three-order linear model of the hydraulic system is obtained, and the output of the model is made to track the required expected output through a control target; secondly, an output feedback self-adaptation controller model of the hydraulic position servo system is established; and thirdly, unknown parameter values of the hydraulic position servo system are estimated, numerical values obtained through the estimation are input into a computer to update parameters of the output feedback self-adaptation controller model in real time, the computer controls the signal output of an amplifier, the displacement of a piston is adjusted in real time, and therefore the operation is completed. By means of the self-adaptation control method, no pressure detection hardware or algorithm needs to be added, and a better tracking effect and the higher control precision can be obtained.

Description

A kind of Hydraulic Position Servo output feedack self-adaptation control method

Technical field

The invention belongs to hydraulic system high precision position tracking control technology field, relate to a kind of Hydraulic Position Servo output feedack self-adaptation control method。

Background technology

Hydraulic system (i.e. Hydraulic Position Servo) is using liquid as working media, it has, and power to volume ratio is big, bearing capacity strong, fast response time, control accuracy are high, inertia is little, speed governing is convenient and safety advantages of higher, and hydraulic technique has been widely used in every field。

But owing to the internal leakage of liquid, liquid are relatively large by the Complex Flows characteristic of valve port, frictional force between hydraulic cylinder and slide block, these factors make the high precision tracking of Hydraulic Position Servo control very difficult。

Summary of the invention

It is an object of the invention to provide a kind of Hydraulic Position Servo output feedack self-adaptation control method, solve prior art to the not high enough problem of the tracing control precision of Hydraulic Position Servo。

The technical solution used in the present invention is, a kind of Hydraulic Position Servo output feedack self-adaptation control method, and the method is embodied as according to following steps:

Step 1, set up the model of Hydraulic Position Servo

The mathematical model of this Hydraulic Position Servo such as following formula (1):

$\left\{\begin{array}{c}{Q}_a=\left\{\begin{array}{c}{C}_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_s-P_a},x_v\&GreaterEqual;0\\ C_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_a-P_r},x_v<0\end{array}\right.\\ Q_b=\left\{\begin{array}{c}{C}_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_b-P_r},x_v\&GreaterEqual;0\\ C_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_s-P_b},x_v<0\end{array}\right.\\ x_v=k_{v}u\\ Q_a-C_t(P_a-P_b)=A_a\stackrel{\&CenterDot;}{y}+\frac{V_a}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_a\\ C_t(P_a-P_b)-Q_b=-A_b\stackrel{\&CenterDot;}{y}+\frac{V_b}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_b\\ P_a{A}_a-P_b{A}_b=M\stackrel{\&CenterDot;\&CenterDot;}{y}+B_p\stackrel{\&CenterDot;}{y}+ky+F_L\end{array}\right.,---\left(1\right)$

Wherein, P_aAnd P_bThe respectively pressure of hydraulic cylinder rodless cavity A and rod chamber B,WithRespectively P_aAnd P_bFirst derivative, P_sAnd P_rRespectively charge oil pressure and return pressure, Q_aAnd Q_bRespectively flow into rodless cavity A and flow out the flow of rod chamber B, A_aAnd A_bFor the piston effective active area at rodless cavity A and rod chamber B, V_aAnd V_bFor the volume of hydraulic cylinder rodless cavity A and rod chamber B, C_dFor discharge coefficient, C_tFor internal leakage coefficient, w is proportioning valve area gradient, x_vFor proportioning valve spool displacement, k_vFor proportioning valve proportionality coefficient, u is control signal, and ρ is fluid density, β_eFor bulk modulus, M is load quality, B_pFor viscous damping coefficient, k is spring loaded coefficient, and y is the displacement of hydraulic cylinder piston, and y is obtained by the detection of displacement detecting instrument,WithThe respectively first derivative of y and second dervative, F_LFor outer carrying,

Introduce load flow Q_LWith load pressure P_LDefinition:

$\left\{\begin{array}{c}{P}_L=P_a-P_b\\ Q_L=\frac{Q_a+Q_b}{2}\end{array}\right.,---\left(2\right)$

Ignore outer carrying F_LAnd the nonlinear load such as Coulomb friction, nonlinear function is carried out linearization process, the mechanism model obtaining this Hydraulic Position Servo is:

$\left\{\begin{array}{c}{Q}_L=K_{xa}{x}_v-K_{pa}{P}_L\\ Q_L=C_t{P}_L+\frac{V}{4{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_L+A_m\stackrel{\&CenterDot;}{y}\\ A_m{P}_L=M\stackrel{\&CenterDot;}{y}+B_p\stackrel{\&CenterDot;}{y}+ky\end{array}\right.,---\left(3\right)$

Wherein, K_xaAnd K_paRespectively flow gain after linearisation and flow pressure coefficient, A_mRepresent the average effective area of hydraulic cylinder,

The state variable defining this Hydraulic Position Servo is:Subscript T therein refers to the transposition of vector,

Then the state equation of this Hydraulic Position Servo is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=-\frac{k}{m}{x}_1-\frac{B_p}{m}{x}_2+\frac{A_m}{m}{x}_3\\ {\stackrel{\&CenterDot;}{x}}_3=-\frac{4\mathrm{\&beta;}e}{V}{A}_m{x}_2-\frac{4B_e}{V}(K_{pa}+C_t)x_3+\frac{4{\mathrm{\&beta;}}_e}{V}{K}_{xa}{K}_{v}u\end{array}\right.,---\left(4\right)$

Three rank linear models of the approximate Hydraulic Position Servo obtained near matching point are as follows:

$\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{y}+{\mathrm{\&alpha;}}_2\stackrel{\&CenterDot;\&CenterDot;}{y}+{\mathrm{\&alpha;}}_1\stackrel{\&CenterDot;}{y}+{\mathrm{\&alpha;}}_{0}y=bu,---\left(5\right)$

WhereinCorrespond to x respectively₁、x₂、x₃First derivative, a₀、a₁、a₂, b be unknown model parameters,For three order derivatives of y, controlling target is make piston displacement y follow the tracks of required desired output y_m；

Step 2, set up the output feedack adaptive controller model of Hydraulic Position Servo

An output feedack adaptive controller is built, its model such as following formula (6) to formula (5):

U '=θ^Tω, (6)

Wherein, u' is the control signal before amplitude limit；θ^TIt is 4 dimensional vectors, θ with ω^TIt is the transposed vector of θ, θ=[k θ₁θ₂θ₀]^T, ω=[y_mω₁ω₂y]^T, ω₁And ω₂Respectively through to input signal y_mObtain with output signal y filtering, namely as shown in formula (7):

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1={\mathrm{\&Lambda;\&omega;}}_1+{\mathrm{hy}}_m\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2={\mathrm{\&Lambda;\&omega;}}_2+hy\end{array}\right.,---\left(7\right)$

Wherein,WithRespectively ω₁And ω₂First derivative, Λ, h are design parameter,

VariableDerivative asked for by Euler's formula, concrete form such as following formula (8):

$\stackrel{\&CenterDot;}{x}\left(k\mathrm{\&Delta;}T\right)=\frac{x\left(\right(k+1\left)\mathrm{\&Delta;}T\right)-x\left(k\mathrm{\&Delta;}T\right)}{\mathrm{\&Delta;}T},---\left(8\right)$

Wherein,It is the first derivative of x (t),RepresentIn the value of k sampling instant, Δ T is the sampling time,

Control signal u is carried out amplitude limit, concrete form such as following formula (9):

$u=\left\{\begin{array}{cc}{U}_{max}& u^{\&prime;}>U_{max}\\ u^{\&prime;}& U_{max}-\&le;u^{\&prime;}<U_{max}\\ -U_{max}& u^{\&prime;}<-U_{max}\end{array}\right.,---\left(9\right)$

Wherein, U_maxAmplitude limit value for control signal u；

Step 3, calculate output feedack adaptive controller model parameter estimated value

Actual hydraulic pressure positional servosystem adopts the transmission function W of formula (5)_p(s) such as following formula:

$W_p\left(s\right)=\frac{b}{s^3+{\mathrm{\&alpha;}}_2{s}^2+{\mathrm{\&alpha;}}_{1}s+{\mathrm{\&alpha;}}_0},---\left(10\right)$

Assuming that transmission function W_mThe reference model of (s) such as following formula:

$W_m\left(s\right)=\frac{b_m}{s^3+{\mathrm{\&alpha;}}_{2m}{s}^2+{\mathrm{\&alpha;}}_{1m}s+{\mathrm{\&alpha;}}_{0m}},---\left(11\right)$

Wherein, b_m、a_2m、a_1m、a_0mParameter for reference model；

Determine the estimated value rule of auto-adaptive parameter, with reference to following formula (12):

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=-\frac{\mathrm{sgn}\left(b\right)\mathrm{\&gamma;}\mathrm{\&epsiv;}\mathrm{\&omega;}}{1+{\underset{\&OverBar;}{\mathrm{\&omega;}}}^T\underset{\&OverBar;}{\mathrm{\&omega;}}}\\ \stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=-\frac{\mathrm{\&gamma;}\mathrm{\&epsiv;}\mathrm{\&eta;}}{1+{\underset{\&OverBar;}{\mathrm{\&omega;}}}^T\underset{\&OverBar;}{\mathrm{\&omega;}}}\end{array}\right.,---\left(12\right)$

Wherein, θ=[k θ₁θ₂θ₀]^T,It it is the first derivative of θ；γ is for regulating parameter；

Sgn (b) is the sign function about b, as b > 0, and sgn (b)=1；As b=0, sgn (b)=0；As b < 0, sgn (b)=-1；

Represent that signal vector ω is W by transmitting function_mOutput signal corresponding to the module of (s),It isTransposed vector；

ε=e+ α η is augmented error, e=y-y_mFor tracking error, y_mBeing input signal, y is output signal,It is the first derivative of α, η=θ^TW_m(ω)-W_m(θ^Tω) for assisted error, W_m(θ^Tω) it is signal vector θ^Tω is W by expecting transmission function_mSignal after the module of (s), θ^TIt is the transposed vector of θ,

First calculate tracking error e, calculate assisted error η again, and then utilized the α value in a upper moment to try to achieve ε, ε is substituted into the θ value trying to achieve current time in the first equation in formula (12), ε is substituted into the α value trying to achieve current time in the second equation in formula (12)

The vectorial θ, i.e. k, θ that estimation is obtained₁、θ₂And θ₀Numerical value for the parameter of real-time update output feedack adaptive controller modular form (6), computer export by the signal of D/A converter, the displacement of the piston of real-time adjustment asymmetrical cylinder。

The inventive method provides the benefit that, design the output feedack adaptive controller based on Hydraulic Position Servo, and it is tracked the Experimental comparison of three kinds of different curves from existing PID controller, experimental result all shows that the inventive method tracking accuracy is higher, specifically include: 1) do not need speed, acceleration and pressure transducer hardware, system simplifies, and controls cost low；2) do not need the accurate parameters of object, just can implement effective control；3) compared with existing PID control method, it is possible to obtain higher control accuracy。

Accompanying drawing explanation

Fig. 1 is the structural representation of the inventive method control object；

Fig. 2 is the controller architecture schematic diagram of the inventive method；

Fig. 3 is the experimental result adopting the inventive method to follow the tracks of S curve；

Fig. 4 is the experimental result adopting the inventive method to follow the tracks of sinusoidal signal；

Fig. 5 is the experimental result adopting the inventive method to follow the tracks of multifrequency sine signal；

Fig. 6 is the experimental result adopting PID approach to follow the tracks of S curve；

Fig. 7 is the experimental result adopting PID approach to follow the tracks of sinusoidal signal；

Fig. 8 is the experimental result adopting PID approach to follow the tracks of multifrequency sine signal。

In figure, 1. piston, 2. load, 3. asymmetrical cylinder, 4. displacement detecting instrument, 5. proportioning valve, 6. computer, 7. air relief valve, 8. oil pump, 9. hydraulic pump fuel reserve tank。

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail。

The Hydraulic Position Servo output feedack self-adaptation control method of the present invention, is embodied as according to following steps:

Step 1, set up the model of Hydraulic Position Servo

With reference to Fig. 1, the structure of the Hydraulic Position Servo of the inventive method (control object) is, including asymmetrical hydraulic cylinder 3, the effective active area of hydraulic cylinder rodless cavity A and rod chamber B is not etc., the effective active area of rodless cavity A is 1.6 times of rod chamber B, piston 1 in hydraulic cylinder 3 is fixing with load 2 to be connected, piston 1 is connected to piston rod, piston rod is correspondingly arranged on displacement detecting instrument 4 on (stretching out the part of cylinder body), the probe of displacement detecting instrument 4 by with plunger rod contacts, detection obtains the displacement information of piston 1, the signal output part of displacement detecting instrument 4 accesses computer 6 by A/D converter；Three position four-way electromagnetic valve selected by proportioning valve 5, the rodless cavity A of hydraulic cylinder 3 can pass through liquid returning end (T-port) UNICOM of the control of valve and the liquid feeding end (P port) of proportioning valve 5 or proportioning valve 5, corresponding, the control of the rod chamber B of hydraulic cylinder 3 passing ratio valve accordingly and liquid returning end or liquid feeding end UNICOM；It addition, the liquid feeding end of proportioning valve 5 (P port) is connected with oil pump 8 by air relief valve 7, the liquid returning end (T-port) of proportioning valve 5 connects with hydraulic pump fuel reserve tank 9；The electromagnetic valve core of proportioning valve 5 is connected with computer 7 with by D/A converter, and when computer 7 exports control signal, this control signal controls proportional valve spool action by D/A converter, it is achieved liquid flowing controls。

Assume that this Hydraulic Position Servo meets following condition:

1) working media (liquid) that system uses is ideal fluid；

2) flow regime when liquid flows through valve port or other restriction is constant entropy adiabatic process；

3) in same cavity volume, fluid pressure and temperature are equal everywhere；

4) leakage not considered is ignored；

5), during piston movement, the change procedure of two intracavity liquids is adiabatic process；

6) hydraulic power source constant pressure；

7) compared with system dynamic characteristic, the inertia of proportioning valve can be ignored,

Obtain the mathematical model such as following formula (1) of this Hydraulic Position Servo accordingly:

$\left\{\begin{array}{c}{Q}_a=\left\{\begin{array}{c}{C}_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_s-P_a},x_v\&GreaterEqual;0\\ C_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_a-P_r},x_v<0\end{array}\right.\\ Q_b=\left\{\begin{array}{c}{C}_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_b-P_r},x_v\&GreaterEqual;0\\ C_{d}w{x}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_s-P_b},x_v<0\end{array}\right.\\ x_v=k_{v}u\\ Q_a-C_t(P_a-P_b)=A_a\stackrel{\&CenterDot;}{y}+\frac{V_a}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_a\\ C_t(P_a-P_b)-Q_b=-A_b\stackrel{\&CenterDot;}{y}+\frac{V_b}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_b\\ P_a{A}_a-P_b{A}_b=M\stackrel{\&CenterDot;\&CenterDot;}{y}+B_p\stackrel{\&CenterDot;}{y}+ky+F_L\end{array}\right.,---\left(1\right)$

Wherein, P_aAnd P_bThe respectively pressure of hydraulic cylinder rodless cavity A and rod chamber B,WithRespectively P_aAnd P_bFirst derivative, P_sAnd P_rRespectively charge oil pressure and return pressure, Q_aAnd Q_bRespectively flow into rodless cavity A and flow out the flow of rod chamber B, A_aAnd A_bFor the piston effective active area at rodless cavity A and rod chamber B, V_aAnd V_bFor the volume of hydraulic cylinder rodless cavity A and rod chamber B, C_dFor discharge coefficient, C_tFor internal leakage coefficient, w is proportioning valve area gradient, x_vFor proportioning valve spool displacement, k_vFor proportioning valve proportionality coefficient, u is control signal, and ρ is fluid density, β_eFor bulk modulus, M is load quality, B_pFor viscous damping coefficient, k is spring loaded coefficient, and y is the displacement of hydraulic cylinder piston, and y is obtained by displacement detecting instrument 4 detection,WithThe respectively first derivative of y and second dervative, F_LFor outer carrying,

Due to asymmetrical cylinder rodless cavity A and rod chamber B effective work area not etc., thus hydraulic cylinder piston is when forward and reverse motion, not etc., various running parameters are not widely different relative to conventional symmetrical structure hydraulic cylinder for system necessary flow, the mathematical model describing working oil path is also significantly different

Therefore, load flow Q it is specifically incorporated_LWith load pressure P_LDefinition:

$\left\{\begin{array}{c}{P}_L=P_a-P_b\\ Q_L=\frac{Q_a+Q_b}{2}\end{array}\right.,---\left(2\right)$

Ignore outer carrying F_LAnd the nonlinear load such as Coulomb friction, nonlinear function is carried out linearization process, the mechanism model obtaining this Hydraulic Position Servo is:

$\left\{\begin{array}{c}{Q}_L=K_{xa}{x}_v-K_{pa}{P}_L\\ Q_L=C_t{P}_L+\frac{V}{4{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_L+A_m\stackrel{\&CenterDot;}{y}\\ A_m{P}_L=M\stackrel{\&CenterDot;}{y}+B_p\stackrel{\&CenterDot;}{y}+ky\end{array}\right.,---\left(3\right)$

Wherein, K_xaAnd K_paRespectively flow gain after linearisation and flow pressure coefficient, A_mRepresent the average effective area of hydraulic cylinder,

The state variable defining this Hydraulic Position Servo is:Subscript T therein refers to the transposition of vector,

Then the state equation of this Hydraulic Position Servo is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=-\frac{k}{m}{x}_1-\frac{B_p}{m}{x}_2+\frac{A_m}{m}{x}_3\\ {\stackrel{\&CenterDot;}{x}}_3=-\frac{4\mathrm{\&beta;}e}{V}{A}_m{x}_2-\frac{4B_e}{V}(K_{pa}+C_t)x_3+\frac{4{\mathrm{\&beta;}}_e}{V}{K}_{xa}{K}_{v}u\end{array}\right.,---\left(4\right)$

Three rank linear models of the approximate Hydraulic Position Servo obtained near matching point are as follows:

$\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{y}+{\mathrm{\&alpha;}}_2\stackrel{\&CenterDot;\&CenterDot;}{y}+{\mathrm{\&alpha;}}_1\stackrel{\&CenterDot;}{y}+{\mathrm{\&alpha;}}_{0}y=bu,---\left(5\right)$

WhereinCorrespond to x respectively₁、x₂、x₃First derivative, a₀、a₁、a₂, b be unknown model parameters,For three order derivatives of y, controlling target is make piston displacement y follow the tracks of required desired output y_m；

Step 2, set up the output feedack adaptive controller model of Hydraulic Position Servo

Such as Fig. 2, it it is the Hydraulic Position Servo output feedack adaptive controller that designs of the present invention。

An output feedack adaptive controller is built, its model such as following formula (6) to formula (5):

U '=θ^Tω, (6)

Wherein, u' is the control signal before amplitude limit；

θ^TIt is 4 dimensional vectors, θ with ω^TIt is the transposed vector of θ, θ=[k θ₁θ₂θ₀]^T,

ω=[y_mω₁ω₂y]^T, ω₁And ω₂Respectively through to input signal y_mObtain with output signal y filtering, namely as shown in formula (7):

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1={\mathrm{\&Lambda;\&omega;}}_1+{\mathrm{hy}}_m\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2={\mathrm{\&Lambda;\&omega;}}_2+hy\end{array}\right.,---\left(7\right)$

Wherein,WithRespectively ω₁And ω₂First derivative, Λ, h are design parameter,

VariableDerivative asked for by Euler's formula, concrete form such as following formula (8):

$\stackrel{\&CenterDot;}{x}\left(k\mathrm{\&Delta;}T\right)=\frac{x\left(\right(k+1\left)\mathrm{\&Delta;}T\right)-x\left(k\mathrm{\&Delta;}T\right)}{\mathrm{\&Delta;}T},---\left(8\right)$

Wherein,It is the first derivative of x (t),

RepresentIn the value of k sampling instant,

Δ T is the sampling time,

Control signal u is carried out amplitude limit, concrete form such as following formula (9):

$u=\left\{\begin{array}{cc}{U}_{max}& u^{\&prime;}>U_{max}\\ u^{\&prime;}& U_{max}-\&le;u^{\&prime;}<U_{max}\\ -U_{max}& u^{\&prime;}<-U_{max}\end{array}\right.,---\left(9\right)$

Wherein, U_maxAmplitude limit value for control signal u；

Step 3, calculate output feedack adaptive controller model parameter estimated value

Actual hydraulic pressure positional servosystem adopts the transmission function W of formula (5)_p(s) such as following formula:

$W_p\left(s\right)=\frac{b}{s^3+{\mathrm{\&alpha;}}_2{s}^2+{\mathrm{\&alpha;}}_{1}s+{\mathrm{\&alpha;}}_0},---\left(10\right)$

Assuming that transmission function W_mThe reference model of (s) such as following formula:

$W_m\left(s\right)=\frac{b_m}{s^3+{\mathrm{\&alpha;}}_{2m}{s}^2+{\mathrm{\&alpha;}}_{1m}s+{\mathrm{\&alpha;}}_{0m}},---\left(11\right)$

Wherein, b_m、a_2m、a_1m、a_0mParameter for reference model；

Determine the estimated value rule of auto-adaptive parameter, with reference to following formula (12):

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=-\frac{\mathrm{sgn}\left(b\right)\mathrm{\&gamma;}\mathrm{\&epsiv;}\mathrm{\&omega;}}{1+{\underset{\&OverBar;}{\mathrm{\&omega;}}}^T\underset{\&OverBar;}{\mathrm{\&omega;}}}\\ \stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=-\frac{\mathrm{\&gamma;}\mathrm{\&epsiv;}\mathrm{\&eta;}}{1+{\underset{\&OverBar;}{\mathrm{\&omega;}}}^T\underset{\&OverBar;}{\mathrm{\&omega;}}}\end{array}\right.,---\left(12\right)$

Wherein, θ=[k θ₁θ₂θ₀]^T,It it is the first derivative of θ；

γ is for regulating parameter；

Sgn (b) is the sign function about b, as b > 0, and sgn (b)=1；As b=0, sgn (b)=0；As b < 0, sgn (b)=-1；

Represent that signal vector ω is W by transmitting function_mOutput signal corresponding to the module of (s),It isTransposed vector；

ε=e+ α η is augmented error, e=y-y_mFor tracking error, y_mBeing input signal, y is output signal,It is the first derivative of α, η=θ^TW_m(ω)-W_m(θ^Tω) for assisted error, W_m(θ^Tω) it is signal vector θ^Tω is W by expecting transmission function_mSignal after the module of (s), θ^TIt is the transposed vector of θ,

First calculate tracking error e, calculate assisted error η again, and then utilized the α value in a upper moment to try to achieve ε, ε is substituted into the θ value trying to achieve current time in the first equation in formula (12), ε is substituted into the α value trying to achieve current time in the second equation in formula (12)

The vectorial θ, i.e. k, θ that estimation is obtained₁、θ₂And θ₀Numerical value for the parameter of real-time update output feedack adaptive controller modular form (6), computer export by the signal of D/A converter, the displacement of the piston of real-time adjustment asymmetrical cylinder,。

Embodiment

In the present embodiment, the product type that the critical piece in Hydraulic Position Servo is selected is:

Asymmetrical cylinder adopts the model of FESTO company to be D:S-HAZ-16-200-LE-SB；

The model that 3-position 4-way proportioning valve adopts is D:H-B-43W-RV-NG6-K；

The model that swept resistance formula linear displacement detecting instrument adopts is D:S-HAZ-16-200-1-SIBU；

The model that universal data collection card adopts is PCI2306；

The model that computer adopts is CPU is P21.2GHz, and the control software design of built-in computer adopts VB establishment, shows the change curve of correlated variables in control process by screen。

The control target of the present embodiment is respectively set to

Reference signal 1:S curve

y_m=-(A/ ω²) sin (ω t)+(A/ ω) t, (13)

The value of A is the value of 55.825, ω is 0.5 π。

Reference signal 2: single frequency sinusoidal signal

y_m=111.65sin0.5 π t, (14)

Reference signal 3: multifrequency sine signal

$\begin{array}{c}{y}_m=167.475\sin \mathrm{\&pi;}t+167.475\sin 0.5\mathrm{\&pi;}t+167.475\sin (2\mathrm{\&pi;}t/7)\\ +167.475\sin (\mathrm{\&pi;}t/6)+167.475\sin (2\mathrm{\&pi;}t/17)\end{array},---\left(15\right)$

Output feedack adaptive controller described in employing formula (7)-Shi (12) is tested, the reference model W in formula (7)-Shi (12)_mS the value of () and filtering parameter Λ, h carries out examination by experiment repeatedly and gathers。

In the present embodiment, parameter is set to:Λ=-20, h=5, regulate parameter γ=200, control amplitude limit U_max=1.56V,

When following the tracks of expectation target respectively formula (13)-Shi (15), curve of output is respectively as shown in Fig. 3, Fig. 4, Fig. 5。

The control law of PID controller is as follows:

$u\left(t\right)=K_{P}e\left(t\right)+K_I{\&Integral;}_0^{t}e\left(t\right)dt+K_D\frac{de\left(t\right)}{dt},---\left(16\right)$

Actual pid control mode is provided by formula (16), and the amplitude limit controlling output is identical with the inventive method, and wherein the parameter of PID controller obtains K through optimizing design_P=10, K_I=15, K_D=0.1。

Such as Fig. 6, Fig. 7, Fig. 8, sets forth the control effect adopting existing PID control method when following the tracks of corresponding desired output。

Visible by the contrast of Fig. 3-Fig. 8, the tracking accuracy of the inventive method is higher。

In order to the control effect of the inventive method is described more intuitively, root-mean-square error RMSE is as follows in definition

$RMSE=\sqrt{\frac{1}{N_2-N_1}\underset{k=N_1}{\overset{N_2}{\&Sigma;}}{e}_k^2},---\left(17\right)$

Wherein, N₁For comparing start time, N₂For comparing finish time, e_k=e (k Δ T)。

For avoiding the impact of Self Adaptive Control difference initial value and random disturbances, every kind of tracking inputting signal having been carried out test of many times, table below provides the steady track root-mean-square error of wherein five experimental results respectively, and its result is shown in table 1 below-Biao 3。

The error contrast when following the tracks of S curve signal of table 1, the inventive method and PID control method

The error contrast when following the tracks of sinusoidal signal of table 2, the inventive method and PID control method

The error contrast when following the tracks of multifrequency sine signal of table 3, the inventive method and existing control method

From three steady track root-mean-square error meansigma methodss contrasted form, when various expectation target, the average tracking error of the inventive method is both less than existing PID control method。

Claims (3)

1. a Hydraulic Position Servo output feedack self-adaptation control method, it is characterised in that the method is embodied as according to following steps:

Step 1, set up the model of Hydraulic Position Servo

The mathematical model of this Hydraulic Position Servo such as following formula (1):

$\left\{\begin{array}{c}{Q}_a=\left\{\begin{array}{c}{C}_d{\mathrm{wx}}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_s-P_a},x_v\&GreaterEqual;0\\ C_d{\mathrm{wx}}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_a-P_r},x_v<0\end{array}\right.\\ Q_b=\left\{\begin{array}{c}{C}_d{\mathrm{wx}}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_b-P_r},x_v\&GreaterEqual;0\\ C_d{\mathrm{wx}}_v\sqrt{\frac{2}{\mathrm{\&rho;}}}\sqrt{P_s-P_b},x_v<0\end{array}\right.\\ x_v=k_{v}u\\ Q_a-C_t\left(P_a-P_b\right)=A_a\stackrel{\&CenterDot;}{y}+\frac{V_a}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_a\\ C_t\left(P_a-P_b\right)-Q_b=-A_b\stackrel{\&CenterDot;}{y}+\frac{V_b}{{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_b\\ P_a{A}_a-P_b{A}_b=M\stackrel{\&CenterDot;\&CenterDot;}{y}+B_p\stackrel{\&CenterDot;}{y}+ky+F_L\end{array}\right.,---\left(1\right)$

Wherein, P_aAnd P_bThe respectively pressure of hydraulic cylinder rodless cavity A and rod chamber B,WithRespectively P_aAnd P_bFirst derivative, P_sAnd P_rRespectively charge oil pressure and return pressure, Q_aAnd Q_bRespectively flow into rodless cavity A and flow out the flow of rod chamber B, A_aAnd A_bFor the piston effective active area at rodless cavity A and rod chamber B, V_aAnd V_bFor the volume of hydraulic cylinder rodless cavity A and rod chamber B, C_dFor discharge coefficient, C_tFor internal leakage coefficient, w is proportioning valve area gradient, x_vFor proportioning valve spool displacement, k_vFor proportioning valve proportionality coefficient, u is control signal, and ρ is fluid density, β_eFor bulk modulus, M is load quality, B_pFor viscous damping coefficient, k is spring loaded coefficient, and y is the displacement of hydraulic cylinder piston, and y is obtained by displacement detecting instrument (4) detection,WithThe respectively first derivative of y and second dervative, F_LFor outer carrying,

Introduce load flow Q_LWith load pressure P_LDefinition:

$\left\{\begin{array}{c}{P}_L=P_a-P_b\\ Q_L=\frac{Q_a+Q_b}{2}\end{array}\right.,---\left(2\right)$

Ignore outer carrying F_LAnd the nonlinear load such as Coulomb friction, nonlinear function is carried out linearization process, the mechanism model obtaining this Hydraulic Position Servo is:

$\left\{\begin{array}{c}{Q}_L=K_{xa}{x}_v-K_{pa}{P}_L\\ Q_L=C_t{P}_L+\frac{V}{4{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_L+A_m\stackrel{\&CenterDot;}{y}\\ A_m{P}_L=M\stackrel{\&CenterDot;\&CenterDot;}{y}+B_p\stackrel{\&CenterDot;}{y}+ky\end{array}\right.,---\left(3\right)$

Wherein, K_xaAnd K_paRespectively flow gain after linearisation and flow pressure coefficient, A_mRepresent the average effective area of hydraulic cylinder,

The state variable defining this Hydraulic Position Servo is:Subscript T therein refers to the transposition of vector,

Then the state equation of this Hydraulic Position Servo is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=-\frac{k}{m}{x}_1-\frac{B_p}{m}{x}_2+\frac{A_m}{m}{x}_3\\ {\stackrel{\&CenterDot;}{x}}_3=-\frac{4{\mathrm{\&beta;}}_e}{V}{A}_m{x}_2-\frac{4{\mathrm{\&beta;}}_e}{V}(K_{pa}+C_t)x_3+\frac{4{\mathrm{\&beta;}}_e}{V}{K}_{xa}{K}_{v}u\end{array}\right.,---\left(4\right)$

Three rank linear models of the approximate Hydraulic Position Servo obtained near matching point are as follows:

$\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{y}+{\mathrm{\&alpha;}}_2\stackrel{\&CenterDot;\&CenterDot;}{y}+{\mathrm{\&alpha;}}_1\stackrel{\&CenterDot;}{y}+{\mathrm{\&alpha;}}_{0}y=bu,---\left(5\right)$

WhereinCorrespond to x respectively₁、x₂、x₃First derivative, a₀、a₁、a₂, b be unknown model parameters,For three order derivatives of y, controlling target is make piston displacement y follow the tracks of required desired output y_m；

Step 2, set up the output feedack adaptive controller model of Hydraulic Position Servo

An output feedack adaptive controller is built, its model such as following formula (6) to formula (5):

U '=θ^Tω, (6)

Wherein, u' is the control signal before amplitude limit；θ^TIt is 4 dimensional vectors, θ with ω^TIt is the transposed vector of θ, θ=[k θ₁θ₂θ₀]^T, ω=[y_mω₁ω₂y]^T, ω₁And ω₂Respectively through to input signal y_mObtain with output signal y filtering, namely as shown in formula (7):

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1={\mathrm{\&Lambda;\&omega;}}_1+{\mathrm{hy}}_m\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2={\mathrm{\&Lambda;\&omega;}}_2+hy\end{array}\right.,---\left(7\right)$

Wherein,WithRespectively ω₁And ω₂First derivative, Λ, h are design parameter,

VariableDerivative asked for by Euler's formula, concrete form such as following formula (8):

$\stackrel{\&CenterDot;}{x}\left(k\mathrm{\&Delta;}T\right)=\frac{x\left(\right(k+1\left)\mathrm{\&Delta;}T\right)-x\left(k\mathrm{\&Delta;}T\right)}{\mathrm{\&Delta;}T},---\left(8\right)$

Wherein,It is the first derivative of x (t),RepresentIn the value of k sampling instant, Δ T is the sampling time,

Control signal u is carried out amplitude limit, concrete form such as following formula (9):

$u=\left\{\begin{array}{cc}{U}_{max}& u^{\&prime;}>U_{max}\\ u^{\&prime;}& U_{max}-\&le;u^{\&prime;}<U_{max}\\ -U_{max}& u^{\&prime;}<-U_{max}\end{array}\right.,---\left(9\right)$

Wherein, U_maxAmplitude limit value for control signal u；

Step 3, calculate output feedack adaptive controller model parameter estimated value

Actual hydraulic pressure positional servosystem adopts the transmission function W of formula (5)_p(s) such as following formula:

$W_p\left(s\right)=\frac{b}{s^3+{\mathrm{\&alpha;}}_2{s}^2+{\mathrm{\&alpha;}}_{1}s+{\mathrm{\&alpha;}}_0},---\left(10\right)$

Assuming that transmission function W_mThe reference model of (s) such as following formula:

$W_m\left(s\right)=\frac{b_m}{s^3+{\mathrm{\&alpha;}}_{2m}{s}^2+{\mathrm{\&alpha;}}_{1m}s+{\mathrm{\&alpha;}}_{0m}},---\left(11\right)$

Wherein, b_m、a_2m、a_1m、a_0mParameter for reference model；

Determine the estimated value rule of auto-adaptive parameter, with reference to following formula (12):

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=-\frac{\mathrm{sgn}\left(b\right)\mathrm{\&gamma;}\mathrm{\&epsiv;}\underset{\&OverBar;}{\mathrm{\&omega;}}}{1+{\underset{\&OverBar;}{\mathrm{\&omega;}}}^T\underset{\&OverBar;}{\mathrm{\&omega;}}}\\ \stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=-\frac{\mathrm{\&gamma;}\mathrm{\&epsiv;}\mathrm{\&eta;}}{1+{\underset{\&OverBar;}{\mathrm{\&omega;}}}^T\underset{\&OverBar;}{\mathrm{\&omega;}}}\end{array}\right.,---\left(12\right)$

Wherein, θ=[k θ₁θ₂θ₀]^T,It it is the first derivative of θ；γ is for regulating parameter；

Sgn (b) is the sign function about b, as b > 0, and sgn (b)=1；As b=0, sgn (b)=0；As b < 0, sgn (b)=-1；

ω=W_m(ω) represent that signal vector ω is W by transmitting function_mOutput signal corresponding to the module of (s),ω ^TIt isωTransposed vector；

ε=e+ α η is augmented error, e=y-y_mFor tracking error, y_mBeing input signal, y is output signal,It is the first derivative of α, η=θ^TW_m(ω)-W_m(θ^Tω) for assisted error, W_m(θ^Tω) it is signal vector θ^Tω is W by expecting transmission function_mSignal after the module of (s), θ^TIt is the transposed vector of θ,

First calculate tracking error e, calculate assisted error η again, and then utilized the α value in a upper moment to try to achieve ε, ε is substituted into the θ value trying to achieve current time in the first equation in formula (12), ε is substituted into the α value trying to achieve current time in the second equation in formula (12)

The vectorial θ, i.e. k, θ that estimation is obtained₁、θ₂And θ₀Numerical value for the parameter of real-time update output feedack adaptive controller modular form (6), computer export by the signal of D/A converter, the displacement of the piston of real-time adjustment asymmetrical cylinder,。

2. Hydraulic Position Servo output feedack self-adaptation control method according to claim 1, it is characterised in that: in described step 1, the structure of described Hydraulic Position Servo is,

Including asymmetrical hydraulic cylinder (3), the effective active area of hydraulic cylinder rodless cavity A and rod chamber B is not etc., piston (1) in hydraulic cylinder (3) is fixing with load (2) to be connected, piston (1) is connected to piston rod, being correspondingly arranged on displacement detecting instrument (4) on piston rod, the signal output part of displacement detecting instrument (4) accesses computer (6) by A/D converter；The liquid feeding end of the rodless cavity A of hydraulic cylinder (3) and proportioning valve (5) or the liquid returning end UNICOM of proportioning valve (5), proportioning valve (5) selects three position four-way electromagnetic valve, the control of the rod chamber B of hydraulic cylinder (3) passing ratio valve accordingly and liquid returning end or liquid feeding end UNICOM；It addition, the P port of proportioning valve (5) is connected with oil pump (8) by air relief valve (7), the T-port of proportioning valve (5) connects with hydraulic pump fuel reserve tank (9)；The electromagnetic valve core of proportioning valve (5) is connected with computer (7) with by D/A converter。

3. Hydraulic Position Servo output feedack self-adaptation control method according to claim 2, it is characterised in that: the effective active area of described hydraulic cylinder (3) rodless cavity A is 1.6 times of rod chamber B。