A novel self-organizing adaptive wavelet cerebellar model articulation controller backstepping (SOWCB) control is proposed, aiming at some nonlinear and uncertain factors that caused difficulties in controlling the AC servo system. This controller consists of self-organizing wavelet cerebellar model articulation controller (CMAC) and robust compensator. It absorbs fast learning and precise approaching advantage of self-organizing wavelet CMAC to mimic a backstepping controller, and then robust compensator is added to inhibit influence of the uncertainties on system performance effectively and realize high accuracy position tracking for AC servo system. Moreover, the stability of the control system can be guaranteed by using Lyapunov method. The results of the simulation and the prototype test prove that the proposed approach can improve the steady state performance and control accuracy and possess a strong robustness to both parameter perturbation and load disturbance.
With the advancement of technology, AC servo systems have become more and more widely utilized. For a servo driving system, the control system is required to have both a strong steady-stage and dynamic performance, and it is necessary to build a precise dynamic model of the system for conducting the analysis, simulation, and control of an AC servo system. As a controlled object, the dynamic mathematical model of an AC motor is a complex system, which is characterized by a heavy varying-load, slow time variation, nonlinearity, and uncertain disturbance. Thus, the practical intelligent control strategy has become a focus in the field of servo system control.
Zhou and Zhu [
Su and He [
Cerebellar model articulation controller (CMAC) is modeled on the principle of the cerebellum control body movement established [
Based on the above analysis, this paper uses self-organizing adaptive wavelet cerebellar model articulation controller (SOWC) to online approximation of backstepping controller, using robust control to eliminate system uncertainties and approximation error; finally, simulation experiments of AC servo system and the prototype test can prove the effectiveness of the proposed method.
The structure diagram of an AC servo system is presented in Figure No saturation effect. Induction electromotive force that is sine wave shape; motor air-gap magnetic field distribution. Excluding the hysteresis and eddy current loss. No rotor excitation winding.
The structure diagram of AC servo system.
Based on the above assumptions, available under
Use the method of vector control technology of
Due to the current in the motor time constant being far smaller than the mechanical time constant, the current loop speed is faster than the response speed of the speed loop and position loop, so the current loop approximation can be simplified as a proportion function.
Let variable
Equation (
Self-organizing wavelet CMAC network structure diagram is as shown in Figure
The structure of self-organizing wavelet CMAC neural networks.
The network consists of input space, store space, accepted domain space, weights of storage space, and output space [
For the convenience of deriving, the parameter of CMAC can be defined as
According to the size of the input to increase or decrease the number of nodes, if a new input is valued within the range of this family, the self-organizing cerebellar neural network will no longer produce new node; it will just change the weight [
Defined in the association storage space,
Set
Translated and scaling parameter in the memory space and weight of the new generation are set to
Consider the exponential function at
In this paper, the control goal is to make the position of the system able to track the given trajectory asymptotically stable signal. For achieving this goal, assume
Define position error:
Define virtual control inputs:
Define
Define Lyapunov function:
In order to make
Put (
Thus, the asymptotic stability of the system can be guaranteed by the design of the control law.
Because the system is characterized by a heavy varying-load, slow time variation, nonlinearity, and uncertain disturbance, the ideal backstepping control algorithm is hard to get directly by (
Assume the optimal SOWC controller for an ideal to approximate backstepping controller, which is shown as
Because the optimal SOWC is not easy to get, thus, get
Put (
Wavelet function becomes a part of the linear form [
Equation (
Equation (
Put (
Substitute (
To set up the system of adaptive parameter,
Self-organizing wavelet CMAC adaptive backstepping control.
The robust compensator is designed as [
Define Lyapunov function
According to (
Put (
Assume
When
When the initial condition parameters
Thus, according to the Barbalat lemma [
The main parameters in the AC system were as follows: the friction coefficient of the system is
In order to test and verify the effectiveness of the self-organization wavelet adaptive CMAC backstepping control, adaptive CMAC controller is used to compare it. The simulation results are as shown in Figures
Step response curve of load disturbance.
The initial moment of inertia of step response curve.
The moment of inertia changes step response curve.
Tracking error curve of the system.
The structure of the node curve.
Figure
As it can be seen from Figure
Figure
As can be seen from Figures
Figure
Figure
To investigate the efficiency of the proposed self-organizing wavelet adaptive CMAC backstepping control as a strategy in establishing AC servo system, a semiphysical simulation platform is constructed to simulate the working conditions of the servo control system. The test results were compared to verify the performance of the controller in this paper superiorly.
The semiphysical simulation test-bed structure diagram and object diagram are as shown in Figures
Schematic of the semiphysical simulation platform.
Photograph of the semiphysical simulation platform.
To investigate the tracking accuracy of the servo system with adaptive self-organizing wavelet CMAC backstepping control system, sinusoidal command tracking with a frequency of 1 Hz and amplitude of 100 degrees is conducted on the semiphysical simulation platform. The corresponding tracking errors of both the SOWCB and adaptive CMAC control systems are illustrated in Figure
System step response tracking error.
The figure also illustrates that the SOWCB control system has a smaller steady-state error and external disturbance error showed stronger inhibitory action and has faster response speed and good robustness.
In this paper, due to the existence of nonlinear servo system problem, self-organizing CMAC adaptive wavelet backstepping control methods have been proposed. The simulation and prototype test results showed that compared to self-organization wavelet algorithm with the traditional CMAC method, it has higher accuracy; the scheme of system uncertainties and external disturbance has strong robustness and good dynamic and steady-state response performance.
The authors declare that there is no conflict of interests regarding the publication of this paper.