CN105186959A - Parameter setting method of sliding mode controller of servo system - Google Patents

Abstract

The invention, which belongs to the motion control field, relates to a parameter setting method of a sliding mode controller of a servo system. The method comprises: step one, a transfer function model of a servo system is established according mechanical and electrical structures of the servo system and needed parameters in the model are obtained; step two, a corresponding system simulink simulation model is established and input and output interfaces needed for a particle swarm optimization algorithm are left; step three, a proper fitness function is selected according to location tracking error and speed tracking error demands; step four, programming is carried out in matlab to optimize a particle swarm; step five, corresponding c,k, and epsilon of location vectors are transferred into the simulink simulation model to obtain a location error response and a speed error response of the system; step six, the speed and location of each particle are updated; step seven, when the k reaches a set maximum iterations number, the iteration process is completed and an optimization result is outputted; otherwise, the operation of the step five is carried out again; and step eight, a global optimal location vector is substituted into a sliding mode controller of the servo system. According to the invention, buffeting amplitude minimization or complete elimination of buffeting can be realized; and the tracking error can be minimized.

Description

A kind of servo system sliding-mode attitude conirol method

Technical field

The present invention is a kind of servo system sliding-mode attitude conirol method, belongs to motion control field.

Background technology

Sliding formwork controls (SlidingModeControl), is proposed the fifties in last century by the former Russian scholar.It is a kind of discontinuous nonlinear control method in essence, maximum feature is that controller architecture is changed in time, in the dynamic process of system, according to the current state set (such as deviation, the derivative of output and different order), structure and the output of controller is changed according to the algorithm preset, guarantee system amount to be controlled does reciprocating motion by a small margin on a preset condition based on the state trajectory expected, can ensure that system has excellent robustness when Parameters variation and external disturbance.

In complicated servo system, exist and such as drive the non-linear factors such as saturated, External force interference, motor force oscillation, for load and variations in temperature sensitivity, have the change of parameter, mechanical resonant and measurement noises, these factors cannot modeling accurately.Sliding mode controller solves this problem, and the characteristic good of the anti-Parameters variation of sliding mode controller disturbance rejection, is suitable in complicated servo system.But owing to there is time, Spatial lag in system, measure inaccuracy, inertial element, makes the system adopting sliding formwork to control there will be chattering phenomenon, and choose reasonable parameter suppresses buffeting and optimization system dynamic response to have very high using value for the application of sliding mode controller in engineering.

Summary of the invention

The object of this invention is to provide a kind of servo system sliding-mode attitude conirol method, is the problem of buffeting problem in order to solve sliding mode controller and the dynamic property optimizing sliding mode controller.

Described object is realized by following scheme: a kind of described servo system sliding-mode attitude conirol method, and its method step is:

Step one: set up servo system transfer function model according to the machinery of servo system and electrical structure, obtain parameter required in model, described parameter comprises: resistance suffered by motor, motor load size, counter electromotive force of motor constant, motor torque constant, armature circuit resistance, armature inductance, according to reality by the above-mentioned corresponding parameter of structure choice controlling motor;

Step 2: the sliding mode controller according to servo system models and employing builds corresponding system simulink simulation model, reserves the input and output interface needed for particle swarm optimization algorithm;

Step 3: according to position tracking error and speed tracing error requirement, select suitable fitness function, be set to wherein parameter k _vand k _sfor being not less than the number of 0, represent the weight of velocity error and site error, e _vrepresent velocity error, e _srepresent site error, t ₀for the initial time of fitness function assessment, t ₁for the end time of fitness function assessment;

Step 4: in conjunction with interface and the fitness function of simulink model, programme in matlab and population is optimized, the population m of initialization population, maximum iteration time N, the dimension D of search volume is set to 3, corresponding 3 parameter c, k and ε to be optimized, space search scope corresponds to 3 parameters and is respectively [c _min, c _max], [k _min, k _max] and [ε _min, ε _max], Studying factors c ₁, c ₂value be all set to 2, habitual weight w gets 0.6, and particle position vector velocity initial value is obtained by random process, three dimensions corresponding three parameter c, k and ε to be optimized respectively of particle position vector, local and global optimum position vector initial value P _iand P _gsubstitute into fitness function by particle initial position to calculate;

Step 5: by c corresponding for position vector, k and ε imports site error and the velocity error response that simulink simulation model obtains system into, the fitness value of particle is calculated according to fitness function, if the fitness value of this particle be less than particle before fitness value, then replace p by the current location of this particle _i; If this particle fitness value is less than the fitness value of population global optimum, then replace p with the position of this particle _g;

Step 6: upgrade the speed of each particle and position, kth time circulation time, i-th particle position vector is now flying speed is current particle personal best particle is p _i=(p _i1, p _i2..., p _iD), current global optimum position is p _g=(p _g1, p _g1..., p _gD), then kth+1 circulation time, i-th particle rapidity is respectively tieed up and can be determined by following equation: $v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1{r}_1(p_{id}-x_{id}^k)+c_2{r}_2(p_{gd}-x_{id}^k),$ Position vector iteration is respectively tieed up and is $x_{id}^{k+1}=x_{id}^k+v_i^{k+1},$ Wherein r ₁and r ₂be the random number between 0 to 1, d is dimension, and value is from 0 to D;

Step 7: after k reaches the maximum iteration time of setting, finishing iteration process, exports optimum results, otherwise returns step 5;

Step 8: the global optimum's position vector after the optimal parameter obtain optimization and iteration terminate substitutes into servo system sliding-mode controller, servo system sliding-mode controller is applied to servo system, whether the property indices of check system meets the demands, if performance index meet, tuning process terminates, otherwise, enter next round optimization until meet.

The present invention can realize buffet amplitude minimum or buffet eliminate completely, tracking error reaches minimum.Parameter after fully optimised is the optimized parameter of setting models under given fitness function.

Accompanying drawing explanation

Fig. 1 is the servo system block diagram of the employing sliding mode controller that the inventive method relates to.

Embodiment

Embodiment one: shown in composition graphs 1, illustrates the technical scheme of this embodiment, and its method step is:

Step one: set up servo system transfer function model according to the machinery of servo system and electrical structure, obtain parameter required in model, described parameter comprises: resistance suffered by motor, motor load size, counter electromotive force of motor constant, motor torque constant, armature circuit resistance, armature inductance, according to reality by the above-mentioned corresponding parameter of structure choice controlling motor;

Step 2: the sliding mode controller according to servo system models and employing builds corresponding system simulink simulation model, reserves the input and output interface needed for particle swarm optimization algorithm;

Step 3: according to position tracking error and speed tracing error requirement, select suitable fitness function, be set to wherein parameter k _vand k _sfor being not less than the number of 0, represent the weight of velocity error and site error, e _vrepresent velocity error, e _srepresent site error, t ₀for the initial time of fitness function assessment, t ₁for the end time of fitness function assessment;

Step 4: in conjunction with interface and the fitness function of simulink model, programme in matlab and population is optimized, the population m of initialization population, maximum iteration time N, the dimension D of search volume is set to 3, corresponding 3 parameter c, k and ε to be optimized, space search scope corresponds to 3 parameters and is respectively [c _min, c _max], [k _min, k _max] and [ε _min, ε _max], Studying factors c ₁, c ₂value be all set to 2, habitual weight w gets 0.6, and particle position vector velocity initial value is obtained by random process, three dimensions corresponding three parameter c, k and ε to be optimized respectively of particle position vector, local and global optimum position vector initial value P _iand P _gsubstitute into fitness function by particle initial position to calculate;

Step 5: by c corresponding for position vector, k and ε imports site error and the velocity error response that simulink simulation model obtains system into, the fitness value of particle is calculated according to fitness function, if the fitness value of this particle be less than particle before fitness value, then replace p by the current location of this particle _i; If this particle fitness value is less than the fitness value of population global optimum, then replace p with the position of this particle _g;

Step 6: upgrade the speed of each particle and position, kth time circulation time, i-th particle position vector is now flying speed is current particle personal best particle is p _i=(p _i1, p _i2..., p _iD), current global optimum position is p _g=(p _g1, p _g1..., p _gD), then kth+1 circulation time, i-th particle rapidity is respectively tieed up and can be determined by following equation: $v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1{r}_1(p_{id}-x_{id}^k)+c_2{r}_2(p_{gd}-x_{id}^k),$ Position vector iteration is respectively tieed up and is $x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1},$ Wherein r ₁and r ₂be the random number between 0 to 1, d is dimension, and value is from 0 to D;

Step 7: after k reaches the maximum iteration time of setting, finishing iteration process, exports optimum results, otherwise returns step 5;

Step 8: the global optimum's position vector after the optimal parameter obtain optimization and iteration terminate substitutes into servo system sliding-mode controller, servo system sliding-mode controller is applied to servo system, whether the property indices of check system meets the demands, whether elimination is buffeted, if performance index meet and do not have chattering phenomenon, then tuning process terminates, otherwise, enter next round optimization until meet.

Operation principle: in Fig. 1, k _ufor controlled quentity controlled variable gain, k _efor counter electromotive force of motor constant, k _tfor electro mechanic time constant, L is armature resistance, and R is armature inductance.Sliding mode controller can be determined by two parts: switching function and tendency rate, switching function determination sliding-mode surface, and tendency rate certainty annuity is convergence sliding-mode surface in which way, and the two meets to meet stability, the behavior of system near sliding-mode surface controlled by tendency rate.Invention is for the typical servo system sliding-mode Controller gain variations of one, and its model can be expressed as $\left\{\begin{array}{c}s=ce+\stackrel{\·}{e}\\ \stackrel{\·}{s}=-\mathrm{\ϵ}\mathrm{sgn}\left(s\right)-ks\end{array}\right.,$ Wherein for switching function.Tendency rate is this tendency rate is called as exponential approach rate, in inhibitory control device chattering phenomenon, have good effect.Optimization is regulated to the parameter ε of exponential approach rate and k, system can be made to move to sliding-mode surface with speed faster, and the high frequency of system can be suppressed to buffet, reach and obtain best balance point in the dynamic quality and chattering suppress of system, significant for the servo system requiring good rapidity.Exponential approach item in tendency rate separate as s=s (0) e ^-kt, make use of in the motion process of state to sliding-mode surface, be first with index speed convergence, shorten the control time, indicial response makes again hourly velocity near arrival sliding-mode surface very little, avoids that to move to hourly velocity near sliding-mode surface excessive.Meanwhile, because simple exponential approach rate is an asymptotic process near sliding-mode surface, can not ensure that finite time arrives, sliding mode not on sliding-mode surface, so add a constant speed convergence item same-action with it.Constant speed convergence item is visible when s → 0 velocity of approach be ε instead of 0, with this ensure finite time arrive sliding-mode surface.In actual use, there is good inhibition to buffeting to have good dynamic characteristic simultaneously, needing the value suitably increasing k, reducing the value of ε.By the optimization to parameter c, k and the ε of 3 in sliding mode controller, reach and system is responded fast, simultaneously adjusting system, eliminate and buffet.The optimal anchor direction correctness of particle swarm optimization algorithm and the reliability of result depend on the fitness function chosen.The performance requirement of servo system is the tracking realizing position and speed, generally three sections can be divided into: accelerate in running, at the uniform velocity and slow down, particle cluster algorithm is adopted to be optimized sliding mode controller, optimizing process can carry out separately for each stage, be met the optimized parameter of each stage running performance requirement, also can give overall consideration to, be met the more excellent parameter of whole service process performance requirement.If at the uniform velocity the section time started is t ₁₁, the end time is t ₁₂, the accelerating sections time started is t ₂₁, end at t ₂₂, the braking section time started is t ₃₁, end at t ₃₂, velocity error is e _v, site error is e _s.If only have higher tracer request at the uniform velocity section, fitness function can be set to wherein parameter k _vand k _sfor being not less than the number of 0, represent the weight of velocity error and site error, concrete numerical value can adjust according to actual conditions, as higher to position error requirements, can increase k _svalue; If higher to accelerating sections tracer request, fitness function can be set to similarly, the fitness function of braking section can be obtained.If all high to the requirement of full section, can be set to t is the control action end time.

Claims (1)

1. a servo system sliding-mode attitude conirol method, is characterized in that its method step is:

Step one: set up servo system transfer function model according to the machinery of servo system and electrical structure, obtain parameter required in model, described parameter comprises: resistance suffered by motor, motor load size, counter electromotive force of motor constant, motor torque constant, armature circuit resistance, armature inductance, according to reality by the above-mentioned corresponding parameter of structure choice controlling motor;

Step 2: the sliding mode controller according to servo system models and employing builds corresponding system simulink simulation model, reserves the input and output interface needed for particle swarm optimization algorithm;

Step 3: according to position tracking error and speed tracing error requirement, select suitable fitness function, be set to wherein parameter k _vand k _sfor being not less than the number of 0, represent the weight of velocity error and site error, e _vrepresent velocity error, e _srepresent site error, t ₀for the initial time of fitness function assessment, t ₁for the end time of fitness function assessment;

Step 4: in conjunction with interface and the fitness function of simulink model, programme in matlab and population is optimized, the population m of initialization population, maximum iteration time N, the dimension D of search volume is set to 3, corresponding 3 parameter c, k and ε to be optimized, space search scope corresponds to 3 parameters and is respectively [c _min, c _max], [k _min, k _max] and [ε _min, ε _max], Studying factors c ₁, c ₂value be all set to 2, habitual weight w gets 0.6, and particle position vector velocity initial value is obtained by random process, three dimensions corresponding three parameter c, k and ε to be optimized respectively of particle position vector, local and global optimum position vector initial value P _iand P _gsubstitute into fitness function by particle initial position to calculate;

Step 5: by c corresponding for position vector, k and ε imports site error and the velocity error response that simulink simulation model obtains system into, the fitness value of particle is calculated according to fitness function, if the fitness value of this particle be less than particle before fitness value, then replace p by the current location of this particle _i; If this particle fitness value is less than the fitness value of population global optimum, then replace p with the position of this particle _g;

Step 6: upgrade the speed of each particle and position, kth time circulation time, i-th particle position vector is now flying speed is current particle personal best particle is p _i=(p _i1, p _i2..., p _iD), current global optimum position is p _g=(p _g1, p _g1..., p _gD), then kth+1 circulation time, i-th particle rapidity is respectively tieed up and can be determined by following equation: $v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1{r}_1(p_{id}-x_{id}^k)+c_2{r}_2(p_{gd}-x_{id}^k),$ Position vector iteration is respectively tieed up and is $x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1},$ Wherein r ₁and r ₂be the random number between 0 to 1, d is dimension, and value is from 0 to D;

Step 7: after k reaches the maximum iteration time of setting, finishing iteration process, exports optimum results, otherwise returns step 5;

Step 8: the global optimum's position vector after the optimal parameter obtain optimization and iteration terminate substitutes into servo system sliding-mode controller, servo system sliding-mode controller is applied to servo system, whether the property indices of check system meets the demands, if performance index meet, tuning process terminates, otherwise, enter next round optimization until meet.