CN103885338B - A kind of input shaper parameter self-tuning control method based on particle swarm optimization algorithm - Google Patents

Abstract

The invention relates to an input shaper parameter self-tuning control method based on a particle swarm optimization algorithm, which belongs to the technical field of drive control methods in the start-up process of coaxial transmission machinery; in view of the chattering problem in the start-up process of coaxial transmission machinery, the invention proposes The control method performs feed-forward control on the transmission mechanism, and the experimental results prove the effectiveness and feasibility of this control method; in the off-line state, the particle swarm optimization algorithm is used to optimize the input shaper of the double pulse, and its Optimum parameters, and then use the obtained optimal input shaper to feed-forward control the actuator; the present invention aims at the torsional vibration problem in the start-up process of the coaxial transmission printing machine, and proposes a parameter automatic input shaper based on particle swarm optimization. Tuned control algorithm. This control greatly suppresses the torsional vibration of the system, while sacrificing the dynamic performance of the system to a small extent, and realizes a fast vibration-free response of the system.

Description

A self-tuning control method of input shaper parameters based on particle swarm optimization algorithm

technical field

The invention relates to a parameter self-tuning control method of an input shaper based on a 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 the 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 self-tuning control method for input shaper parameters based on 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 feedforward control on the transmission mechanism, And the 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 self-tuning control method of input shaper parameters based on particle swarm optimization algorithm. In an offline state, the particle swarm optimization algorithm is used to optimize the input shaper of double pulses. , to obtain its optimal parameters, and then use the obtained optimal input shaper to feed-forward control the actuator, the method includes the following specific steps,

S1 inputs the speed signal x(t) to the original system, drives the mechanical system to move, uses the encoder to collect the speed curve v(t) and the final stable speed u from the output shaft of the system;

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 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 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 the too large value range of t ₂ will make the particle swarm algorithm premature and fall into the local minimum value, but the too small value range optimization The optimal solution will be missed, and the delay time of the signal must be estimated according to the system model firstly. The delay time of the multi-substance rotating platform is relatively small, so the value range of given t ₂ is [0～5];

Set particle swarm related parameters; including determining the size of particle swarm m=100, particle search space dimension D=2, that is, two particles A ₂ and t ₂ , the maximum number of iterations k is 60, and the range of search space L _d = [00], U _d = [00], that is, determined according to the range of A ₂ and t ₂ , learning factor c ₁ =c ₂ =2, range of inertial weight w _min =0.6, optimal position of the i-th particle for in for all The optimal in , randomly initialize the position and velocity of each particle;

S2.2 The position vector of each particle is used as the input shaper parameter in turn, and the speed curve collected is simulated in turn to obtain the simulation curve; the fitness value of each particle is calculated according to the simulation curve, and it is used as a measure of the particle position The basis of pros and cons; set the fitness function as

$\begin{array}{cc}\mathrm{<span\; class="notranslate">\; min</span>}& \mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; r</span>}\end{array}$

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 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 penalty function value k _t ; when the time reaches the rise time, ftr is set to 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 when the k+1th cycle, the i-th particle velocity iteration equation is position vector iterative equation w, r ₁ , r ₂ represent the random weight of each iteration equation parameter;

S2.5 When k reaches the set number of iterations, end the rolling optimization process, and output parameter optimization values; otherwise, go to step S2.2;

S3 uses the obtained optimal shaper to perform feed-forward control on the actuator.

Compared with the prior art, the beneficial effect of the present invention lies in that the present invention proposes a control algorithm for self-tuning of input shaper parameters based on particle swarm optimization 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, while sacrificing the dynamic performance of the system to a small extent, and realizes a 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 particle swarm optimization process.

Figure 3 is the optimization model diagram under simulink.

Fig. 4 is the start-stop curve diagram of the original system.

Figure 5 is a system start-stop curve diagram with an input shaper.

Figure 6 is a frequency domain comparison diagram of the start-stop curves of the original system and the system with an input shaper.

detailed description

The present invention is a control method based on particle swarm optimization for parameter self-tuning of the input shaper. Referring to Figure 1, the input signal enters the mechanical system in the online state and collects the output shaft speed motion curve, and then uses the particle swarm optimization algorithm to go offline according to the collected curve. Optimize the parameters of the input shaper, and then feed-forward control the optimized input shaper to the mechanical system, so that the frequency points that resonate with the actuator in the start signal can be filtered out, and the torsional vibration of the system can be greatly suppressed while being relatively small. The dynamic performance is sacrificed to achieve a fast vibration-free response of the system. .

The off-line optimization method of particle swarm optimization is shown in Figure 2. The bridge between the 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 4 is the start-stop curve of the original system. When a step signal with an amplitude of 25,000 is used to excite the multi-mass rotating system, due to the existence of the resonance point, the system vibrates very obviously during the start-up and stop process. During the starting process, the vibration peak can reach 4.78×10 ⁴ pulses/second, the maximum overshoot is 55.7%, the oscillation time can reach 15 seconds, and the oscillation is obvious after a long response time.

Figure 5 is the start-stop curve diagram of the system with input shaper. Under the excitation of the step signal with the same amplitude, the multi-mass rotating system outputs a final value of 24490 pulses/s with an open-loop system, and the error is less than 5% of the steady-state signal. % think the system is stable, the overshoot of the system is only 2.327%, the system enters a stable state without oscillation, and the response time is only 700ms. The response speed is greatly improved and the oscillation is suppressed.

Figure 6 is a frequency domain comparison diagram of the start-stop curves of the original system and the system with an input shaper. It can be seen that the main cause of system oscillation is a low-frequency vibration point of about 1HZ. The input signal enters the input shaper and then enters the mechanical system. , this resonance point is eliminated.

Claims (1)

1. A kind of input shaper parameter self-tuning control method based on particle swarm optimization algorithm, it is characterized in that: under off-line state, utilize particle swarm optimization algorithm to optimize the input shaper of double pulse, obtain its optimum parameter, Then use the obtained optimal input shaper to feed-forward control the actuator, the method includes the following specific steps, S1 inputs the speed signal x(t) to the original system, drives the mechanical system to move, uses the encoder to collect the speed curve v(t) and the final stable speed u from the output shaft of the system; 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 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 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 the too large value range of t ₂ will make the particle swarm algorithm premature and fall into the local minimum value, but the too small value range optimization The optimal solution will be missed, and the delay time of the signal must be estimated according to the system model firstly. The delay time of the multi-substance rotating platform is relatively small, so the value range of given t ₂ is [0～5]; Set particle swarm related parameters; including determining the size of particle swarm m=100, particle search space dimension D=2, that is, two particles A ₂ and t ₂ , the maximum number of iterations k is 60, and the range of search space L _d =[0 0], U _d =[0 0], that is, determined according to the range of A ₂ and t ₂ , the learning factor c ₁ =c ₂ =2, the inertia weight range w _min =0.6, the i-th individual particle The best position is in for all The optimal in , randomly initialize the position and velocity of each particle; S2.2 The position vector of each particle is used as the input shaper parameter in turn, and the speed curve collected is simulated in turn to obtain the simulation curve; the fitness value of each particle is calculated according to the simulation curve, and it is used as a measure of the particle position The basis of pros and cons; set the fitness function as $\begin{array}{cc}\mathrm{<span\; class="notranslate">\; min</span>}& \mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; r</span>}\end{array}$ 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 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 penalty function value k _t ; when the time reaches the rise time, ftr is set to 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 when the k+1th cycle, the i-th particle velocity iteration equation is position vector iterative equation w, r ₁ , r ₂ represent the random weight of each iteration equation parameter; S2.5 When k reaches the set number of iterations, end the rolling optimization process, and output parameter optimization values; otherwise, go to step S2.2; S3 uses the obtained optimal shaper to perform feed-forward control on the actuator.