CN104460321A - Hydraulic motor preset performance tracking control method with hysteresis compensating - Google Patents

Abstract

The invention provides a hydraulic motor preset performance tracking control method with hysteresis compensating. The method comprises the steps that 1. a double-vane motor position servo system mathematical model with hysteresis is established; 2. a preset performance tracking control method with hysteresis compensating is designed; and 3. system parameters are designed. Preset performance requirements are fully considered, system hysteresis nonlinearity and high gain feedback are considered, the hydraulic motor preset performance tracking control method with hysteresis compensating is provided, according to the method, hysteresis nonlinearity is subjected to modeling to form the sum of a linear term and a bounded disturbance term, designing of a following moving controller is very convenient, for system parameter uncertainty and a non-modeling disturbance term, a self-adaptation robust control method is used, and meanwhile good parameter estimation and robust boundedness stability are guaranteed.

Description

A kind of oil motor default capabilities tracking and controlling method containing Hysteresis compensation

Technical field

The present invention relates to a kind of control method, particularly a kind of oil motor default capabilities tracking and controlling method containing Hysteresis compensation.

Background technology

Electrohydraulic servo system has the outstanding advantages such as power density is large, response is fast, power output/moment is large, is widely used, such as mechanical arm, aircraft manipulation, load simulator etc. in industry and national defence.And among this, hydraulic servo motor is due to can direct output torque, and having, the applications of rotary motion requirements is extensive.But extensively there is many model uncertainties in electrohydraulic servo system, comprise parameter uncertainty (flow gain, the bulk modulus of hydraulic oil, the leakage coefficient etc. of motor as servo-valve) and Uncertain nonlinear (as non-modeling disturb outward, non-linear friction, magnetic hysteresis etc.), these bring great difficulty all to the design of controller.

For parameter uncertainty, adaptive control is conventional means, it is to the parameterisable part in parameter uncertainty and Uncertain nonlinear, effectively can estimate and realize certain model compensation, but for can not parameterized uncertain nonlinearities, adaptive control is helpless, and there is the occasion of comparatively strong outer interference, and adaptive control even faces the danger of dispersing.For Uncertain nonlinear, synovial membrane, robust control, ANN (Artificial Neural Network) Control are all attempted, and achieve good control effects, but the chatter phenomenon that in synovial membrane controller, discontinuous sign function brings, easily cause the decay of system control performance, cause system unstability, existing improve synovial membrane shake measure control method less and complicated; The control performance that robust control realizes is usually with the risk of High Gain Feedback; The calculated amount of ANN (Artificial Neural Network) Control is comparatively large, and real-time is affected, and there is with the high response speed characteristic of electrohydraulic servo system conflict, causes it to occur bottleneck in the application of Practical Project.

For the occasion that some are special, as turntable, aircraft steering engine etc., the tracking performance Index For Steady-state that not only demand fulfillment is certain of electrohydraulic servo system, and the loading methods such as the speed of convergence of tracking error, overshoot, also must meet the boundary preset sometimes.In addition, torque-motor ubiquity magnetic hysteresis nonlinear characteristic in electrohydraulic servo valve, although it does not constitute a serious threat to the stability of valve-controlled motor servo-drive system, but very easily cause the delayed phase of system when low frequency, thus affect the final performance of controller.

Generally speaking, the weak point of existing motor servo system control technology mainly contain following some: (1) for system default capabilities pay close attention to less.When there is default capabilities demand for system in engineering reality, how in Controller gain variations, to be integrated into these preset need, how to ensure the loading methods such as the speed of convergence of tracking error, overshoot, take into account again the Index For Steady-states such as steady-state tracking precision, be the thorny problem faced at present simultaneously; (2) do not consider that magnetic hysteresis is non-linear.The non-linear inherent characteristic as torque-motor of magnetic hysteresis, if do not taken in Controller gain variations, but very easily causes valve-controlled motor servo-drive system at the delayed phase of low-frequency range, the final performance of the designed motion controller of impact; (3) High Gain Feedback.This is comparatively common in traditional robust controller, reduce tracking error using the Greatest lower bound of indeterminate as negative feedback, although good tracking performance can be obtained, have to face the risk of High Gain Feedback, easy activating system high frequency Unmarried pregnancy, causes system unstability.

Summary of the invention

In order to overcome prior art Problems existing, the present invention takes into full account that default capabilities demand, system magnetic hysteresis are non-linear and there is the problem of High Gain Feedback, proposes a kind of oil motor default capabilities tracking and controlling method containing Hysteresis compensation.

Containing an oil motor default capabilities tracking and controlling method for Hysteresis compensation, comprise the following steps:

Step 1, set up the twayblade motor position servo-drive system mathematical model containing magnetic hysteresis, detailed process is as follows:

Step 1.1, according to characteristic and the oil motor operating characteristic of Newton second law, electrohydraulic servo valve, the twayblade motor position dynamics of servosystem equation set up containing magnetic hysteresis turns

$J\stackrel{\·}{y}=P_L{D}_m-B\stackrel{\·}{y}+f(t,y,\stackrel{\·}{y})---\left(3\right)$

$\frac{V_t}{4{\mathrm{\β}}_e}{\stackrel{\·}{P}}_L=-D_m\stackrel{\·}{y}-C_t{P}_L+Q_L+\tilde{Q}---\left(4\right)$

$Q_L=k_{t}u\sqrt{P_s-\mathrm{sign}\left(u\right)P_L}---\left(5\right)$

u＝cv(t)+d(v) (5-1)

The kinetics equation that formula (3) is inertia load, wherein J is inertia load, y, with be respectively alliance, speed and acceleration, P _l=P ₁-P ₂for oil motor load pressure, P ₁and P ₂for motor two cavity pressure, D _mfor motor volume discharge capacity, B is total viscous damping coefficient, for all non-modeling distracters;

The pressure flow equation that formula (4) is motor, wherein V _tfor total containing volume in motor two chamber, β _efor the effective bulk modulus of hydraulic oil, C _tfor total leakage coefficient of motor, Q _l=(Q ₁+ Q ₂)/2 are load flow, Q ₁and Q ₂be respectively oil-feed and oil return flow, represent all non-modeling distracters in pressure flow equation;

K in formula (5) _t=k _ik _qfor the overall throughput gain relative to control inputs voltage, k _ifor voltage-spool displacement gain coefficient, c _dfor servo-valve throttle orifice coefficient, w is servo-valve throttle hole area gradient, and ρ is hydraulic oil density, P _sfor system charge oil pressure, system oil return pressure P _r=0, sign (u) is sign function;

Formula (5-1) is the hysteresis model after simplifying, and wherein u is that hysteresis model exports, and c is hysteresis characteristic parameter, the output controlled quentity controlled variable that v (t) is t controller, and d (v) is the BOUNDED DISTURBANCES of being given birth to by nonlinear magnetism bradytoia;

Step 1.2, definition status variable then kinetics equation is converted into:

$\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=x_3-{\mathrm{\θ}}_1{x}_2+d_1\\ {\stackrel{\·}{x}}_3={\mathrm{\θ}}_2\mathrm{gv}-{\mathrm{\θ}}_3{f}_1-{\mathrm{\θ}}_4{f}_2+d_2\end{array}---\left(8\right)$

θ in formula (8) ₁=B/J, θ ₂=c β _ek _t/ J, θ ₃=β _e/ J, θ ₄=β _ec _t, g,f ₁, f ₂, d ₂be defined as follows:

$\begin{array}{c}g=\frac{4D_m}{V_t}\sqrt{P_s-\mathrm{sign}\left(u\right)\frac{J}{D_m}{x}_3},f_1=\frac{4D_m^2}{V_t}{x}_2\\ f_2=\frac{4x_3}{V_t},d_2=\frac{{\mathrm{\θ}}_{2}g{d}_n\left(v\right)}{c}+\frac{4{\mathrm{\β}}_e{D}_m\tilde{Q}}{V_{t}J}\end{array}---\left(9\right)$

Step 2, design, containing the default capabilities tracking and controlling method of Hysteresis compensation, comprises following steps:

Step 2.1, definition default capabilities function:

$S\left(z_1\right)=\frac{\stackrel{\‾}{\mathrm{\δ}}{e}^{z_1}-\underset{\‾}{\mathrm{\δ}}{e}^{-z_1}}{e^{z_1}+e^{-z_1}}=\frac{e\left(t\right)}{\mathrm{\ρ}\left(t\right)}=\mathrm{\λ}---\left(13\right)$

Tracking error e=x in formula (13) ₁-x _1d, x _1dfor the position command of system keeps track, z ₁for transformed error amount, δwith for positive can design parameter, ρ (t) is the positive smooth function that increases progressively; Tracking error e meets following performance index:

$-\underset{\&OverBar;}{\mathrm{\&delta;}}\left(t\right)<e\left(t\right)<\stackrel{\&OverBar;}{\mathrm{\&delta;}}\mathrm{\&rho;}\left(t\right),\&ForAll;t>0---\left(10\right)$

Can obtain formula (13) function of negating:

$z_1=\frac{1}{2}\ln \frac{\mathrm{\&lambda;}+\mathrm{\&delta;}}{\stackrel{\&OverBar;}{\mathrm{\&delta;}}-\mathrm{\&lambda;}}---\left(14\right)$

Step 2.2, definition assisted error amount z ₃=x ₃-α ₂, wherein k ₁for programmable feedback gain, α ₂for virtual controlling amount, then can be obtained by formula (8) and formula (14):

$\begin{array}{c}{\stackrel{\&CenterDot;}{z}}_2={\stackrel{\&CenterDot;\&CenterDot;}{z}}_1+k_1{\stackrel{\&CenterDot;}{z}}_1\\ =\left(\stackrel{\&CenterDot;}{\mathrm{\&beta;}}{+k}_1\mathrm{\&beta;}\right)(x_2-{\stackrel{\&CenterDot;}{x}}_{1d}-e\stackrel{\&CenterDot;}{\mathrm{\&rho;}}/\mathrm{\&rho;})+\mathrm{\&beta;}[-{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{1d}-(\stackrel{\&CenterDot;}{e}\stackrel{\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}+e\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}-e{\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}^2)/{\mathrm{\&rho;}}^2]\\ +\mathrm{\&beta;}[z_3+{\mathrm{\&alpha;}}_2-{\mathrm{\&theta;}}_1{x}_2+d_1]\end{array}---\left(17\right)$

In formula (17) $\mathrm{\&beta;}=(\stackrel{\&OverBar;}{\mathrm{\&delta;}}+\underset{\&OverBar;}{\mathrm{\&delta;}})/[2\mathrm{\&rho;}(\mathrm{\&lambda;}+\underset{\&OverBar;}{\mathrm{\&delta;}})(\stackrel{\&OverBar;}{\mathrm{\&delta;}}-\mathrm{\&lambda;})],$ Design virtual controlling amount α ₂for:

$\begin{array}{c}{\mathrm{\&alpha;}}_2=({\mathrm{\&alpha;}}_{2a}+{\mathrm{\&alpha;}}_{2s1}+{\mathrm{\&alpha;}}_{2s2})/\mathrm{\&beta;}\\ \begin{array}{c}{\mathrm{\&alpha;}}_{2a}={\widehat{\mathrm{\&theta;}}}_1\mathrm{\&beta;}{x}_2+\mathrm{\&beta;}[{\stackrel{\&CenterDot;}{x}}_{1d}+\left(\stackrel{\&CenterDot;}{e}\stackrel{\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}+e\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}-e{\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}^2\right)/{\mathrm{\&rho;}}^2]-\\ (\stackrel{\&CenterDot;}{\mathrm{\&beta;}}+k_1\mathrm{\&beta;})-(x_2-{\stackrel{\&CenterDot;}{x}}_{1d}-e\stackrel{\&CenterDot;}{\mathrm{\&rho;}}/\mathrm{\&rho;})\end{array}\\ {\mathrm{\&alpha;}}_{2s1}=-k_2{z}_2\end{array}---\left(18\right)$

K in formula (18) ₂>0 is feedback gain to be designed, α _2afor model compensation item, α _2sfor robust item, ε ₁>0 be arbitrarily small can design parameter, for θ ₁estimated value;

Step 2.3, definition assisted error amount z ₃

${\stackrel{\&CenterDot;}{z}}_3={\stackrel{\&CenterDot;}{x}}_3-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_2={\mathrm{\&theta;}}_2\mathrm{gv}-{\mathrm{\&theta;}}_3{f}_1-{\mathrm{\&theta;}}_4{f}_2-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2c}-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2u}+d_2---\left(22\right)$

In formula (12) with represent virtual controlling amount α respectively ₂derivative in can calculating section and can not calculating section.

Step 2.4, determines working control device input v

V in formula (13) _arepresent model compensation controller, v _srepresent robust controller, v _s1for linear robust feedback term, v _s1for non linear robust feedback term, the each unknown parameter estimated value of expression system, represent parameter update law, Γ represents self-adaptation regression parameter matrix, all represent parametric regression device, k ₃for positive feedback gain, ε ₂for can design parameter, θ _m=θ _max-θ _minrepresent the maximal oxygen momentum of parameter, θ _maxand θ _minrepresent the estimation upper bound of each parameter respectively and estimate lower bound;

Step 2.5, definition Liapunov function is as follows:

$V=\frac{1}{2}(z_1^2+z_2^2+z_3^2);---\left(26\right)$

Step 2.6, definition matrix Λ

$\mathrm{\&Lambda;}=\left[\begin{array}{ccc}{k}_1& 1/2& 0\\ 1/2& k_2& \mathrm{\&beta;}/2\\ 0& \mathrm{\&beta;}/2& k_3\end{array}\right].---\left(28\right)$

Step 3, design k ₁, k ₂, k ₃, ε ₁, ε _2, δwith system is met the following conditions: matrix Λ is positive definite matrix, and tracking error e is minimum.

The present invention compared with prior art, have the following advantages: (1) the present invention selects twayblade oil motor positional servosystem as research object, consider systematic parameter uncertainty simultaneously, non-modeling disturb outward and magnetic hysteresis non-linear, devise excellent tracking control unit; (2) non-linear for magnetic hysteresis, be linear term and BOUNDED DISTURBANCES item sum by magnetic hysteresis Nonlinear Modeling, greatly facilitate the design of subsequent motion controller; (3) and non-modeling distracter uncertain for systematic parameter, adopts adaptive robust control method, ensure that good parameter estimation and robust bounded stability simultaneously; (4) for default capabilities demand, adopt default capabilities function, achieve making rational planning for tracking error speed of convergence and maximum overshoot, by the tracking control unit to transformed error excellent in design, and then ensure that tracking error meets default performance requirement.

Accompanying drawing explanation

Fig. 1 is twayblade oil motor positional servosystem schematic diagram of the present invention;

Fig. 2 is control method principle schematic of the present invention;

The position command curve of Fig. 3 system keeps track;

Fig. 4 is system tracking error correlation curve;

Fig. 5 formula system speed exports correlation curve;

Fig. 6 is system parameters estimated value curve;

Fig. 7 Systematical control input curve;

Fig. 8 is the inventive method process flow diagram.

Embodiment

Composition graphs 1, Fig. 2 and Fig. 8, a kind of concrete steps of the oil motor default capabilities tracking and controlling method containing Hysteresis compensation are as follows:

Step 1, hysteresis characteristic model.Due to the discontinuous characteristic of conventional gap class hysteresis model, the Controller gain variations for nonlinear system is very unfavorable, and the present invention uses following hysteresis model:

$\frac{\mathrm{du}}{\mathrm{dt}}=\mathrm{\&alpha;}\left|\frac{\mathrm{dv}}{\mathrm{dt}}\right|(\mathrm{cv}-u)+B_1\frac{\mathrm{dv}}{\mathrm{dt}}---\left(1\right)$

In formula (1), u is that hysteresis model exports, i.e. effective control inputs voltage, c, α and B ₁for hysteresis characteristic parameter, and meet c > B ₁, v is the output controlled quentity controlled variable of controller, provides expression by follow-up Controller gain variations.Formula (1) can be converted into:

U in formula (2) ₀and v ₀represent initial value.Analytical formula (2) is known, and the linear term that the hysteresis model after changing is c by slope and distracter d (v) form, and the boundary of d (v) item is known.

Step 1.1, set up the twayblade oil motor positional servosystem model containing magnetic hysteresis, according to Newton second law, inertia load kinetics equation is:

$J\stackrel{\&CenterDot;}{y}=P_L{D}_m-B\stackrel{\&CenterDot;}{y}+f(t,y,\stackrel{\&CenterDot;}{y})---\left(3\right)$

In formula (3), J is inertia load, y, with be respectively alliance, speed and acceleration, P _l=P ₁-P ₂for oil motor load pressure, P ₁and P ₂for motor two cavity pressure, D _mfor motor volume discharge capacity, B is total viscous damping coefficient (comprising loading section and motor portion), for all non-modeling distracters.The pressure flow equation of motor is:

$\frac{V_t}{4{\mathrm{\&beta;}}_e}{\stackrel{\&CenterDot;}{P}}_L=-D_m\stackrel{\&CenterDot;}{y}-C_t{P}_L+Q_L+\tilde{Q}---\left(4\right)$

V in formula (4) _tfor total containing volume in motor two chamber, β _efor the effective bulk modulus of hydraulic oil; C _tfor total leakage coefficient of motor, Q _l=(Q ₁+ Q ₂)/2 are load flow, Q ₁and Q ₂be respectively oil-feed and oil return flow, represent all non-modeling distracters in pressure flow equation.Load flow Q _lwith valve core of servo valve displacement x _vpass be:

$Q_L=k_{t}u\sqrt{P_s-\mathrm{sign}\left(u\right)P_L}---\left(5\right)$

Flow gain k in formula (5) _qwith sign (x _v) as shown in the formula:

$k_q=C_{d}w\sqrt{1/\mathrm{\&rho;}},\mathrm{sign}\left(u\right)=\left\{\begin{array}{cc}1,& \mathrm{if}{x}_v>0\\ -1,& \mathrm{if}{x}_v<0\end{array}\right.---\left(6\right)$

C in formula (6) _dfor servo-valve throttle orifice coefficient; W is servo-valve throttle hole area gradient; ρ is hydraulic oil density; P _sfor system charge oil pressure, system oil return pressure P _r=0.Because the frequency range of servo-valve is higher, reach hundreds of Hz, be far longer than the frequency range of system during work, therefore during modeling, we ignore the dynamic process of servo-valve, the control inputs of valve and spool displacement are considered as proportional component, i.e. x _v=k _iu, wherein u is control inputs voltage, k _ifor voltage-valve position moves gain coefficient, therefore formula (6) is converted into:

$Q_L=k_{t}u\sqrt{P_s-\mathrm{sign}\left(u\right)P_L}---\left(7\right)$

K in formula (7) _t=k _ik _qfor the overall throughput gain relative to control inputs voltage u.

Step 1.2, definition status variable in conjunction with formula (3), formula (4) and formula (7), substitute into hysteresis model (2), the total mathematical model of system can be expressed as following state space form simultaneously:

$\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=x_3-{\mathrm{\&theta;}}_1{x}_2+d_1\\ {\stackrel{\&CenterDot;}{x}}_3={\mathrm{\&theta;}}_2\mathrm{gv}-{\mathrm{\&theta;}}_3{f}_1-{\mathrm{\&theta;}}_4{f}_2+d_2\end{array}---\left(8\right)$

θ in formula (8) ₁=B/J, θ ₂=c β _ek _t/ J, θ ₃=β _e/ J, θ ₄=β _ec _t, g,f ₁, f ₂, d ₂be defined as follows:

$\begin{array}{c}g=\frac{4D_m}{V_t}\sqrt{P_s-\mathrm{sign}\left(u\right)\frac{J}{D_m}{x}_3},f_1=\frac{4D_m^2}{V_t}{x}_2\\ f_2=\frac{4x_3}{V_t},d_2=\frac{{\mathrm{\&theta;}}_{2}g{d}_n\left(v\right)}{c}+\frac{4{\mathrm{\&beta;}}_e{D}_m\tilde{Q}}{V_{t}J}\end{array}---\left(9\right)$

Before Controller gain variations, first make the following assumptions: systematic parameter θ ₁, θ ₂, θ ₃, θ ₄be unknown constant value; Nonlinear perturbations item d ₁with bounded, d in analytical formula (9) ₂expression formula, in systems in practice, always can ensure g item bounded, know d again by (3) formula _h(v) item bounded, thus known Nonlinear perturbations item d ₂bounded, namely || d ₁||≤δ ₁, || d ₂||≤δ ₂, δ ₁and δ ₂be known constant.The target of next step Controller gain variations is that guarantee system exports x ₁trace command x as much as possible _1d.

Step 2, design is containing the default capabilities tracking and controlling method of Hysteresis compensation, and concrete steps are as follows:

Step 2.1, definition default capabilities function:

Definition tracking error e=x ₁-x _1d, suppose that it need meet following performance index:

In formula (7) δwith for positive can design parameter, ρ (t) is the positive smooth function that increases progressively, and tool form is as follows:

ρ in formula (11) ₀, ρ _∞with k be positive can design parameter.Obviously, formula (10) performance to tracking error gives concrete planning ,- δρ ₀with constrain maximum lower momentum and the maximum overshoot of error respectively; Parameter k constrains the speed of convergence of tracking error; ρ _∞constrain the stable state of tracking error.For the ease of Controller gain variations subsequently, be defined as follows increasing function S (z ₁):

$\left\{\begin{array}{c}-\underset{\&OverBar;}{\mathrm{\&delta;}}<S\left(z_1\right)<\stackrel{\&OverBar;}{\mathrm{\&delta;}},\&ForAll;t>0\\ {\lim }_{z_1\&RightArrow;+\&infin;}S\left(z_1\right)=\stackrel{\&OverBar;}{\mathrm{\&delta;}}\\ {\lim }_{z_1\&RightArrow;-\&infin;}S\left(z_1\right)=-\underset{\&OverBar;}{\mathrm{\&delta;}}\end{array}\right.---\left(12\right)$

Z in formula (12) ₁for transformed error amount, for Controller gain variations subsequently, analytical formula (12) is known, and formula (10) is equivalent to e (t)=ρ (t) S (z ₁), and z ₁during bounded, formula (10) meets all the time, S (z ₁) form of specifically choosing as follows:

$S\left(z_1\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&delta;}}{e}^{z_1}-\underset{\&OverBar;}{\mathrm{\&delta;}}{e}^{-z_1}}{e^{z_1}+e^{-z_1}}=\frac{e\left(t\right)}{\mathrm{\&rho;}\left(t\right)}=\mathrm{\&lambda;}---\left(13\right)$

By function of negating to formula (13), can obtain:

$z_1=\frac{1}{2}\ln \frac{\mathrm{\&lambda;}+\mathrm{\&delta;}}{\stackrel{\&OverBar;}{\mathrm{\&delta;}}-\mathrm{\&lambda;}}---\left(14\right)$

Step 2.2, definition assisted error variable:

For formula (14), differentiate is known:

$\begin{array}{c}{\stackrel{\&CenterDot;}{z}}_1=\frac{1}{2}\frac{\stackrel{\&OverBar;}{\mathrm{\&delta;}}+\underset{\&OverBar;}{\mathrm{\&delta;}}}{(\mathrm{\&lambda;}+\underset{\&OverBar;}{\mathrm{\&delta;}})(\stackrel{\&OverBar;}{\mathrm{\&delta;}}-\mathrm{\&lambda;})}\&CenterDot;\stackrel{\&CenterDot;}{\mathrm{\&lambda;}}\\ =\mathrm{\&beta;}(\stackrel{\&CenterDot;}{e}-e\stackrel{\&CenterDot;}{\mathrm{\&rho;}}/\mathrm{\&rho;})\\ =\mathrm{\&beta;}(x_2-{\stackrel{\&CenterDot;}{x}}_{1d}-e\stackrel{\&CenterDot;}{\mathrm{\&rho;}}/\mathrm{\&rho;})\end{array}---\left(15\right)$

In formula (15) $\mathrm{\&beta;}=(\stackrel{\&OverBar;}{\mathrm{\&delta;}}+\underset{\&OverBar;}{\mathrm{\&delta;}})/[2\mathrm{\&rho;}(\mathrm{\&lambda;}+\underset{\&OverBar;}{\mathrm{\&delta;}})(\stackrel{\&OverBar;}{\mathrm{\&delta;}}-\mathrm{\&lambda;})],$ Can obtain further:

${\stackrel{\&CenterDot;\&CenterDot;}{z}}_1=\stackrel{\&CenterDot;}{\mathrm{\&beta;}}(x_2-{\stackrel{\&CenterDot;}{x}}_{1d}-e\stackrel{\&CenterDot;}{\mathrm{\&rho;}}/\mathrm{\&rho;})+\mathrm{\&beta;}[-{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{1d}-(\stackrel{\&CenterDot;}{e}\stackrel{\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}+e\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}-e{\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}^2)/{\mathrm{\&rho;}}^2]+\mathrm{\&beta;}{\stackrel{\&CenterDot;}{x}}_2---\left(16\right)$

Definition assisted error amount z ₃=x ₃-α ₂, wherein α ₂for virtual controlling amount, then:

$\begin{array}{c}{\stackrel{\&CenterDot;}{z}}_2={\stackrel{\&CenterDot;\&CenterDot;}{z}}_1+k_1{\stackrel{\&CenterDot;}{z}}_1\\ =\left(\stackrel{\&CenterDot;}{\mathrm{\&beta;}}{+k}_1\mathrm{\&beta;}\right)(x_2-{\stackrel{\&CenterDot;}{x}}_{1d}-e\stackrel{\&CenterDot;}{\mathrm{\&rho;}}/\mathrm{\&rho;})+\mathrm{\&beta;}[-{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{1d}-(\stackrel{\&CenterDot;}{e}\stackrel{\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}+e\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}-e{\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}^2)/{\mathrm{\&rho;}}^2]\\ +\mathrm{\&beta;}[z_3+{\mathrm{\&alpha;}}_2-{\mathrm{\&theta;}}_1{x}_2+d_1]\end{array}---\left(17\right)$

Design virtual controlling amount α ₂for:

$\begin{array}{c}{\mathrm{\&alpha;}}_2=({\mathrm{\&alpha;}}_{2a}+{\mathrm{\&alpha;}}_{2s1}+{\mathrm{\&alpha;}}_{2s2})/\mathrm{\&beta;}\\ \begin{array}{c}{\mathrm{\&alpha;}}_{2a}={\widehat{\mathrm{\&theta;}}}_1\mathrm{\&beta;}{x}_2+\mathrm{\&beta;}[{\stackrel{\&CenterDot;}{x}}_{1d}+\left(\stackrel{\&CenterDot;}{e}\stackrel{\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}+e\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&rho;}}\mathrm{\&rho;}-e{\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}^2\right)/{\mathrm{\&rho;}}^2]-\\ (\stackrel{\&CenterDot;}{\mathrm{\&beta;}}+k_1\mathrm{\&beta;})-(x_2-{\stackrel{\&CenterDot;}{x}}_{1d}-e\stackrel{\&CenterDot;}{\mathrm{\&rho;}}/\mathrm{\&rho;})\end{array}\\ {\mathrm{\&alpha;}}_{2s1}=-k_2{z}_2\end{array}---\left(18\right)$

K in formula (18) ₂>0 is feedback gain to be designed; α _2afor model compensation item, for compensating corresponding system dynamic component and default capabilities function part; α _2sfor robust item.Formula (18) is substituted into formula (17) can obtain:

${\stackrel{\&CenterDot;}{z}}_2=-k_2{z}_2+\mathrm{\&beta;}{z}_3+({\mathrm{\&alpha;}}_{2s2}+{\widetilde{\mathrm{\&theta;}}}_1\mathrm{\&beta;}{x}_2+\mathrm{\&beta;}{d}_1)---\left(19\right)$

Design robust item α _2s2meet following Stabilization Conditions:

$\begin{array}{c}{z}_2({\mathrm{\&alpha;}}_{2s2}+{\widetilde{\mathrm{\&theta;}}}_1\mathrm{\&beta;}{x}_2+\mathrm{\&beta;}{d}_1)\&le;{\mathrm{\&epsiv;}}_1\\ z_2{\mathrm{\&alpha;}}_{2s2}\&le;0\end{array}---\left(20\right)$

ε in formula (20) ₁>0 be arbitrarily small can design parameter, meet the α of formula (20) _2s2design as follows:

${\mathrm{\&alpha;}}_{s2}=z_2{h}_1^2/\left(4{\mathrm{\&epsiv;}}_1\right),h_1\&GreaterEqual;\left|{\mathrm{\&theta;}}_1\right|\left|\mathrm{\&beta;}\right|\left|x_2\right|+\left|\mathrm{\&beta;}\right|\&CenterDot;{\mathrm{\&delta;}}_1---\left(21\right)$

Step 2.3, definition assisted error amount z ₃, by formula (8) and assisted error amount z ₃definition, have further:

${\stackrel{\&CenterDot;}{z}}_3={\stackrel{\&CenterDot;}{x}}_3-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_2={\mathrm{\&theta;}}_2\mathrm{gv}-{\mathrm{\&theta;}}_3{f}_1-{\mathrm{\&theta;}}_4{f}_2-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2c}-{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2u}+d_2---\left(22\right)$

In formula (22) with represent virtual controlling amount α respectively ₂derivative in can calculating section and can not calculating section, be defined as follows respectively:

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_2={\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2c}+{\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2u}\\ {\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2c}=\frac{\&PartialD;{\mathrm{\&alpha;}}_2}{\&PartialD;t}+\frac{\&PartialD;{\mathrm{\&alpha;}}_2}{\&PartialD;x_1}{x}_2+\frac{\&PartialD;{\mathrm{\&alpha;}}_2}{\&PartialD;x_1}{\widehat{\stackrel{\&CenterDot;}{x}}}_2+\frac{\&PartialD;{\mathrm{\&alpha;}}_2}{\&PartialD;{\widehat{\mathrm{\&theta;}}}_1}{\widehat{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}}_1\\ {\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}_{2u}=\frac{\&PartialD;{\mathrm{\&alpha;}}_2}{\&PartialD;x_2}{\widehat{\stackrel{\&CenterDot;}{x}}}_2,{\widehat{\stackrel{\&CenterDot;}{x}}}_2=x_3-{\widehat{\mathrm{\&theta;}}}_1{x}_2,{\widehat{\stackrel{\&CenterDot;}{x}}}_2=-{\widetilde{\mathrm{\&theta;}}}_1{x}_2+d_1\end{array}---\left(23\right)$

Step 2.4, determine working control device input v:

According to formula (22), final motion controller can be designed as follows:

V in formula (13) _arepresent model compensation controller, v _srepresent robust controller, the each unknown parameter estimated value of expression system, represent parameter update law, Γ represents self-adaptation regression parameter matrix, all represent parametric regression device, k ₃for positive feedback gain, ε ₂for can design parameter, θ _m=θ _max-θ _minrepresent the maximal oxygen momentum of parameter, θ _maxand θ _minrepresent the estimation upper bound of each parameter respectively and estimate lower bound;

Formula (24) is substituted into formula (22) can obtain:

Step 2.5, verification system stability:

Selecting system starting condition meets $-\underset{\&OverBar;}{\mathrm{\&delta;}}\mathrm{\&mu;}\left(0\right)<\mathrm{e\&lambda;}\left(0\right)<\stackrel{\&OverBar;}{\mathrm{\&delta;}}\mathrm{\&mu;}\left(0\right),$ Namely $-\underset{\&OverBar;}{\mathrm{\&delta;}}<\mathrm{\&lambda;}\left(0\right)<\stackrel{\&OverBar;}{\mathrm{\&delta;}}.$

Definition Liapunov function is as follows:

$V=\frac{1}{2}(z_1^2+z_2^2+z_3^2)---\left(26\right)$

To formula (26) differentiate, and substitute into formula (19), (25) can obtain:

Z=[z in formula (22) ₁, z ₂, z ₃] ^t, ε=ε ₁+ ε ₂.

Step 2.6, definition matrix Λ

$\mathrm{\&Lambda;}=\left[\begin{array}{ccc}{k}_1& 1/2& 0\\ 1/2& k_2& \mathrm{\&beta;}/2\\ 0& \mathrm{\&beta;}/2& k_3\end{array}\right]---\left(28\right)$

Obviously, by rational design parameter k ₁, k ₂make matrix Λ be positive definite matrix, following formula can be made to meet:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;-2{\mathrm{\&lambda;}}_{\min }\left(\mathrm{\&Lambda;}\right)V+\mathrm{\&epsiv;}\\ V\left(t\right)\&le;V\left(0\right)\exp (-2{\mathrm{\&lambda;}}_{\min }t)+\frac{\mathrm{\&epsiv;}}{2{\mathrm{\&lambda;}}_{\min }}[1-\exp (-2{\mathrm{\&lambda;}}_{\min }t)]\end{array}---\left(29\right)$

λ in formula (29) _min(Λ) minimal eigenvalue of representing matrix Λ, analytical formula (29) is known, and controller (24) finally can ensure transformed error z ₁stable state bounded, further by rational design parameter δ and and function ρ (t), can ensure that, under system realizes the prerequisite of accurate tracking, tracking performance meets the characteristic preset.

Below in conjunction with embodiment, the present invention will be further described.

Twayblade oil motor positional servosystem parameter is inertia load: J=0.2kgm ²; B=90Nms/rad; k _t=1.1969 × 10 ^-8m ²/ s/V/Pa ^-1/2, V _t=1.16 × 10 ^-4m ³; β _e=700MPa; C _t=1 × 10 ¹²m ³/ s/Pa; D _m=5.8 × 10 ^-5m ³/ rad; P _s=10MPa; P _r=0.

In order to fully verify the validity of designed controller herein, choose traditional adaptive robust control (ARC) to carry out as a comparison, the design procedure of tradition ARC controller is similar to the controller designed herein, but lacked the Planning effect of default capabilities function, corresponding parameter choose is k ₁=150, k ₂=1000, k ₃=30.

CONTROLLER DESIGN (being designated as PPARC) herein, i.e. formula (24): parameter choose is: k ₁=150, k ₂=2000, k ₃=30, ρ ₀=0.3, ρ _∞=0.001, k=0.5, δ=5, adaptation law coefficient is chosen for Γ ₁=0.01, Γ ₂=8e-6, Γ ₃=1000, Γ ₄=1e-10.Systematic parameter estimation range is chosen for: θ _min=[100,10,2e9,1e-4] ^t, θ _max=[1000,100,5e9,4e-3] ^t.

System interference be chosen for d=0.1sin (2 π t) (Fig. 3), system initial position is chosen for x ₁(0)=0.1rad, this initial position obviously meets choosing trace command is x _1d=0.8sin (t).

Control method action effect:

Fig. 4 is tracking error correlation curve, can find out in figure, because initial position does not mate, at tracking initial segment, under two controller actions, tracking error all restrains with fast speed, but there is larger overshoot in traditional ARC controller, design PPARC herein to control, under the effect of default capabilities function, occur without obvious overshoot, and speed of convergence to be faster than ARC.

Fig. 5 is the system output speed correlation curve under two kinds of controller actions, obvious unmatched initial position makes both all occur larger velocity perturbation at initial segment, PPARC very rapid convergence be tending towards smooth, but still there is velocity perturbation at about 0.25s place in traditional ARC controller.

Fig. 6 designs each parameter estimation curve under PPARC controller herein, although there is larger shake in initial segment estimation curve, but each parameter very rapid convergence, and tend towards stability.

Fig. 7 is control inputs curve, the smooth and bounded all the time of control inputs.

Claims (4)

1., containing an oil motor default capabilities tracking and controlling method for Hysteresis compensation, it is characterized in that, comprise the following steps:

Step 1, sets up the twayblade motor position servo-drive system mathematical model containing magnetic hysteresis;

Step 2, design is containing the default capabilities tracking and controlling method of Hysteresis compensation;

Step 3, design system parameter.

2. the oil motor default capabilities tracking and controlling method containing Hysteresis compensation according to claim 1, it is characterized in that, step 1 detailed process is as follows:

Step 1.1, according to characteristic and the oil motor operating characteristic of Newton second law, electrohydraulic servo valve, the twayblade motor position dynamics of servosystem equation set up containing magnetic hysteresis turns

$J\stackrel{.}{y}=P_L{D}_m-B\stackrel{.}{y}+f(t,y,\stackrel{.}{y})---\left(3\right)$

$\frac{V_t}{4{\mathrm{\&beta;}}_e}{\stackrel{.}{P}}_L=-D_m\stackrel{.}{y}-C_t{P}_L+Q_L+\tilde{Q}---\left(4\right)$

$Q_L=k_{t}u\sqrt{P_s-\mathrm{sign}\left(u\right)P_L}---\left(5\right)$

u＝cv(t)+d(v) (5-1)

The kinetics equation that formula (3) is inertia load, wherein J is inertia load, y, with be respectively alliance, speed and acceleration, P _l=P ₁-P ₂for oil motor load pressure, P ₁and P ₂for motor two cavity pressure, D _mfor motor volume discharge capacity, B is total viscous damping coefficient, for all non-modeling distracters;

The pressure flow equation that formula (4) is motor, wherein V _tfor total containing volume in motor two chamber, β _efor the effective bulk modulus of hydraulic oil, C _tfor total leakage coefficient of motor, Q _l=(Q ₁+ Q ₂)/2 are load flow, Q ₁and Q ₂be respectively oil-feed and oil return flow, represent all non-modeling distracters in pressure flow equation;

K in formula (5) _t=k _ik _qfor the overall throughput gain relative to control inputs voltage, k _ifor voltage-spool displacement gain coefficient, c _dfor servo-valve throttle orifice coefficient, w is servo-valve throttle hole area gradient, and ρ is hydraulic oil density, P _sfor system charge oil pressure, system oil return pressure P _r=0, sign (u) is sign function;

Formula (5-1) is the hysteresis model after simplifying, and wherein u is that hysteresis model exports, and c is hysteresis characteristic parameter, the output controlled quentity controlled variable that v (t) is t controller, and d (v) is the BOUNDED DISTURBANCES of being given birth to by nonlinear magnetism bradytoia;

Step 1.2, definition status variable $x={[x_1,x_2,x_3]}^T={[y,\stackrel{.}{y},P_L{D}_m/J]}^T,$ Then kinetics equation is converted into:

${\stackrel{.}{x}}_1=x_2$

${\stackrel{.}{x}}_2=x_3-{\mathrm{\&theta;}}_1{x}_2+d_1---\left(8\right)$

${\stackrel{.}{x}}_3={\mathrm{\&theta;}}_2\mathrm{fv}-{\mathrm{\&theta;}}_3{f}_1-{\mathrm{\&theta;}}_4{f}_2+d_2$

θ in formula (8) ₁=B/J, θ ₂=c β _ek _t/ J, θ ₃=β _e/ J, θ ₄=β _ec _t, wherein

$g=\frac{4D_m}{V_t}\sqrt{P_s-\mathrm{sign}\left(u\right)\frac{J}{D_m}{x}_3},f_1=\frac{4D_m^2}{V_t}{x}_2$

(9)

$f_2=\frac{4x_3}{V_t},d_2=\frac{{\mathrm{\&theta;}}_{2}g{d}_h\left(v\right)}{c}+\frac{4{\mathrm{\&beta;}}_e{D}_m\tilde{Q}}{V_{t}J}$

3. the oil motor default capabilities tracking and controlling method containing Hysteresis compensation according to claim 1, it is characterized in that, in step 2, control method comprises following steps:

Step 2.1, definition default capabilities function:

$S\left(z_1\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&delta;}}{e}^{z_1}-\underset{\&OverBar;}{\mathrm{\&delta;}}{e}^{-z_1}}{e^{z_1}+e^{-z_1}}=\frac{e\left(t\right)}{\mathrm{\&rho;}\left(t\right)}=\mathrm{\&lambda;}---\left(13\right)$

Formula (13) tracking error e=x ₁-x _1d, x _1dfor the position command of system keeps track, z ₁for transformed error amount, δwith for positive can design parameter, ρ (t) is the positive smooth function that increases progressively; Tracking error e meets following performance index:

$-\underset{\&OverBar;}{\mathrm{\&delta;}}\mathrm{\&rho;}\left(t\right)<e\left(t\right)<\stackrel{\&OverBar;}{\mathrm{\&delta;}}\mathrm{\&rho;}\left(t\right),\&ForAll;t>0---\left(10\right)$

Can obtain formula (13) function of negating:

$z_1=\frac{1}{2}\ln \frac{\mathrm{\&lambda;}+\underset{\&OverBar;}{\mathrm{\&delta;}}}{\stackrel{\&OverBar;}{\mathrm{\&delta;}}-\mathrm{\&lambda;}}---\left(14\right)$

Step 2.2, definition assisted error amount z ₃=x ₃-α ₂, wherein k ₁for programmable feedback gain, α ₂for virtual controlling amount, then can be obtained by formula (8) and formula (14):

$\begin{array}{c}{\stackrel{.}{z}}_2={\stackrel{..}{z}}_1+k_1{\stackrel{.}{z}}_1\\ =\left(\stackrel{.}{\mathrm{\&beta;}}+k_1\mathrm{\&beta;}\right)(x_2-{\stackrel{.}{x}}_{1d}-e\stackrel{.}{\mathrm{\&rho;}}/\mathrm{\&rho;})+\mathrm{\&beta;}[-{\stackrel{..}{x}}_{1d}-(\stackrel{.}{e}\stackrel{.}{\mathrm{\&rho;}}\mathrm{\&rho;}+e\stackrel{..}{\mathrm{\&rho;}}\mathrm{\&rho;}-e{\stackrel{.}{\mathrm{\&rho;}}}^2)/{\mathrm{\&rho;}}^2]\\ +\mathrm{\&beta;}[z_3+{\mathrm{\&alpha;}}_2-{\mathrm{\&theta;}}_1{x}_2+d_1]\end{array}---\left(17\right)$

In formula (17) $\mathrm{\&beta;}=(\stackrel{\&OverBar;}{\mathrm{\&delta;}}+\underset{\&OverBar;}{\mathrm{\&delta;}})/\left[2\mathrm{\&rho;}(\mathrm{\&lambda;}+\underset{\&OverBar;}{\mathrm{\&delta;}})(\stackrel{\&OverBar;}{\mathrm{\&delta;}}-\mathrm{\&lambda;})\right],$ Design virtual controlling amount α ₂for:

α ₂＝(α _2a+α _2s1+α _2s2)/β

$\begin{array}{c}{\mathrm{\&alpha;}}_{2a}={\widehat{\mathrm{\&theta;}}}_1\mathrm{\&beta;}{x}_2+\mathrm{\&beta;}[{\stackrel{..}{x}}_{1d}+(\stackrel{.}{e}\stackrel{.}{\mathrm{\&rho;}}\mathrm{\&rho;}+e\stackrel{..}{\mathrm{\&rho;}}\mathrm{\&rho;}-e{\stackrel{.}{\mathrm{\&rho;}}}^2)/{\mathrm{\&rho;}}^2]-\\ (\stackrel{.}{\mathrm{\&beta;}}+k_1\mathrm{\&beta;})(x_2-{\stackrel{.}{x}}_{1d}-e\stackrel{.}{\mathrm{\&rho;}}/\mathrm{\&rho;})\end{array}---\left(18\right)$

α _2s1＝-k ₂z ₂

${\mathrm{\&alpha;}}_{s2}=z_2{h}_1^2/\left(4{\mathrm{\&epsiv;}}_1\right),$ h ₁≥|θ ₁||β||x ₂|+|β|·|d ₁| _max

K in formula (18) ₂>0 is feedback gain to be designed, α _2afor model compensation item, α _2sfor robust item, ε ₁>0 be arbitrarily small can design parameter, for θ ₁estimated value;

Step 2.3, definition assisted error amount z ₃

${\stackrel{.}{z}}_3={\stackrel{.}{x}}_3-{\stackrel{.}{\mathrm{\&alpha;}}}_2={\mathrm{\&theta;}}_2\mathrm{gv}-{\mathrm{\&theta;}}_3{f}_1-{\mathrm{\&theta;}}_4{f}_2-{\stackrel{.}{\mathrm{\&alpha;}}}_{2c}-{\stackrel{.}{\mathrm{\&alpha;}}}_{2u}+d_2---\left(22\right)$

In formula (22) with represent virtual controlling amount α respectively ₂derivative in can calculating section and can not calculating section.

Step 2.4, determines working control device input v

$v=\frac{1}{{\widehat{\mathrm{\&theta;}}}_{2}g}(v_a+v_{s1}+v_{s2})$

$v_a={\widehat{\mathrm{\&theta;}}}_3{f}_1+{\widehat{\mathrm{\&theta;}}}_4{f}_2+{\stackrel{.}{\mathrm{\&alpha;}}}_{2c}$

v _s1＝-k ₃z ₃(24)

$v_{s2}=z_3{h}_2^2/\left(4{\mathrm{\&epsiv;}}_2\right)$

V in formula (13) _arepresent model compensation controller, v _srepresent robust controller, v _s1for linear robust feedback term, v _s2for non linear robust feedback term, the each unknown parameter estimated value of expression system, represent parameter update law, Γ represents self-adaptation regression parameter matrix, all represent parametric regression device, k ₃for positive feedback gain, ε ₂for can design parameter, θ _m=θ _max-θ _minrepresent the maximal oxygen momentum of parameter, θ _maxand θ _minrepresent the estimation upper bound of each parameter respectively and estimate lower bound;

Step 2.5, definition Liapunov function is as follows:

$V=\frac{1}{2}(z_1^2+z_2^2+z_3^2);---\left(26\right)$

Step 2.6, definition matrix Λ

$\mathrm{\&Lambda;}=\left[\begin{array}{ccc}{k}_1& 1/2& 0\\ 1/2& k_2& \mathrm{\&beta;}/2\\ 0& \mathrm{\&beta;}/2& k_3\end{array}\right].---\left(28\right)$

4. the oil motor default capabilities tracking and controlling method containing Hysteresis compensation according to claim 1, is characterized in that, design k in step 3 ₁, k ₂, k ₃, ε ₁, ε ₂, δ, system is met the following conditions: matrix Λ is positive definite matrix, and tracking error e is minimum.