CN114326372A - Non-smooth feedback optimal tracking control method of position servo system - Google Patents
Non-smooth feedback optimal tracking control method of position servo system Download PDFInfo
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Abstract
The invention discloses a non-smooth feedback optimal tracking control method of a position servo system, relates to the technical field of electromechanical control, and suppresses buffeting of the system while transient and steady-state performances of a tracking error of the position servo system are improved. The scheme comprises the following steps: a reference signal of the position servo system is set. Model parameters of the position servo system are obtained and a discrete model of the position servo system is constructed. And setting the one-time simulation duration according to the discrete model and the model parameters of the position servo system. The non-smoothing controller is designed based on the discrete values of the reference signal and the discrete model of the position servo system. And designing a discrete ITAE performance index according to the discrete value of the reference signal, the discrete model of the position servo system and the one-time simulation duration. And performing off-line optimization on the parameters of the non-smooth controller by adopting a particle swarm optimization algorithm and combining discrete ITAE performance indexes. And obtaining the optimal parameters of the non-smooth controller according to the optimization result.
Description
Technical Field
The invention relates to the technical field of electromechanical control, in particular to a non-smooth feedback optimal tracking control method of a position servo system.
Background
The position servo system can be used for performing track following control on electromechanical equipment such as a mechanical arm and the like, and in the practical application of the position servo system, in order to obtain expected control performance, parameters in a controller need to be set off-line or on-line. On the other hand, for various control performances and complex system working environments, it is necessary to design a control method which takes different control performances and disturbance rejection capabilities into consideration.
In the research of high-performance tracking control of a position servo system, a typical method comprises the following steps: the method can play a certain compensation role in regular interference, but has high computational complexity and poor compensation effect on white noise signals; the dynamic surface control method based on the preset performance can set the control performance of the system at will in theory, but is difficult to process the problem of 'escape' caused by random interference; the sliding mode control method has a simple control structure, can completely inhibit system model errors, external disturbance and the like, but is difficult to apply to engineering practice due to the inherent buffeting problem; the method has the capabilities of limited time convergence, small overshoot and disturbance suppression, and is widely concerned and applied in engineering. However, the non-smooth feedback control method still has the problems that the optimal control parameters are difficult to calculate directly in theory and the system can have buffeting.
Disclosure of Invention
In view of this, the present invention provides a non-smooth feedback optimal tracking control method for a position servo system, which suppresses buffeting of the system while improving transient and steady-state performance of a tracking error of the position servo system.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
s1: setting a reference signal of the position servo system, wherein the reference signal comprises a reference position, a reference speed and a reference acceleration.
S2: model parameters of the position servo system are obtained and a discrete model of the position servo system is constructed.
S3: and setting the one-time simulation duration according to the discrete model and the model parameters of the position servo system.
S4: the non-smoothing controller is designed based on the discrete values of the reference signal and the discrete model of the position servo system.
S5: and designing a discrete ITAE performance index according to the discrete value of the reference signal, the discrete model of the position servo system and the one-time simulation duration.
S6: and performing off-line optimization on the parameters of the non-smooth controller by adopting a particle swarm optimization algorithm and combining discrete ITAE performance indexes.
S7: and obtaining the optimal parameters of the non-smooth controller according to the optimization result of the S6.
Further, in the second step, obtaining model parameters of the position servo system and constructing a discrete model of the position servo system, specifically:
the open loop transfer function of the position servo system is:
wherein G(s) is a system model, s is Laplace operator, k0For system input amplification factor, omegakIs the system natural frequency, pkThe damping coefficient of the system is;
the dynamic model of the position servo system obtained from the open-loop transfer function is:
wherein, [ x ]1,x2,x3]TIs a system state vector, x1、x2And x3Respectively representing the position, velocity and acceleration of the position servo system, u being the input to the position servo system, b2、b3And k is three intermediate variables, wherein
b3＝2ρkωkAnd an
The discrete model of the position servo system is constructed according to the dynamic model of the position servo system as follows:
wherein, tsN is the total number of simulation steps, xj(n) and u (n) represent the system state and input, respectively, at the current time, xj(n +1) represents the system state at the next time, j ═ 1,2, or 3; at the current time n.tsThe time of day.
Further, setting the one-time simulation duration according to the discrete model and the model parameters of the position servo system specifically comprises: setting one-time simulation duration as T-N.t according to the discrete model and the model parameter of the position servo systemsAnd N is the total simulation step number.
Further, in step four, designing the non-smoothing controller according to the discrete value of the reference signal and the discrete model of the position servo system, specifically:
wherein u (n) the system input at the current time,
when j is 1,2,3, ej(n) tracking errors of position, velocity and acceleration at the present time, xj(n) is the system state at the current time,
for the discrete value of the reference signal at the current time, the control parameters of the non-smoothing controller include six, which are: k is a radical of1,k2,k3，α1,α2,α3Wherein k is1,k2,k3> 0 and alpha1,α2,α3E (0,1) is not lightControl parameters of the slip controller.
Further, a discrete ITAE performance index is designed according to the discrete value of the reference signal, the discrete model of the position servo system and the one-time simulation duration, and the discrete ITAE performance index specifically comprises the following steps:
wherein i is an integer and takes the value from 0 to T/Ts。
Further, a particle swarm optimization algorithm is adopted and discrete ITAE performance indexes are combined to perform offline optimization on parameters of the non-smooth controller, and the optimization process specifically comprises the following steps:
s601: parameter k to the non-smoothing controller according to the initialization procedure1、k2、k3、α3The random position and speed of the formed particle group are subjected to range setting and initialization, and the inertia weight and the acceleration of the particle group are assigned.
S602: calculating an adaptive value of each particle, namely a discrete ITAE performance index calculated according to a simulation result of a discrete system under the non-smooth controller and the discrete value of the reference signal.
S603: for each particle, the adaptation value is compared to the adaptation value for the best position experienced, and if better, is taken as the current best position.
S604: for each particle, the adaptation value is compared with the adaptation value of the global best position, and if better, it is taken as the current global best position.
S605: evolving the speed and position of the particles, wherein the evolution equation is as follows;
where v and x represent the position and velocity of the particle, respectively, subscript i represents the ith particle, subscript j represents the jth dimension of the particle, z represents the z th generation, Pij(z) and Pgj(z) represents the best position experienced by the individual and the population in that dimension, respectively, c1、c2Is an acceleration constant, r1、r2The method is characterized in that the method is two independent random numbers meeting standard normal distribution, omega is an inertia weight, and the method has the function of maintaining the balance of global and local search capacities.
S606: if the preset iteration number M is reached or the preset optimization performance index is met, the optimization process is ended, otherwise, the operation returns to the step S602.
Further, the parameters of the non-smoothing controller need to satisfy the following relationship:
has the advantages that:
1. the invention introduces a penalty term e of speed buffeting into the original ITAE performance index2The traditional ITAE performance index is improved, so that the problem of high-frequency oscillation of a traditional non-smooth controller under the action of a sign function is solved. According to the method, the particle swarm optimization and the improved ITAE performance index are used for optimizing the control parameters of the non-smooth controller, and the obtained optimal control parameters not only improve the transient and steady-state performances of the position servo system, but also avoid the problem of buffeting.
2. The embodiment of the invention constructs the optimized discrete ITAE index and the discrete form of the original ITAE index
Compared with the prior art, the optimized discrete ITAE index increases a buffeting punishment item
Non-smooth controller parameters are advantageously obtained that allow the system to avoid jitter. It can be seen that when the system tracking error is not converged, the punishment to the speed tracking error is small; and after the system tracking error is converged, the punishment degree on the speed tracking error is increased. Thus, after optimizationThe system of (2) can avoid jitter while maintaining fast convergence characteristics.
Drawings
FIG. 1 is a flow chart illustrating the steps of a non-smooth feedback optimal tracking control method for a position servo system;
FIG. 2 is an optimized block diagram of a non-smooth feedback optimal tracking control method for a position servo system;
FIG. 3 is a position tracking curve of a three-order hydraulic servo system under the optimization of original ITAE performance indexes;
FIG. 4 is a velocity tracking curve of a three-order hydraulic servo system under the optimization of original ITAE performance indexes;
FIG. 5 is a position tracking curve of a third-order hydraulic servo system under optimization of new ITAE performance indicators;
fig. 6 is a velocity tracking curve of the third-order hydraulic servo system under the new ITAE performance index optimization.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
Fig. 1 is a flowchart illustrating steps of a non-smooth feedback optimal tracking control method for a position servo system, which specifically includes:
s1: setting a reference signal of a position servo system, wherein the reference signal comprises a reference position, a reference speed and a reference acceleration; in the embodiment of the invention: setting the reference signal as
Wherein y isdIs a reference position,
For the purpose of reference to the speed,
is a reference acceleration.
S2: obtaining model parameters of a position servo system and constructing a discrete model of the position servo system; the embodiment of the invention is realized by the following modes:
the open loop transfer function of the hydraulic servo system is as follows:
wherein G(s) is a system model, s is Laplace operator, k0For system input amplification factor, omegakIs the system natural frequency, pkIs the system damping coefficient.
The kinetic model of the system (1) is described as:
wherein, [ x ]1,x2,x3]TIs a system state vector, x1、x2And x3Respectively representing the position, velocity and acceleration of the position servo system, u being the input to the position servo system, b2、b3And k is three intermediate variables, wherein
b3＝2ρkωkAnd an
Discretizing the dynamic model (2) in a differential mode to obtain a discrete dynamic model:
wherein, tsN is the total number of simulation steps, xj(n) and u (n) represent the system state and input, respectively, at the current time, xj(n +1) represents the system state at the next time, j ═ 1,2, or 3; at the current time n.tsThe time of day.
S3: servo system dispersion according to positionSetting one-time simulation duration by the model and the model parameters; based on the model (3) and its model parameters
b3＝2ρkωk，
The one-time simulation time length T in S3 is set to N · Ts。
S4: designing a non-smoothing controller according to the discrete value of the reference signal and the discrete model of the position servo system; the non-smoothing controller in the embodiment of the invention is designed as follows:
wherein u (n) the system input at the current time,
when j is 1,2,3, ej(n) tracking errors of position, velocity and acceleration at the present time, xj(n) is the system state at the current time,
for the discrete value of the reference signal at the current time, the control parameters of the non-smoothing controller include six, which are: k is a radical of1,k2,k3，α1,α2,α3Wherein k is1,k2,k3> 0 and alpha1,α2,α3E (0,1) is the control parameter of the unsmooth controller.
Meanwhile, in order to ensure the finite time convergence of the system tracking error, the parameters of the non-smooth controller need to satisfy the following relationship:
s5: designing a discrete ITAE performance index according to a discrete value of a reference signal, a discrete model of a position servo system and one-time simulation duration; according to the discrete value y of the reference signald(n),
Discrete model (3) of position servo system and one-time simulation time length T ═ N · TsThe discrete ITAE performance index in S5 is designed as follows:
wherein i is an integer and takes the value from 0 to T/Ts。
Discrete form of original ITAE index
Compared with the prior art, the optimized discrete ITAE index increases a buffeting punishment item
Non-smooth controller parameters are advantageously obtained that allow the system to avoid jitter. It can be seen that when the system tracking error is not converged, the punishment to the speed tracking error is small; and after the system tracking error is converged, the punishment degree on the speed tracking error is increased. Thus, the optimized system can avoid jitter while maintaining fast convergence characteristics.
S6: and designing a particle swarm optimization algorithm and performing off-line optimization on the parameters of the non-smooth controller by combining discrete ITAE performance indexes. The optimization process of the particle swarm optimization is as follows:
s601: parameter k to the non-smoothing controller according to the initialization procedure1、k2、k3、α3Setting and initializing the range of the random position and speed of the formed particle group;
s602: calculating an adaptive value of each particle, namely a discrete ITAE performance index (6) calculated according to a simulation result of a discrete system under the discrete values of the non-smooth controller and the reference signal;
s603: for each particle, comparing the adaptation value with the adaptation value of the best position experienced, and if better, taking the adaptation value as the current best position;
s604: for each particle, comparing the adaptive value with the adaptive value of the global best position, and if the adaptive value is better, taking the adaptive value as the current global best position;
s605: evolving the speed and position of the particles, wherein the evolution equation is as follows;
where v and x represent the position and velocity of the particle, respectively, subscript i represents the ith particle, subscript j represents the jth dimension of the particle, z represents the z th generation, Pij(z) and Pgj(z) represents the best position experienced by the individual and the population in that dimension, respectively, c1、c2Is an acceleration constant, r1、r2The method is characterized in that the method is two independent random numbers meeting standard normal distribution, omega is an inertia weight, and the method has the function of maintaining the balance of global and local search capacities.
S606: if the preset iteration number M is reached or the preset optimization performance index is met, the operation is finished, otherwise, the operation returns to the step 2).
S7: and according to the optimization result, the optimal parameters of the non-smooth controller can be obtained.
FIG. 2 is an optimized block diagram of a non-smooth feedback optimal tracking control method of a position servo system, which is composed of a control block diagram under a system discrete model and a particle swarm optimization algorithm with discrete ITAE performance indexes. By combining with the improved ITAE performance index, the obtained optimal control parameter ensures the transient and steady-state performance of the position servo system, and simultaneously avoids the problem of buffeting in the system.
The technical scheme disclosed by the invention is subjected to simulation verification, and the method specifically comprises the following steps:
step 1: hydraulic servo system model parameter and particle swarm algorithm hyper-parameter design
According to the natural frequency omega of the hydraulic servo systemk10rad/s, damping coefficient ρk0.2, magnification factor k0Calculating each parameter b in the dynamic equation (2) of the hydraulic servo system as 52＝100，b 34, k 500. The sampling step size in the discrete dynamics model (3) is set to ts0.01s, and in order to ensure the rapid convergence of the system and take the buffeting condition possibly existing in the system into consideration, 10 times of the upper bound of the system regulation time obtained by simulation is selected as an integral upper bound, namely T is 4s 400Ts。
As can be seen from the discrete dynamic model (3), the non-smooth controller (4) and the parameter relation (5), only the parameter k is needed1、k2、k3、α3And (6) optimizing. Therefore, take the dimension of the particle to be 4, the number of particles to be 500, and the learning factor c1、c2Respectively taking 1.2 and 2, the inertia weight is 0.6, the maximum iteration frequency is 1000, and the condition of stopping iteration is that the performance index is less than 0.5. At the same time, a parameter k is defined1,k2,k3∈[0,50]And alpha3∈(0,1)。
Step 2: discrete ITAE performance index based on tradition
Optimizing the parameters in the non-smooth controller (4) by using a particle swarm algorithm to obtain the optimal parameters (k) of the non-smooth controller under the current index1＝50，k2＝12.05，k3＝0.61，α30.76) and tracking results under optimal parameters (fig. 3-4).
And 3, step 3: based on the improved discrete ITAE performance index (6), parameters in the non-smooth controller (4) are optimized by using a particle swarm algorithm to obtain the optimal parameters (k) of the non-smooth controller under the current index1＝50，k2＝8.58，k3＝0.27，α30.86) and tracking results under the optimal parameters (fig. 5-6).
Fig. 3-4 are the tracking curve and tracking error curve of the third-order hydraulic servo system under the original ITAE performance index optimization. After the original ITAE performance index is optimized, the system obtains a faster convergence speed, the position and speed signals realize fast tracking within 0.25 second, but the speed signals of the system have obvious high-frequency buffeting in certain time periods.
Fig. 5-6 are the tracking curve and tracking error curve of the third-order hydraulic servo system under the optimization of the new ITAE performance index. After the improved ITAE performance index is adopted for optimization, the buffeting of the system is eliminated under the condition that the convergence rate is not reduced.
Based on the technical content, a particle swarm optimization algorithm of the non-smooth controller can be obtained, and the obtained non-smooth controller parameters can eliminate system buffeting while maintaining the system convergence speed by using an improved ITAE index as a particle swarm fitness function.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A non-smooth feedback optimal tracking control method of a position servo system is characterized by comprising the following steps:
s1: setting a reference signal of a position servo system, wherein the reference signal comprises a reference position, a reference speed and a reference acceleration;
s2: obtaining model parameters of the position servo system and constructing a discrete model of the position servo system;
s3: setting one-time simulation duration according to the discrete model and the model parameters of the position servo system;
s4: designing a non-smoothing controller according to the discrete value of the reference signal and a discrete model of a position servo system;
s5: designing a discrete ITAE performance index according to the discrete value of the reference signal, the discrete model of the position servo system and the one-time simulation duration;
s6: performing off-line optimization on the parameters of the non-smooth controller by adopting a particle swarm optimization algorithm and combining the discrete ITAE performance index;
s7: and obtaining the optimal parameters of the non-smooth controller according to the optimization result of the S6.
2. The method as claimed in claim 1, wherein in the second step, the model parameters of the position servo system are obtained and the discrete model of the position servo system is constructed, specifically:
the open loop transfer function of the position servo system is:
wherein G(s) is a system model, s is Laplace operator, k0For system input amplification factor, omegakIs the system natural frequency, pkThe damping coefficient of the system is;
and obtaining a dynamic model of the position servo system by the open-loop transfer function as follows:
wherein, [ x ]1,x2,x3]TIs a system state vector, x1、x2And x3Respectively representing the position, velocity and acceleration of the position servo system, u being the input to the position servo system, b2、b3And k is three intermediate variables, wherein
b3＝2ρkωkAnd an
The discrete model of the position servo system is constructed according to the dynamic model of the position servo system as follows:
wherein, tsN is the total number of simulation steps, xj(n) and u (n) represent the system state and input, respectively, at the current time, xj(n +1) represents the system state at the next time, j ═ 1,2, or 3; at the current time n.tsThe time of day.
3. The method as claimed in claim 2, wherein the setting of the simulation time duration according to the discrete model and the model parameters of the position servo system comprises:
setting one-time simulation duration as T-N.t according to the discrete model and the model parameters of the position servo systemsAnd N is the total simulation step number.
4. The method as claimed in claim 3, wherein the step four comprises designing the unsmooth controller according to the discrete values of the reference signal and the discrete model of the position servo system, and specifically comprises:
wherein u (n) the system input at the current time,
when e is presentj(n) tracking errors of position, velocity and acceleration at the present time, xj(n) is the system state at the current time,
for the discrete value of the reference signal at the current time, the control parameters of the non-smoothing controller include six, which are: k is a radical of1,k2,k3，α1,α2,α3Wherein k is1,k2,k3> 0 and alpha1,α2,α3E (0,1) is the control parameter of the unsmooth controller.
5. The method as claimed in claim 4, wherein the discrete ITAE performance index is designed according to the discrete value of the reference signal, the discrete model of the position servo system and the one-time simulation duration, and the discrete ITAE performance index is specifically:
wherein i is an integer and takes the value from 0 to T/Ts。
6. The method according to claim 1, wherein the parameters of the non-smooth controller are optimized offline by using a particle swarm optimization algorithm and combining the discrete ITAE performance indicators, and the optimization process specifically includes the following steps:
s601: according to the initialization procedure, the parameter k of the non-smooth controller1、k2、k3、α3Setting and initializing the range of the random position and speed of the formed particle group, and assigning the inertia weight and the acceleration of the particle group;
s602: calculating an adaptive value of each particle, namely calculating the discrete ITAE performance index according to a simulation result of the discrete system under the discrete values of the non-smooth controller and the reference signal;
s603: for each particle, comparing the adaptation value with the adaptation value of the best position experienced, and if better, taking the adaptation value as the current best position;
s604: for each particle, comparing the adaptive value with the adaptive value of the global best position, and if the adaptive value is better, taking the adaptive value as the current global best position;
s605: evolving the speed and position of the particles, wherein the evolution equation is as follows;
where v and x represent the position and velocity of the particle, respectively, subscript i represents the ith particle, subscript j represents the jth dimension of the particle, z represents the z th generation, Pij(z) and Pgj(z) represents the best position experienced by the individual and the population in that dimension, respectively, c1、c2Is an acceleration constant, r1、r2The method is characterized in that the method is two independent random numbers meeting standard normal distribution, omega is an inertia weight, and the method has the function of maintaining the balance of global and local search capacities.
S606: if the preset iteration number M is reached or the preset optimization performance index is met, the optimization process is ended, otherwise, the operation returns to the step S602.
7. The method as claimed in claim 1, wherein the parameters of the non-smooth controller satisfy the following relationship:
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