Introduction to Motion Control

1. Introduction to Motion Control Application of an Auto-Tuning NeurontoSliding Mode Control Wei-Der Chang, Rey-Chue Hwang, and Jer-Guang Hsieh IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 32, NO. 4, NOVEMBER 2002 Professor:Ming-Shyan Wang Student: Yi-De Lin

2. Outline Abstract Introduction ILLUSTRATIVE EXAMPLES CONCLUSION REFERENCES

3. Abstract This paper presents a control strategy that incorporates an auto-tuning neuron into the sliding mode control (SMC) in order to eliminate the high control activity and chattering due to the SMC. The main difference between the auto-tuning neuron and the general one is that a modified hyperbolic tangent function with adjustable parameters is employed. In this proposed control structure, an auto-tuning neuron is then used as the neural controller without any connection weights.. The control law will be switched from the sliding control to the neural control, when the state trajectory of system enters in some boundary layer. In this way, the chattering phenomenon will not occur. The results of numerical simulationsare provided to show the control performance of our proposed method.

4. Introduction A useful and powerful control scheme to deal with the existence of the model uncertainty, or imprecision, is the sliding mode control (SMC) [1]. As we know, the model uncertainty or imprecision may arise from insufficient information about the system or from the purposeful simplification of mathematical model representation of plant, e.g., order reduction. The control law of SMC, however, is an intense switching action similar to that of bang-bang control, when the state trajectory of system reaches around the sliding surface. This leads to the appearance of chattering across the sliding surface and may excite the high-frequency unmodeled dynamics of the system, undesirable in most real applications. A simple method for solving the discontinuous control law and chattering action is to introduce a boundary layer. This method, however, does not ensure the convergence of the state trajectory of system to the sliding surface, and probably results in the existence of the steady-state error. In addition, analysis of a system dynamics within the boundary layer is very complicated [2]. For solving the drawbacks, a number of studies have been published. In [2], a control strategy was proposed based upon an on-line estimator constructed by a recurrent neural network to eliminate the chattering. In [3], the controller consists of the traditional SMC and Gaussian neural network. At the beginning, the SMC is used to force the state trajectory of system toward the sliding surface. Then the control law is switched from the SMC to Gaussian neural network control if the state trajectory of system reaches the boundary layer.

5. Introduction Fig. 1. Basic structure of an auto-tuning neuron.

6. Introduction Fig. 2. Modified activation functions for different a and b.

7. Introduction Fig. 3. Control structure using an auto-tuning neuron with the SMC.

8. Introduction Fig. 4. Boundary layer and intermediate region.

9. ILLUSTRATIVE EXAMPLES To illustrate the use of the proposed method, the following two examples are provided. Note, that the sampling time is set to be 0.02 in these simulations. Example 1: Consider a first-order unstable nonlinear system described as [7] In (18), the nonlinear function

10. ILLUSTRATIVE EXAMPLES The parameters used in the neural control are given by = 0:0001 and (0) = ['(0); a(0); b(0)]T = [􀀀0:5; 2; 0]T . Our control objective is also to regulate the system output x1 from the initial state (x1(0); x2(0)) = (1:5; 0) to the desired output xd = 0. The results are shown in Figs. 7 and 8 by using only the traditional SMC and the proposed method, respectively. Again, we can find out that better control performance can be achieved by using our proposed method.

11. CONCLUSION In this paper, we have proposed a control strategy that consists of a general SMC and a neural control constructed by an auto-tuning neuron. In order to eliminate the high control activity and chattering due to the SMC, the control law here is smoothly switched from the sliding control to the neural control, when the state trajectory of system enters in some boundary layer. Thus, the chattering phenomenon around the sliding surface will never occur. For the adaptive neural control, we have presented a stable tuning mechanism based on the Lyapunov stability theory to guarantee the convergence of the system output. From the results of two numerical simulations, we conclude that the proposed method can perform successful control. It is interesting to consider the switching between SMC and PID control, whether the PID control is produced by some classical rules, e.g., Ziegler-Nichols tuning, or by rules based on auto-tuning neurons. The latter is still under our investigation. No fair comments can be made at this point.

12. REFERENCES [1] J. J. E. Slotine and W. P. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991. [2] Y. Fang, T.W. S. Chow, and X. D. Li, “Use of a recurrent neural network in discrete sliding-mode control,” in Proc. Inst. Electr. Eng., Control Theory Appl., vol. 146, Jan. 1999, pp. 84–90. [3] R. M. Sanner and J. J. E. Slotine, “Gaussian networks for direct adaptive control,” IEEE Trans. Neural Networks, vol. 3, pp. 837–863, Nov. 1992. [4] F. P. Da andW. Z. Song, “Sliding mode adaptive control based on fuzzy neural networks,” Control and Decision, vol. 13, no. 4, pp. 301–305, 1998. in Chinese. [5] C. T. Chen andW. D. Chang, “A feedforward neural network with function shape autotuning,” Neural Netw., vol. 9, no. 4, pp. 627–641, 1996. [6] W. D. Chang, R. C. Hwang, and J. G. Hsieh, “Adaptive control of multivariable dynamic systems using independent self-tuning neurons,” in Proc. 10th Int. Conf. Tools with Artificial Intelligence, Taipei, Taiwan, R.O.C, 1998, pp. 68–73. [7] L. X. Wang, A Course in Fuzzy Systems and Control. Englewood Cliffs, NJ: Prentice-Hall, 1997.

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