CN103885338A - Input reshaper parameter self-tuning control method based on particle swarm optimization algorithm - Google Patents

Abstract

The invention relates to an input reshaper parameter self-tuning control method based on a particle swarm optimization algorithm, and belongs to the technical field of drive control methods in the staring process of coaxial transmission machines. According to the buffeting problem in the staring process of coaxial transmission machines, a transmission mechanism is controlled in a feedforward mode through the control method, and effectiveness and feasibility of the control method are proved through experimental results; in the off-line state, a dipulse input reshaper is optimized by using the particle swarm optimization algorithm to obtain the optimal parameter, and then an actuator is controlled in a feedforward mode by using the obtained optimal input reshaper. According to the torsional vibration problem in the staring process of the coaxial transmission printing machines, an input reshaper parameter self-tuning control algorithm based on particle swarm optimization is provided. According to the control method, while torsional vibration of a system is restrained substantially, dynamic performance of the system is sacrificed little, and a rapid vibration-free response of the system is achieved.

Description

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

Technical field

The present invention relates to a kind of input shaper parameter self-tuning control method based on 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.

Adopted the method for input shaper to carry out time-domain filtering to system for above reason, but zero traditional vibration input shaper need Accurate Model, between parameter, influences each other, the difficulty of adjusting.The present invention introduces particle swarm optimization algorithm controller parameter is optimized, by system process is passed to letter conversion, 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 parameter self-tuning control method based on particle swarm optimization algorithm, there is buffeting problem for coaxial gearing start-up course, the present invention propose control method gear train is carried out to feedforward control, 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 parameter self-tuning control method based on particle swarm optimization algorithm, 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 topworks's feedforward control, the method comprises following concrete steps

S1 is to primal system input speed signal x (t), and 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 particle swarm optimization algorithm to obtain the parameter of dipulse input shaper, and the frequency-domain expression of dipulse input shaper is

wherein A _iand t _ibe respectively amplitude and the corresponding time lag thereof of pulse train, can make t by time optimal 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 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 precocity, be absorbed in local minimum, however too small span optimize time can miss optimum solution, first carry out the delay time of estimating signal according to the model of system, 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=100, and particle search space dimensionality D=2(is A ₂, t ₂two particles), iterations k is 60 to the maximum, search volume scope

(L _d=[0 0], U _d=[0 0], 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 the 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; Calculate the fitness value of each particle according to simulation curve, and set it as the foundation of weighing particle position quality; Fitness function is set is

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

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 do not reach the rise time within the appointment emulation cycle time, ftr is a larger penalty value; In the time that 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, replace by the current location of this particle

if this particle fitness value is less than the fitness value before population, replace with the position of this particle

S2.4 upgrades speed and the position to each particle, the k time circulation time, and now i particle position vector is

flying speed is 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, when k reaches after the iterations of setting, finishes rolling optimization process, output parameter optimal value.Otherwise, forward step S2.2 to.

S3 uses the optimum reshaper obtaining to carry out feedforward 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 control algolithm of the input shaper parameter self-tuning based on particle group optimizing.When this is controlled at the torsional oscillation that has significantly suppressed system, less sacrifice the dynamic property of system, realized the quick without vibration response of system.

Accompanying drawing explanation

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

Fig. 2 is particle group optimizing procedure chart.

Fig. 3 is the Optimized model figure under simulink.

Fig. 4 is primal system start and stop curve maps.

Fig. 5 is the system start and stop curve map of tape input reshaper.

Fig. 6 is the system start and stop curve frequency domain comparison diagram of primal system and tape input reshaper.

Embodiment

The present invention is a kind of control method of the input shaper parameter self-tuning based on particle group optimizing, with reference to Fig. 1, after input signal enters mechanical system in online situation, gather output shaft speed curve movement, go out again the parameter of input shaper according to collection application of curve particle swarm optimization algorithm offline optimization, then by the input shaper of optimization to mechanical system feedforward control, can filter like this frequency resonating with topworks in enabling signal, sacrifice dynamic property that can be smaller in significantly having suppressed Torsional vibration, realize the quick without vibration response of system.。

As shown in Figure 2, the bridge linking between particle cluster algorithm and simulink model is that particle (is the A in input shaper formula to the optimization method of population 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 then simulink model of operation control system, obtains the fitness value of this particle, finally judges whether to exit algorithm, if do not exit, the speed to particle and position are 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 is primal system start and stop curve maps, and at the step signal excitation multimass rotation system of amplitude 25000, due to the existence of resonance point, in startup and stopped process, system vibration is fairly obvious.In start-up course, vibration peak can reach 4.78 × 10 ⁴pulse/sec, maximum overshoot 55.7%, duration of oscillation can reach 15 seconds, and long vibration of response time is obviously.

Fig. 5 is the system start and stop curve map of tape input reshaper, under the step signal excitation of same amplitude, multimass rotation system is less than 5% of steady-state signal and thinks system stability take open cycle system output final value as 24490 pulse/s errors, the overshoot of system is only 2.327%, the dead-beat steady state (SS) that enters of system, the response time is only 700ms.Response speed significantly improves, and vibration is inhibited.

Fig. 6 is the system start and stop curve frequency domain comparison diagram of primal system and tape input reshaper, can find out that causing the main cause of system oscillation is the low frequency vibration point that has a 1HZ left and right, input signal enters mechanical system after entering input shaper again, and this resonance point is eliminated.

Claims (2)

1. the input shaper parameter self-tuning control method based on 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 topworks's feedforward control, the method comprises following concrete steps

S1 is to primal system input speed signal x (t), and 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 particle swarm optimization algorithm to obtain the parameter of dipulse input shaper, and the frequency-domain expression of dipulse input shaper is

wherein A _iand t _ibe respectively amplitude and the corresponding time lag thereof of pulse train, can make t by time optimal 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 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 precocity, be absorbed in local minimum, however too small span optimize time can miss optimum solution, first carry out the delay time of estimating signal according to the model of system, 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=100, and particle search space dimensionality D=2(is A ₂, t ₂two particles), iterations k is 60 to the maximum, search volume scope

(L _d=[0 0], U _d=[0 0], 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, the position of the 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; Calculate the fitness value of each particle according to simulation curve, and set it as the foundation of weighing particle position quality; Fitness function is set is

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

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 do not reach the rise time within the appointment emulation cycle time, ftr is a larger penalty value; In the time that 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, replace by the current location of this particle

if this particle fitness value is less than the fitness value before population, replace with the position of this particle

S2.4 upgrades speed and the position to each particle, the k time circulation time, and now i particle position vector is flying speed is

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, when k reaches after the iterations of setting, finishes rolling optimization process, output parameter optimal value; Otherwise, forward step S2.2 to;

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

2. a kind of input shaper parameter self-tuning control method based on particle swarm optimization algorithm according to claim 1, is characterized in that: described in

for all

in optimum be global optimum.

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