CN104090490A - Input shaper closed-loop control method based on chaotic particle swarm optimization algorithm - Google Patents

Abstract

The invention relates to an input shaper closed-loop control method based on a chaotic particle swarm optimization algorithm and belongs to the technical field of methods for drive control in the coaxial transmission machine start process. In order to solve the buffeting problem in the coaxial transmission machine start process, closed-loop control is performed on a transmission mechanism with the control method, and the effectiveness and the feasibility of the control method are proved by experimental results. In an offline state, a double-pulse input shaper is optimized through the chaotic particle swarm optimization algorithm, optimization parameters of the double-pulse input shaper are obtained, and then a PD closed-loop actuating mechanism is controlled through the optimized input shaper. The input shaper parameter self-tuning control algorithm based on chaotic particle swarm optimization is provided for solving the buffeting problem in the coaxial transmission printing machine start process. Due to the control, a system can respond fast without vibration while torsional vibration of the system is substantially suppressed.

Description

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

Technical field

The present invention relates to a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm, belong to the driving control method technical field of coaxial gearing start-up course.

Background technology

Coaxial transmission printer is in start-up course, owing to adopting major axis to connect, between axle and axle, transmission range is long, system stiffness is low, load quality can twist vibration when heavily etc. the impact of factors has caused startup, phenomenon of torsional vibration has not only affected the stable state time of start-up course, and also can bring very large impact to transmission shaft, thereby affect the serviceable life of printing machine.

For above reason, adopted the method for input shaper to carry out time-domain filtering to system, yet zero traditional vibration input shaper need Accurate Model, between parameter, influences each other, the difficulty of adjusting.The present invention introduces Chaos particle swarm optimization algorithm controller parameter is optimized, and by system process is passed to letter, converts, realized system signal online acquisition, offline optimization, kept compared with highland precision simultaneously.

Summary of the invention

The object of the present invention is to provide a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm, for coaxial gearing start-up course, there is buffeting problem, the control method that the present invention proposes is carried out PD control to gear train, and through the results show validity and the feasibility of this control method.

For achieving the above object, the technical solution adopted in the present invention is a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm, under the state of off-line, use Chaos particle swarm optimization algorithm to be optimized the input shaper of dipulse, obtain its optimized parameter, then use the optimum input shaper obtaining to PD actuating mechanism controls, the method comprises following concrete steps

S1 moves with simple PD parameter adjustment actuating mechanism, remains unchanged later, and system input speed signal x (t), driving device system motion, uses scrambler to collect its rate curve v (t) and final stabilized speed u from system output shaft;

S2, according to the stabilized speed u of system output shaft, adopts Chaos particle swarm optimization algorithm to obtain the parameter of dipulse input shaper, and the frequency-domain expression of dipulse input shaper is a wherein _iand t _ibe respectively amplitude and the corresponding time lag thereof of pulse train, by time optimal, can make t ₁=0, must formula be: for making system output reach stabilized speed u, add equation of constraint A ₁+ A ₂=1, A _i> 0;

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

S2.1 initialization also arranges input shaper correlation parameter; Comprise A ₁, A ₂and t ₂span, due to A ₁+ A ₂=1, A _i> 0, therefore A ₂span [0～1], A ₁=1-A ₂; t ₂choose important because excessive t ₂span can make Chaos particle swarm optimization algorithm precocious, be absorbed in local minimum, yet can miss optimum solution when too small span is optimized, first according to the model of system, carry out the delay time of estimating signal, the time delay of many matter rotatable platform is less, therefore given t ₂span be [0～5].

Chaos-Particle Swarm Optimization correlation parameter is set; Comprise and determine population scale m=30, particle search space dimensionality D=2 (is A ₂, t ₂two particles), iterations k is 30 to the maximum, and the maximum step number n of Chaos Search is 10, search volume scope $x_i^k\∈[x_{\min },x_{\max }](x_{\min }=[\mathrm{0,0}],x_{\max }=[\mathrm{1,5}],$ According to A ₂, t ₂scope is determined), study factor c ₁=c ₂=2, inertia weight scope w _min=0.6, i particle personal best particle is wherein for all in optimum (being global optimum), the position of each particle of random initializtion and speed;

S2.2 successively as input shaper parameter, carries out emulation to gathering the speed curve movement of returning using the position vector of each particle successively, obtains simulation curve; According to simulation curve, calculate the fitness value of each particle, and using it as the foundation of weighing particle position quality; Fitness function is set is

$\begin{array}{cc}\min & J=\underset{0}{\overset{\∞}{\∫}}|v\left(t\right)-u|\mathrm{dt}+\mathrm{ftr}\end{array}$

In formula, the instantaneous velocity that v (t) is simulation curve, u is the final stabilized speed of system output shaft, and ftr is a larger penalty value, and specific definition is

$\mathrm{ftr}=\left\{\begin{array}{cc}{k}_t& \mathrm{false}\\ t_r& \mathrm{true}\end{array}\right.$

Wherein, t _rfor the simulation curve rise time, when not reaching the rise time within the appointment emulation cycle, ftr is a larger penalty value; When the time reaches the rise time, ftr value is t _r;

S2.3 calculates the fitness value of each particle according to fitness function, if the fitness value of this particle is less than particle self fitness value in the past, by the current location of this particle, replace if this particle fitness value is less than the fitness value before population, with the position of this particle, replace

S2.4 upgrades the speed of each particle and position, the k time circulation time, and now i particle position vector is $x_i^k=(x_{i1}^k,x_{i2}^k...,x_{\mathrm{iD}}^k),$ Flying speed is $v_i^k=(v_{i1}^k,v_{i2}^k,...v_{\mathrm{iD}}^k),$ Current particle personal best particle is $p_{\mathrm{id}}^k=(p_{i1}^k,p_{i2}^k,...,p_{\mathrm{id}}^k,...p_{\mathrm{iD}}^k),$ Current global optimum position is $p_{\mathrm{gd}}^k=(p_{g1}^k,p_{g2}^k,...,p_{\mathrm{gd}}^k,...p_{\mathrm{gD}}^k)$ (d=1,2..., D), the k+1 time circulation time, i particle rapidity iterative equation is $v_{\mathrm{id}}^{k+1}={\mathrm{wv}}_{\mathrm{id}}^k+c_1{r}_1(p_{\mathrm{id}}^k-x_{\mathrm{id}}^k)+c_2{r}_2(p_{\mathrm{gd}}^k-x_{\mathrm{id}}^k),$ Position vector iterative equation $x_{\mathrm{id}}^{k+1}=x_{\mathrm{id}}^k+v_{\mathrm{id}}^{k+1}.$

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

S2.6 carries out chaos Local Search to best particle, and upgrades with

The process of described chaos local search algorithm is as follows,

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

S2.6.2 uses i particle position vector d dimension variable, obtain according to the following formula Chaos Variable d=1,2 ... D, wherein x _{max, d}and x _{min, d}it is the search bound of d dimension variable;

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

S2.6.4 is according to Chaos Variable obtain position vector if d=D, turns S2.6.5, otherwise d=d+1 turns S2.6.2;

S2.6.5 is according to new position vector obtain fitness value, compare with original position vector, if fitness value is better or Chaos Search has reached greatest iteration step number, using reposition vector as Chaos Search result, otherwise put k=k+1, turn S2.6.2.

S2.7, when k reaches after the iterations of setting, finishes rolling optimization process, output parameter optimal value.Otherwise, forward step S2.8 to.

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

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)}

X wherein _{g, d}represent current the value of d dimension variable, r is the random number of [0,1];

S2.9, when k reaches after the iterations of setting, finishes rolling optimization process, output parameter optimal value; Otherwise in the space after contraction, random remaining 80% the particulate that produces in colony, turns S2.2;

S3 uses the optimum reshaper obtaining to carry out PD control to topworks.

Compared with prior art, beneficial effect of the present invention is: the present invention is directed to the Torsional Vibration in coaxial transmission printer tool start-up course, proposed a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm.When being controlled at the torsional oscillation that has significantly suppressed system, this realizes the quick without vibration response of system.

Accompanying drawing explanation

Fig. 1 is this control method application system structured flowchart.

Fig. 2 is chaotic particle swarm optimization procedure chart.

Fig. 3 is the Optimized model figure under simulink.

Fig. 4 a is original PD system start up curve figure.

Fig. 4 b is original PD system start up curve Fourier transform figure.

Fig. 5 a is the PD system start up curve figure of tape input reshaper.

Fig. 5 b is the PD system start up curve Fourier transform figure of tape input reshaper.

Embodiment

The present invention is a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm, with reference to Fig. 1, after input signal enters mechanical system in online situation, gather output shaft speed curve movement, according to collection application of curve Chaos particle swarm optimization algorithm offline optimization, go out again the parameter of input shaper, then the input shaper of optimization is controlled to PD mechanical system motion, the frequency that can filter like this resonance of enabling signal Zhong Yu topworks, the system that realized when significantly having suppressed Torsional vibration is fast without vibration response.

As shown in Figure 2, the bridge linking between Chaos particle swarm optimization algorithm and simulink model is that particle (is the A in input shaper formula to the optimization method of Chaos-Particle Swarm Optimization off-line ₂, t ₂).Optimizing process is as follows, produces at random population, by the particle in this population successively assignment to the parameter A in simulink mode input reshaper ₂, t ₂, the simulink model of operation control system then, obtains the fitness value of this particle, finally judges whether to exit algorithm, if do not exit, the speed of particle and position is upgraded, to A ₂, t ₂upgrade.

Fig. 3 is the Optimized model figure under simulink, and the rate signal of collection obtains simulation curve after input shaper module, then obtains fitness value through fitness function module.

Fig. 4 a is primal system start up curve figure, is the response that multimass PD closed loop rotation system is inputted the step signal that amplitude is 8600, and system oscillation exists always, and overshoot is about 13.953%; Fig. 4 b is original PD system start up curve Fourier transform figure, can obviously find out and have a low frequency vibration point.

Fig. 5 a is the PD system start up curve figure of tape input reshaper, and under the step signal excitation of same amplitude, the overshoot of system is only 3.488%, and vibration is inhibited, and the adjustment time is only 700ms; Fig. 5 b is the PD system start up curve Fourier transform figure of tape input reshaper, finds out low frequency vibration point elimination.

Claims (3)

1. the input shaper closed loop control method based on Chaos particle swarm optimization algorithm, it is characterized in that: under the state of off-line, use particle swarm optimization algorithm to be optimized the input shaper of dipulse, obtain its optimized parameter, then use the optimum input shaper obtaining to PD actuating mechanism controls, the method comprises following concrete steps

S1 moves with simple PD parameter adjustment actuating mechanism, remains unchanged later, and system input speed signal x (t), driving device system motion, uses scrambler to collect its rate curve v (t) and final stabilized speed u from system output shaft;

S2, according to the stabilized speed u of system output shaft, adopts Chaos particle swarm optimization algorithm to obtain the parameter of dipulse input shaper, and the frequency-domain expression of dipulse input shaper is a wherein _iand t _ibe respectively amplitude and the corresponding time lag thereof of pulse train, by time optimal, can make t ₁=0, must formula be: for making system output reach stabilized speed u, add equation of constraint A ₁+ A ₂=1, A _i> 0;

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

S2.1 initialization also arranges input shaper correlation parameter; Comprise A ₁, A ₂and t ₂span, due to A ₁+ A ₂=1, A _i> 0, therefore A ₂span [0～1], A ₁=1-A ₂; t ₂choose important because excessive t ₂span can make particle cluster algorithm precocious, be absorbed in local minimum, yet can miss optimum solution when too small span is optimized, first according to the model of system, carry out the delay time of estimating signal, the time delay of many matter rotatable platform is less, therefore given t ₂span be [0～5];

Population correlation parameter is set; The scale that comprises definite population is counted m=30, particle search space dimensionality D=2, i.e. A ₂, t ₂two particles, iterations k is 30 to the maximum, search volume scope study factor c ₁=c ₂=2, inertia weight scope w _min=0.6, i particle personal best particle is wherein for all in optimum, the position of each particle of random initializtion and speed;

S2.2 successively as input shaper parameter, carries out emulation to gathering the speed curve movement of returning using the position vector of each particle successively, obtains simulation curve; According to simulation curve, calculate the fitness value of each particle, and using it as the foundation of weighing particle position quality; Fitness function is set is

$\begin{array}{cc}\min & J=\underset{0}{\overset{\∞}{\∫}}|v\left(t\right)-u|\mathrm{dt}+\mathrm{ftr}\end{array}$

In formula, the instantaneous velocity that v (t) is simulation curve, u is the final stabilized speed of system output shaft, and ftr is a larger penalty value, and specific definition is

$\mathrm{ftr}=\left\{\begin{array}{cc}{k}_t& \mathrm{false}\\ t_r& \mathrm{true}\end{array}\right.$

Wherein, t _rfor the simulation curve rise time, when not reaching the rise time within the appointment emulation cycle, ftr is a larger penalty value; When the time reaches the rise time, ftr value is t _r;

S2.3 calculates the fitness value of each particle according to fitness function, if the fitness value of this particle is less than particle self fitness value in the past, by the current location of this particle, replace if this particle fitness value is less than the fitness value before population, with the position of this particle, replace

S2.4 upgrades the speed of each particle and position, the k time circulation time, and now i particle position vector is $x_i^k=(x_{i1}^k,x_{i2}^k...,x_{\mathrm{iD}}^k),$ Flying speed is $v_i^k=(v_{i1}^k,v_{i2}^k,...v_{\mathrm{iD}}^k),$ Current particle personal best particle is $p_{\mathrm{id}}^k=(p_{i1}^k,p_{i2}^k,...,p_{\mathrm{id}}^k,...p_{\mathrm{iD}}^k),$ Current global optimum position is $p_{\mathrm{gd}}^k=(p_{g1}^k,p_{g2}^k,...,p_{\mathrm{gd}}^k,...p_{\mathrm{gD}}^k)$ (d=1,2..., D), the k+1 time circulation time, i particle rapidity iterative equation is $v_{\mathrm{id}}^{k+1}={\mathrm{wv}}_{\mathrm{id}}^k+c_1{r}_1(p_{\mathrm{id}}^k-x_{\mathrm{id}}^k)+c_2{r}_2(p_{\mathrm{gd}}^k-x_{\mathrm{id}}^k),$ Position vector iterative equation $x_{\mathrm{id}}^{k+1}=x_{\mathrm{id}}^k+v_{\mathrm{id}}^{k+1};$

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

S2.6 carries out chaos Local Search to best particle, and upgrades with

The process of described chaos local search algorithm is as follows,

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

S2.6.2 uses i particle position vector d dimension variable, obtain according to the following formula Chaos Variable d=1,2 ... D, wherein x _{max, d}and x _{min, d}it is the search bound of d dimension variable;

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

S2.6.4 is according to Chaos Variable obtain position vector if d=D, turns S2.6.5, otherwise d=d+1 turns S2.6.2;

S2.6.5 is according to new position vector obtain fitness value, compare with original position vector, if fitness value is better or Chaos Search has reached greatest iteration step number, using reposition vector as Chaos Search result, otherwise put k=k+1, turn S2.6.2;

S2.7, when k reaches after the iterations of setting, finishes rolling optimization process, output parameter optimal value; Otherwise, forward step S2.8 to;

S2.8 shrinks region of search by formula below 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 _man,j,x _g,d-r*(x _max,d-x _min,d)},0＜r＜1

X wherein _{g, d}, represent current the value of d dimension variable;

S2.9, when k reaches after the iterations of setting, finishes rolling optimization process, output parameter optimal value; Otherwise in the space after contraction, random remaining 80% the particulate that produces in colony, turns S2.2;

S3 uses the optimum reshaper obtaining to carry out PD control to topworks.

2. a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm according to claim 1, is characterized in that: described in for all in optimum be global optimum.

3. a kind of input shaper closed loop control method based on Chaos particle swarm optimization algorithm according to claim 1, is characterized in that: described search volume scope x _min=[0,0], x _max=[1,5], according to A ₂, t ₂scope is determined.