CN104090490B - A kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm - Google Patents

Abstract

The invention relates to a closed-loop control method of an input shaper based on a chaotic particle swarm optimization algorithm, which belongs to the technical field of drive control methods in the start-up process of coaxial transmission machinery; for the chattering problem in the start-up process of coaxial transmission machinery, the control proposed by the invention The method performs closed-loop control on the transmission mechanism, and the effectiveness and feasibility of this control method are proved by the experimental results; in the off-line state, the double pulse input shaper is optimized by using the chaotic particle swarm optimization algorithm, and its optimized parameters are obtained , and then use the optimized input shaper to control the PD closed-loop actuator; the present invention aims at the torsional vibration problem during the start-up process of the coaxial transmission printing machine, and proposes a control based on chaotic particle swarm optimization for the parameter self-tuning of the input shaper algorithm. This control greatly suppresses the torsional vibration of the system and at the same time realizes the fast vibration-free response of the system.

Description

A closed-loop control method of input shaper based on chaotic particle swarm optimization algorithm

technical field

The invention relates to a closed-loop control method of an input shaper based on a chaotic particle swarm optimization algorithm, and belongs to the technical field of drive control methods in the start-up process of coaxial transmission machinery.

Background technique

During the start-up process of the coaxial transmission printing machine, due to the long-axis connection, the long transmission distance between the shafts, the low stiffness of the system, the heavy load and many other factors, the torsional vibration will occur during the start-up. The torsional vibration phenomenon is not only It affects the steady-state time of the start-up process, and it will also bring a great impact to the transmission shaft, thereby affecting the service life of the printing press.

For the above reasons, the input shaper method is used to filter the system in time domain. However, the traditional zero-oscillation input shaper requires precise modeling, and the parameters interact with each other, making tuning difficult. The invention introduces a chaotic particle swarm optimization algorithm to optimize the controller parameters, realizes the online collection and offline optimization of system signals, and maintains high precision at the same time by transforming the system process transfer function.

Contents of the invention

The purpose of the present invention is to provide a closed-loop control method of input shaper based on chaotic particle swarm optimization algorithm. In view of the chattering problem in the start-up process of coaxial transmission machinery, the control method proposed by the present invention performs PD control on the transmission mechanism, and through Experimental results prove the effectiveness and feasibility of this control method.

In order to achieve the above object, the technical solution adopted in the present invention is a closed-loop control method of the input shaper based on the chaotic particle swarm optimization algorithm. In the off-line state, the input shaper of the double pulse is optimized by using the chaotic particle swarm optimization algorithm. , to obtain its optimal parameters, and then use the obtained optimal input shaper to control the PD actuator, the method includes the following specific steps,

S1 uses simple PD parameters to adjust the movement of the actuator, and it will remain unchanged in the future. The system inputs the speed signal x(t) to drive the movement of the mechanical system, and uses the encoder to collect the speed curve v(t) and the final stable speed from the system output shaft. u;

S2 According to the stable speed u of the output shaft of the system, the parameters of the double-pulse input shaper are obtained by using the chaotic particle swarm optimization algorithm. The frequency domain expression of the double-pulse input shaper is: Among them, A _i and t _i are respectively the amplitude of the pulse sequence and its corresponding time lag, and t ₁ = 0 can be set for optimal time, then the formula is: In order to make the system output reach a stable speed u, add the constraint equation A ₁ +A ₂ =1, A _i >0;

The process of the chaotic particle swarm optimization algorithm is as follows,

S2.1 Initialize and set the relevant parameters of the input shaper; including the value range of A ₁ , A ₂ and t ₂ , since A ₁ +A ₂ =1, A _i >0, the value range of A ₂ is [0～ 1], A ₁ ＝1-A ₂ ; the selection of t ₂ is more important, because too large value range of t ₂ will make the chaotic particle swarm optimization algorithm premature and fall into local minimum value, but too small value range optimizes When the optimal solution is missed, the delay time of the signal should be estimated according to the model of the system first. The delay time of the multi-substance rotating platform is small, so the value range of _t2 is given as [0-5].

Set the relevant parameters of chaotic particle swarm; including determining the size of particle swarm m=30, particle search space dimension D=2 (that is, two particles A ₂ and t ₂ ), the maximum number of iterations k is 30, and the maximum number of steps n of chaotic search is 10. Search space range That is, it is determined according to the range of A ₂ and t ₂ ), the learning factor c ₁ =c ₂ =2, the range of inertial weight w _min =0.6, and the individual optimal position of the i-th particle is the optimal among all (that is, the global optimal ), randomly initialize the position and velocity of each particle;

S2.2 Use the position vector of each particle as the input shaper parameter in turn, and simulate the speed motion curve collected back in turn to obtain the simulation curve; calculate the fitness value of each particle according to the simulation curve, and use it as a measure of particle The basis of the position is good or bad; set the fitness function as

In the formula, v(t) is the instantaneous speed of the simulation curve, u is the final stable speed of the system output shaft, ftr is a large penalty function value, specifically defined as

Among them, t _r is the rise time of the simulation curve, when the rise time is not reached within the specified simulation period, ftr is a larger penalty function value; when the time reaches the rise time, ftr takes the value t _r ;

S2.3 Calculate the fitness value of each particle according to the fitness function, if the fitness value of the particle is less than the previous fitness value of the particle itself, replace it with the current position of the particle If the fitness value of the particle is less than the previous fitness value of the particle swarm, replace it with the particle's position

S2.4 Update the velocity and position of each particle. In the kth cycle, the position vector of the i-th particle is The flight speed is The optimal position of the current particle individual is The current global optimal position is (d=1,2...,D), then during the k+1th cycle, the i-th particle velocity iterative equation is position vector iterative equation

S2.5 Calculate the fitness value of each particle, and retain the best 20% of the best particles in the group;

S2.6 Perform a chaotic local search for the best particle, and update and

The process of the chaotic local search algorithm is as follows,

S2.6.1 loop initialization n=0, d=1;

S2.6.2 Using the i-th particle position vector The d-th dimension variable of , according to the following formula to get the chaotic variable d=1,2,...D, where x _max,d and x _min,d are the upper and lower bounds of the search for the d-th dimension variable;

S2.6.3 Calculate the chaotic variables for the next iteration d=1,2,3...D;

S2.6.4 According to chaotic variables get the position vector If d=D, then go to S2.6.5, otherwise d=d+1, go to S2.6.2;

S2.6.5 According to the new position vector Get the fitness value, compare it with the original position vector, if the fitness value is better or the chaotic search has reached the maximum number of iteration steps, use the new position vector as the result of the chaotic search, otherwise set k=k+1, go to S2.6.2 .

S2.7 When k reaches the set number of iterations, end the rolling optimization process, and output parameter optimization values. Otherwise, go to step S2.8.

S2.8 Shrink the search area for each space variable of the vector according to the following formula:

x _min,d ＝max{x _min,d ,x _g,d -r*(x _max,d -x _min,d )}

x _max,d ＝min{x _man,j ,x _g,d -r*(x _max,d -x _min,d )}

where x _{g, d} represent the current The value of the d-th dimension variable, r is a random number of [0,1];

S2.9 When k reaches the set number of iterations, end the rolling optimization process, and output the parameter optimization value; otherwise, randomly generate the remaining 80% of the particles in the group in the shrunk space, and turn to S2.2;

S3 uses the obtained optimal shaper to perform PD control on the actuator.

Compared with the prior art, the beneficial effect of the present invention is that the present invention proposes a closed-loop control method of the input shaper based on the chaotic particle swarm optimization algorithm for the torsional vibration problem during the start-up process of the coaxial transmission printing machine. This control greatly suppresses the torsional vibration of the system and at the same time realizes the fast vibration-free response of the system.

Description of drawings

Figure 1 is a structural block diagram of the control method application system.

Figure 2 is a diagram of the chaotic particle swarm optimization process.

Figure 3 is the optimization model diagram under simulink.

Figure 4a is the original PD system start-up curve.

Fig. 4b is a Fourier transform diagram of the start-up curve of the original PD system.

Figure 5a is a graph showing the start-up of a PD system with an input shaper.

Figure 5b is a Fourier transform diagram of the start-up curve of a PD system with an input shaper.

Detailed ways

The present invention is an input shaper closed-loop control method based on chaotic particle swarm optimization algorithm. Referring to Fig. 1, the input signal enters the mechanical system in the online state and collects the output shaft speed motion curve, and then uses the chaotic particle swarm optimization algorithm to go offline according to the collection curve. Optimize the parameters of the input shaper, and then use the optimized input shaper to control the movement of the PD mechanical system, which can filter out the frequency points that resonate with the actuator in the start signal, greatly suppressing the torsional vibration of the system and realizing fast system speed. No vibration response.

The off-line optimization method of chaotic particle swarm optimization is shown in Figure 2. The bridge between the chaotic particle swarm algorithm and the simulink model is the particle (that is, A ₂ and t ₂ in the input shaper formula). The optimization process is as follows: randomly generate a particle swarm, assign the particles in the particle swarm to the simulink model in turn and input the parameters A ₂ and t ₂ in the shaper, then run the simulink model of the control system to obtain the fitness value of the particle, and finally Judging whether it is possible to exit the algorithm, if not, update the velocity and position of the particles, that is, update A ₂ and t ₂ .

Figure 3 is an optimization model diagram under simulink. The collected speed signal is input to the shaper module to obtain the simulation curve, and then the fitness value is obtained through the fitness function module.

Figure 4a is the start-up curve of the original system, which is the response to a step signal with an input amplitude of 8600 in the multi-mass PD closed-loop rotating system. System oscillation always exists, and the overshoot is about 13.953%; From the leaf transformation diagram, it can be clearly seen that there is a low-frequency vibration point.

Figure 5a is the start-up curve of the PD system with an input shaper. Under the excitation of the same amplitude step signal, the overshoot of the system is only 3.488%, the oscillation is suppressed, and the adjustment time is only 700ms; Figure 5b is The Fourier transform plot of the start-up curve of the PD system with an input shaper, and it can be seen that the low-frequency vibration point is eliminated.

Claims (2)

1. a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm, it is characterised in that：Offline Under state, the input shaper of dipulse is optimized with Chaos particle swarm optimization algorithm, obtains its optimized parameter, then PD control is carried out to executing agency with obtained optimal input shaper, this method comprises the following specific steps that,

S1 is moved with PD parameter regulations executing agency, system input speed signal x (t), mechanical system motion is driven, with coding Device collects its rate curve v (t) and final stabilized speed u from system output shaft；

S2 obtains dipulse input shaper according to the stabilized speed u of system output shaft using Chaos particle swarm optimization algorithm The frequency-domain expression of parameter, dipulse input shaper isWherein A_iAnd t_iIt is pulse train respectively Amplitude and its corresponding time lag, t is enabled by time optimal₁=0, then obtaining formula is：To keep system defeated Go out to reach stabilized speed u, addition constraint equation A₁+A₂=1, A_i> 0；

The process of the Chaos particle swarm optimization algorithm is as follows,

S2.1 is initialized and input shaper relevant parameter is arranged；Including A₁、A₂And t₂Value range, due to A₁+A₂=1, A_i > 0, therefore A₂Value range [0~1], A₁=1-A₂；The delay time of signal is estimated according to the model of system first, it is more The delay of mass block rotatable platform is small, therefore given t₂Value range be [0~5]；

Population relevant parameter is set：Scale number m=30, particle search space dimensionality D=2, i.e. arteries and veins including determining population Rush the amplitude A of sequence₂, pulse train time lag t₂, iterations k is up to 30, and Chaos Search maximum step number n is 10, and search is empty Between rangeStudying factors c₁=c₂=2, inertia weight w=0.6, i-th of particle personal best particle areWhereinIt is allIn optimal, the position of each particle in random initializtion population It sets and speed；

S2.2 regard the position vector of each particle as input shaper parameter successively, is moved successively to the speed of acquisition back bent Line is emulated, and simulation curve is obtained；The fitness value of each particle is calculated according to simulation curve, and as measurement particle The foundation of position quality；Fitness function, which is arranged, is

In formula, v (t) is the instantaneous velocity of simulation curve, and u is the final stabilized speed of system output shaft, and ftr is penalty value, It is specifically defined as

Wherein, t_rFor the simulation curve rise time, when not reaching the rise time in specified emulation cycle, ftr values are k_t；When the time reaching the rise time, ftr values are t_r；

S2.3 calculates the fitness value of each particle according to fitness function, if the fitness value of the particle is less than particle certainly The pervious fitness value of body is then replaced with the current location of the particleIf the particle fitness value is less than before population Fitness value, then with the position of the particle replace

S2.4 is updated the speed of each particle and position, and when kth time recycles, i-th of particle position vector is at this timeSpeed isCurrent particle personal best particle isCurrent global optimum position isD=1,2..., D, Then when+1 cycle of kth, i-th of particle rapidity iterative equation isPosition Vector iterative equation

S2.5 calculates the fitness value of each particle, retains in group 20% best particle；

S2.6 executes chaos local search to best particle, and updatesWith

The process of the chaos local search is as follows,

S2.6.1 loop initializations k=0, d=1；

S2.6.2 uses i-th of particle position vectorD tie up variable, obtain Chaos Variable according to the following formulaD=1,2 ... D, wherein X_max,dAnd X_min,dThe search bound of variable is tieed up for d；

S2.6.3 calculates the Chaos Variable of lower step iterationD=1,2,3...D；

S2.6.4 is according to Chaos VariableObtain position vector If d =D then turns S2.6.5, otherwise d=d+1, turns S2.6.2；

S2.6.5 is according to new position vectorFitness value is obtained, compared with original position vector, if optimal adaptation Angle value or Chaos Search have reached greatest iteration step number, using new position vector as Chaos Search as a result, otherwise setting k=k+1, Turn S2.6.2；

S2.7 terminates rolling optimization process, output parameter optimal value after k reaches the iterations of setting；Otherwise, step is gone to S2.8；

S2.8 shrinks region of search by following formula to each space variable of vector：

x_min,d=max { x_min,d,x_g,d-r*(x_max,d-x_min,d)},0≤r≤1

x_max,d=min { x_max,d,x_g,d-r*(x_max,d-x_min,d)},0≤r≤1

Wherein X_{G, d}, indicate currentD dimension variable value；

S2.9 terminates rolling optimization process, output parameter optimal value after k reaches the iterations of setting；Otherwise after shrinking Space in randomly generate in group remaining 80% particle, turn S2.2；

S3 carries out PD control with obtained optimal reshaper to executing agency.

2. a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm according to claim 1, It is characterized in that：Described search spatial dimensionX_min=[0,0], X_max=[1,5], i.e., according to A₂、t₂Range It determines.