CN106788036A - The modified active disturbance rejection positioner and its method for designing of a kind of direct current generator - Google Patents

Abstract

The invention discloses the modified active disturbance rejection positioner structure and method for designing of a kind of direct current generator, with direct current generator as controlled device, outgoing position signal as controlled variable, the controller is mainly made up of Nonlinear Tracking Differentiator, nonlinear state error feedback, extended state observer, four parts of disturbance compensation.Fal functions in the main nonlinear function improved in extended state observer of the invention, it is the function for determining extended state observer and controller tracking performance, it is to increase linear feedback region in nonlinear feedback specifically to change measure, on the basis of system stabilization is ensured, overcome in conventional method when the problem that systematic error is excessive and cannot control in time during too low gain.Emulation row before and after being improved by controller is compared, and, in the case where direct current generator site error is larger, output signal response speed is accelerated, so as to improve the overall control performance of system for structure proposed by the present invention and method for designing.

Description

The modified active disturbance rejection positioner and its method for designing of a kind of direct current generator

Technical field

The invention belongs to industrial stokehold technical field, and in particular to a kind of modified active disturbance rejection position of direct current generator Controller architecture and method for designing.

Background technology

In the controls, direct current generator is common executing agency, such as Control System of Inverted Pendulum needs motor to drive Belt transmission, joint of robot etc..Motor position or angle are an important output quantities of motor, are often needed in real system The controlled quentity controlled variable wanted., it is necessary to motor reaches a certain settling position within a certain period of time in many actual productions, and active disturbance rejection control The features such as device processed does not need the accurate model of controlled device by it and can compensate overall disturbance, makes it to direct current generator position The research of control has most direct realistic meaning.

Automatic disturbance rejection controller is proposed that its core is that controlled device is turned to simply " integration string by Mr. Han Jingqing Connection type " is controlled, being processed as " total disturbance " different from the part of " integration tandem type " in object.Which overcome PID Error is processed with differential signal in (Proportion Integration Differentiation) control imperfection and product Divide side effect of the feedback to closed-loop system.It is born in ADRC (Active Disturbance Rejection Control) technology At the beginning of, it is not general always the problems such as due to ESO (Extended state observer) convergences in controller and stability And, until yellow one et al. from the angle analysis in " self-stabilization domain " evaluated error and its convergence of second order ESO, second order ADRC's Correlation analysis is just further improved and popularization.Auto Disturbances Rejection Control Technique is initially applied to industry, especially in second order ADRC After improving, it is widely used in motor speed regulation system, time-varying, height coupled system., US Airways space flight in 2002 Office solves problem present in spacecraft electrical management distribution system using ADRC technologies；, state aviation boat in 2004 Its office is controlled using auto-disturbance rejection technology to jet engine, and design parameter is reduced to 5,6 further drops from more than 100 by it Low design difficulty；Meanwhile, it is being carried out largely at aspects such as accurate control, magnetic suspension system, motion control, signal transactings Research application.

In actual application, although can be good at realizing control effect using ADRC technologies, but, it is to direct current Motor position is rotated very in the control of wide-angle, when the error of system is excessive and during too low gain, system is unable to quick response, control Amount processed cannot play control effect to system.

The content of the invention

The present invention realizes second order active disturbance rejection control to brshless DC motor according to the imperfection and deficiency of now using background technology Make and the fal functions in extended state observer in automatic disturbance rejection controller are improved, ensureing the basis of system stabilization On, overcome in conventional method when the problem that systematic error is excessive and cannot control in time during too low gain.

In order to realize the technical purpose of the above, the present invention will take following technical scheme：

A kind of modified active disturbance rejection positioner of direct current generator, with direct current generator as controlled device, carry-out bit confidence Number it is controlled variable, including Nonlinear Tracking Differentiator, nonlinear state error feedback, extended state observer and disturbance compensation；Tracking The input of differentiator is expectation input signal；Two output ends of Nonlinear Tracking Differentiator respectively with two of extended state observer Output end is connected, and obtains the error of error and differential；Two inputs of nonlinear state error feedback are error and differential Error, obtains feedforward control amount；Disturbance compensation is the feedforward control amount and expansion state of nonlinear state error feedback output end Another output end is connected in observer, and disturbance compensation obtains final controlled quentity controlled variable；Fal functions are carried out in extended state observer Improve, using error threshold values e_cIncrease linear feedback region in the nonlinear feedback of fal functions to change function structure, expand Two inputs of state observer are respectively disturbance quantity and outgoing position signal；

Controlled device brshless DC motor, it is to the state model that motor outgoing position is controlled：

In formula, x₁=θ, θ turn over angle, x for motor₂=ω, ω are motor angular velocity；

k_eIt is back EMF coefficient, k_mIt is motor torque constant, T_LIt is load torque, R_mArmature resistance, J be load with The rotary inertia of rotor, k_e、k_m、T_L、R_mConstant collection is belonged to J；Y is outgoing position signal.

A kind of method for designing of the modified active disturbance rejection positioner of direct current generator, comprises the following steps：

The design of A, Nonlinear Tracking Differentiator：

Second order Nonlinear Tracking Differentiator is that signal is processed using discrete steepest Nonlinear Tracking Differentiator, and target is quick without super The tracking input signal of tune, while providing good differential signal, its input is expectation input signal r；

Described expectation input signal r by below equation calculating：

Obtain the output signal r of Nonlinear Tracking Differentiator₁And r₂, r₁It is after expecting that input signal r is processed through Nonlinear Tracking Differentiator Signal；r₂It is signal r₁Differential signal, in formula, k is current step, and T is sampling period, h_oIt is filtering factor, r₀For speed because Son, T, h_oAnd r₀Belong to constant collection；

Fhan (x in formula₁,x₂, r, h) and it is time-optimal control comprehensive function, its expression is：

In formula, r₁It is to expect input signal r through the signal after Nonlinear Tracking Differentiator treatment；r₂It is signal r₁Differential signal, D=hr, h are step-length, and a is intermediate variable,

Sign (x) is sign function, and expression formula is：

The design of B, extended state observer：

Two inputs of three rank extended state observers are respectively disturbance quantity b₀U and outgoing position signal y, first to expanding The fal functions opened in state observer are improved, the function expression fal after its improvement₁It is：

Wherein, e_cIt is fal₁Increase the error threshold values in linear feedback region in the nonlinear feedback of function, q is linear feedback Gain, a and δ is adjustable parameter, and e is error signal；Two described input signals are by following calculating：

Obtain the output signal z of three rank extended state observers₁、z₂And z₃, respectively one, two and three-stage shape state variable Tracking signal, wherein, β₀₁、β₀₂、β₀₃It is the gain of ESO feedback control amount, a₁、a₂, δ be adjustable parameter, b₀It is to object control The estimation of flow gain b processed, u is final controlled quentity controlled variable；

The design of C, nonlinear state error feedback：

The input signal of second nonlinear state error feedback is error e₁, differential error e₂, e₁=x₁-z₁、e₂=x₂- z₂, z₁、z₂It is respectively first and second output state of ESO, described input signal is calculated by below equation：

u₀=β₁fal(e₁,a₁,δ)+β₂fal(e₂,a₂,δ)；

Obtain the feedforward control amount u of nonlinear state error feedback output₀, in formula, β₁、β₂It is that nonlinear state error is anti- The feedback control flow gain of feedback, a₁、a₂It is adjustable parameter with δ, fal functions are original function, and its expression formula is：

A and δ are adjustable parameters, and e is error signal；

The design of D, disturbance compensation：

The output feedforward control amount u fed back by nonlinear state error₀The three-stage shape state exported with extended state observer Variation-tracking signal z₃, by following calculating：

Final controlled quentity controlled variable u is obtained, wherein, b₀It is the estimation to object control flow gain.

Compared with prior art, its advantage is technical scheme：

(1) modified automatic disturbance rejection controller of the invention, can in real time to " total disturbance " compared with classical PID controller Estimated and eliminated；Rapidly input signal can be made a response, quickly desired signal is realized to track, reach expectation Anti- external disturbance is stronger after value, the time needed for making motor reach settling position is less, speed faster, with more robustness.

(2) compared with traditional automatic disturbance rejection controller, it is directed to expansion state to modified automatic disturbance rejection controller of the invention The structure of fal functions is improved in observer, uses error threshold values e_cIncrease linear feedback in the nonlinear feedback of fal functions Region, makes in the case where direct current generator site error is larger, and output signal response speed is accelerated, so as to improve the whole of system Body control performance.

Brief description of the drawings

Fig. 1 is the structural representation of the modified active disturbance rejection positioner of direct current generator of the invention；

Fig. 2 is the illustraton of model of direct current generator；

Fig. 3 is the response curve of modified ADRC and PID control contrast, wherein input be step signal, it is non-loaded；

Fig. 4 is the response curve of modified ADRC and PID control contrast, wherein being input into as step signal, load are step Signal；

Fig. 5 is the response curve of modified ADRC and PID control contrast, wherein being input into as step signal, load are sine Signal；

Fig. 6 is modified ADRC and tradition ADRC contrast curves, wherein amplitude 200rad of the input for step signal；

Fig. 7 is modified ADRC and tradition ADRC contrast curves, wherein amplitude 500rad of the input for step signal；

Fig. 8 is modified ADRC and tradition ADRC contrast curves, wherein amplitude 800rad of the input for step signal.

Specific embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to accompanying drawing and emulation, to the present invention It is explained in further detail.

As shown in figure 1, a kind of modified active disturbance rejection positioner of direct current generator, with direct current generator as controlled device, Outgoing position signal is controlled variable, including Nonlinear Tracking Differentiator, nonlinear state error feedback, extended state observer and disturbance Compensation；The input of Nonlinear Tracking Differentiator is expectation input signal；Two output ends of Nonlinear Tracking Differentiator are seen with expansion state respectively Two output ends for surveying device are connected, and obtain the error of error and differential；Two inputs of nonlinear state error feedback are to miss Difference and the error of differential, obtain feedforward control amount；Disturbance compensation is the feedforward control amount of nonlinear state error feedback output end It is connected with another output end in extended state observer, disturbance compensation obtains final controlled quentity controlled variable；It is right in extended state observer Fal functions are improved, using error threshold values e_cIncrease linear feedback region in the nonlinear feedback of fal functions to change letter Table structure, two inputs of extended state observer are respectively disturbance quantity and outgoing position signal；

As shown in Fig. 2 controlled device brshless DC motor, mathematical modeling is carried out with mechanism method to motor, it is to motor Outgoing position control state model be：

In formula, x₁=θ, θ turn over angle, x for motor₂=ω, ω are motor angular velocity；

k_eIt is back EMF coefficient, k_mIt is motor torque constant, T_LIt is load torque, R_mArmature resistance, J be load with The rotary inertia of rotor, k_e、k_m、T_L、R_mConstant collection is belonged to J；Y is outgoing position signal.

A kind of method for designing of the modified active disturbance rejection positioner of direct current generator, comprises the following steps：

The design of A, Nonlinear Tracking Differentiator：

Second order Nonlinear Tracking Differentiator is that signal is processed using discrete steepest Nonlinear Tracking Differentiator, and target is quick without super The tracking input signal of tune, while providing good differential signal, its input is expectation input signal r；

Described expectation input signal r by below equation calculating：

Obtain the output signal r of Nonlinear Tracking Differentiator₁And r₂, r₁It is after expecting that input signal r is processed through Nonlinear Tracking Differentiator Signal；r₂It is signal r₁Differential signal, in formula, k is current step, and T is sampling period, h_oIt is filtering factor, r₀For speed because Son, T, h_oAnd r₀Belong to constant collection；

Fhan (x in formula₁,x₂, r, h) and it is time-optimal control comprehensive function, its expression is：

In formula, r₁It is to expect input signal r through the signal after Nonlinear Tracking Differentiator treatment；r₂It is signal r₁Differential signal, D=hr, h are step-length, and a is intermediate variable,

Sign (x) is sign function, and expression formula is：

The design of B, extended state observer：

Two inputs of three rank extended state observers are respectively disturbance quantity b₀U and outgoing position signal y, first to expanding The fal functions opened in state observer are improved, the function expression fal after its improvement₁It is：

Wherein, e_cIt is fal₁Increase the error threshold values in linear feedback region in the nonlinear feedback of function, q is linear feedback Gain, a and δ is adjustable parameter, and e is error signal；Two described input signals are by following calculating：

Obtain the output signal z of three rank extended state observers₁、z₂And z₃, respectively one, two and three-stage shape state variable Tracking signal, wherein, β₀₁、β₀₂、β₀₃It is the gain of ESO feedback control amount, a₁、a₂, δ be adjustable parameter, b₀It is to object control The estimation of flow gain b processed, u is final controlled quentity controlled variable；

The design of C, nonlinear state error feedback：

The input signal of second nonlinear state error feedback is error e₁, differential error e₂, e₁=x₁-z₁、e₂=x₂- z₂, z₁、z₂It is respectively first and second output state of ESO, described input signal is calculated by below equation：

u₀=β₁fal(e₁,a₁,δ)+β₂fal(e₂,a₂,δ)；

Obtain the feedforward control amount u of nonlinear state error feedback output₀, in formula, β₁、β₂It is that nonlinear state error is anti- The feedback control flow gain of feedback, a₁、a₂It is adjustable parameter with δ, fal functions are original function, and its expression formula is：

In formula, a and δ is adjustable parameter, and e is error signal；

The design of D, disturbance compensation：

The output feedforward control amount u fed back by nonlinear state error₀The three-stage shape state exported with extended state observer Variation-tracking signal z₃, by following calculating：

Final controlled quentity controlled variable u is obtained, wherein, b₀It is the estimation to object control flow gain.

Embodiment

The present invention, as motor body, carries out mathematical modeling to motor, with mechanism method shown in Fig. 2 originally from DC torque The DC motor model figure for using is invented, the state model of its motor position control is：

Wherein, k_eIt is that back EMF coefficient is 6, k_mIt is that motor torque constant is 2, T_LIt is load torque, R_mIt is armature resistance It is that 2, J is load and the rotary inertia of rotor is 1, belongs to constant collection.X in formula₁=θ, x₂=ω, θ turn over angle for motor, ω is motor angular velocity.

In this instance, the purpose of system control is that input signal r tracking velocities are accelerated, and motor is reached settling position institute Need time is few, speed fast, stronger with more robustness and anti-external disturbance.

For the system, following controller can be designed according to Fig. 1：

The new automatic disturbance rejection controller of Position Control System of the Direct Current moter：

Wherein fal functions are traditional fal functions, fal₁Function is improved fal functions, and its expression formula is：

Parameter is adjusted using the thought of " modularization ", by connecting each other for existing between parameter in each module, The value that relative adaptation is determined by emulation experiment repeatedly is T=0.005, h₀=0.06, r₀=60, a₁=0.75, a₂= 1.25, β₁=100, β₂=10, β₀₁=200, β₀₂=1000, β₀₃=200, b₀=1.3, δ=0.01, q=0.001.

Simulation result as shown in figures 3-8, it can be seen from Fig. 3,4,5：When input is expected for step signal, follow-on Automatic disturbance rejection controller and classical PID controller compare, and rotate the angular displacement of 1rad, and the former reaches needed for settling position than the latter Time is few, and speed is fast, and especially when there is load disturbance, modified automatic disturbance rejection controller is not only than classical PID controller speed Degree is fast, and anti-interference is stronger.Fig. 6,7,8 understand：With the increase of input amplitude, reach and expect that the time of input can be more next It is more long, in the case of remaining parameter constant, change the structure of fal functions in extended state observer, can cause that output reaches To the time relative reduction of stabilization；Meanwhile, in the case where direct current generator site error is larger, follow-on automatic disturbance rejection controller Before steady-state value is reached, it accelerates to output signal response speed, so as to improve the overall control performance of system.

Claims (2)

1. the modified active disturbance rejection positioner of a kind of direct current generator, it is characterised in that：It is defeated with direct current generator as controlled device Out position signal is controlled variable, including Nonlinear Tracking Differentiator, nonlinear state error are fed back, extended state observer and disturbance are mended Repay；The input of Nonlinear Tracking Differentiator is expectation input signal；Two output ends of Nonlinear Tracking Differentiator are observed with expansion state respectively Two output ends of device are connected, and obtain the error of error and differential；Two inputs of nonlinear state error feedback are errors With the error of differential, feedforward control amount is obtained；Disturbance compensation be nonlinear state error feedback output end feedforward control amount with Another output end is connected in extended state observer, and disturbance compensation obtains final controlled quentity controlled variable；To fal in extended state observer Function is improved, using error threshold values e_cIncrease linear feedback region in the nonlinear feedback of fal functions to change function Structure, two inputs of extended state observer are respectively disturbance quantity and outgoing position signal；

Controlled device brshless DC motor, it is to the state model that motor outgoing position is controlled：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=-\frac{k_e{k}_m}{{\mathrm{JR}}_m}{x}_2-\frac{T_L}{J}+\frac{K_m}{{\mathrm{JR}}_m}\\ y=x_1\end{array}\right.;$

In formula, x₁=θ, θ turn over angle, x for motor₂=ω, ω are motor angular velocity；

k_eIt is back EMF coefficient, k_mIt is motor torque constant, T_LIt is load torque, R_mIt is armature resistance, J is load and rotor Rotary inertia, k_e、k_m、T_L、R_mBelong to constant to integrate y with J is outgoing position signal.

2. the method for designing of the modified active disturbance rejection positioner of a kind of direct current generator according to claim 1, it is special Levy and be：Comprise the following steps：

The design of A, Nonlinear Tracking Differentiator：

Second order Nonlinear Tracking Differentiator is that signal is processed using discrete steepest Nonlinear Tracking Differentiator, and target is quick non-overshoot Tracking input signal, while providing good differential signal, its input is expectation input signal r；Described expectation input letter Number r by below equation calculating：

$\left\{\begin{array}{c}{r}_1(k+1)=r_1\left(k\right)+{\mathrm{Tr}}_2\left(k\right)\\ r_2(k+1)=r_2\left(k\right)+Tfhan\left(r_1\right(k)-v_0(k),r_2(k),r_0,h_0)\end{array}\right.;$

Obtain the output signal r of Nonlinear Tracking Differentiator₁And r₂, r₁It is to expect input signal r through the letter after Nonlinear Tracking Differentiator treatment Number；r₂It is signal r₁Differential signal, in formula, k is current step, and T is sampling period, h_oIt is filtering factor, r₀It is velocity factor, T、h_oAnd r₀Belong to constant collection；

Fhan (x in formula₁,x₂, r, h) and it is time-optimal control comprehensive function, its expression is：

$\left\{\begin{array}{c}a=\left\{\begin{array}{c}{r}_2+\frac{(\sqrt{d^2+8r\left|r_1+{\mathrm{hr}}_2\right|}-rh)}{2}sign(r_1+{\mathrm{hr}}_2),\left|r_1+{\mathrm{hr}}_2\right|>h^{2}r\\ r_2+\frac{r_1+{\mathrm{hr}}_2}{h},\left|r_1+{\mathrm{hr}}_2\right|<h^{2}r\end{array}\right.\\ fhan=-\left\{\begin{array}{c}rsign\left(a\right),\left|a\right|>rh\\ r\frac{a}{d},\left|a\right|\&le;rh\end{array}\right.\end{array}\right.;$

In formula, r₁It is to expect input signal r through the signal after Nonlinear Tracking Differentiator treatment；r₂It is signal r₁Differential signal, d= Hr, h are step-length, and a is intermediate variable,

Sign (x) is sign function, and expression formula is：

$sign\left(x\right)=\left\{\begin{array}{c}1,x>0\\ 0,x=0\\ -1,x<0\end{array}\right.;$

The design of B, extended state observer：

Two inputs of three rank extended state observers are respectively disturbance quantity b₀U and outgoing position signal y, first to expansion shape Fal functions in state observer are improved, the function expression fal after its improvement₁It is：

${\mathrm{fal}}_1(e,a,\mathrm{\&delta;})=\left\{\begin{array}{c}\frac{e}{{\mathrm{\&delta;}}^{1-a}},\left|e\right|\&le;\mathrm{\&delta;}\\ {\left|e\right|}^{a}sign\left(e\right),\mathrm{\&delta;}<\left|e\right|<e_c\\ qe,\left|e\right|\&GreaterEqual;e_c\end{array}\right.$

Wherein, e_cIt is fal₁Increase the error threshold values in linear feedback region in the nonlinear feedback of function, q is the increasing of linear feedback Benefit, a and δ are adjustable parameters, and e is error signal；Two described input signals are by following calculating：

$\left\{\begin{array}{c}e=z_1-y\\ {\stackrel{\&CenterDot;}{z}}_1=z_2-{\mathrm{\&beta;}}_{01}{\mathrm{fal}}_1(e,a_0,{\mathrm{\&delta;}}_1)\\ {\stackrel{\&CenterDot;}{z}}_2=z_3-{\mathrm{\&beta;}}_{02}{\mathrm{fal}}_1(e,a_1,{\mathrm{\&delta;}}_1)+b_{0}u\\ {\stackrel{\&CenterDot;}{z}}_3=-{\mathrm{\&beta;}}_{03}{\mathrm{fal}}_1(e,a_2,{\mathrm{\&delta;}}_1)\end{array}\right.;$

Obtain the output signal z of three rank extended state observers₁、z₂And z₃, respectively one, two and three-stage shape state variable tracking Signal, wherein, β₀₁、β₀₂、β₀₃It is the gain of ESO feedback control amount, a₁、a₂, δ be adjustable parameter, b₀It is to object control amount The estimation of gain b, u is final controlled quentity controlled variable；

The design of C, nonlinear state error feedback：

The input signal of second nonlinear state error feedback is error e₁, differential error e₂, e₁=x₁-z₁、e₂=x₂-z₂, z₁、z₂It is respectively first and second output state of ESO, described input signal is calculated by below equation：u₀=β₁fal(e₁, a₁,δ)+β₂fal(e₂,a₂,δ)；

Obtain the feedforward control amount u of nonlinear state error feedback output₀, in formula, β₁、β₂It is nonlinear state error feedback Feedback control flow gain, a₁、a₂It is adjustable parameter with δ, fal functions are original function, and its expression formula is：

$fal(e,a,\mathrm{\&delta;})=\left\{\begin{array}{cc}{\left|e\right|}^{a}sign\left(e\right),& \left|e\right|>\mathrm{\&delta;}\\ \frac{e}{{\mathrm{\&delta;}}^{1-a}},& \left|e\right|\&le;\mathrm{\&delta;}\end{array}\right.;$

A and δ are adjustable parameters, and e is error signal；

The design of D, disturbance compensation：

The output feedforward control amount u fed back by nonlinear state error₀With extended state observer export three-stage shape state variable with Track signal z₃, by following calculating：

$u=u_0-\frac{z_3}{b_0};$

Final controlled quentity controlled variable u is obtained, wherein, b₀It is the estimation to object control flow gain.