Introduction to Motion Control Application of an Auto-Tuning Neuronto Sliding Mode Control Wei-Der...

Introduction to Motion Control

Application of an Auto-Tuning Neuronto Sliding Mode Control

Wei-Der Chang Rey-Chue Hwang and Jer-Guang Hsieh

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICSmdashPART C APPLICATIONS AND REVIEWS

VOL 32 NO 4 NOVEMBER 2002

Professor Ming-Shyan WangStudent Yi-De Lin

Outline

Abstract

Introduction

ILLUSTRATIVE EXAMPLES

CONCLUSION

REFERENCES

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 simulations are provided to show the control performance of our proposed method

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 eg 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

Fig 1 Basic structure of an auto-tuning neuron

Introduction

Fig 2 Modified activation functions for different a and b

Introduction

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

Introduction

Fig 4 Boundary layer and intermediate region

Introduction

To illustrate the use of the proposed method the following two examples

are provided Note that the sampling time is set to be 002 in

these simulations

Example 1 Consider a first-order unstable nonlinear system described

as [7]

In (18) the nonlinear function


The parameters used in the neural control are given by = 00001 and (0) = [(0) a(0) b(0)]T = [104857605 2 0]T

Our control objective is also to regulate the system output x1 from the initial state (x1(0) x2(0)) = (15 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


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 eg 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

REFERENCES

[1] J J E Slotine and W P Li Applied Nonlinear Control Englewood

Cliffs NJ Prentice-Hall 1991

[2] Y Fang TW S Chow and X D Li ldquoUse of a recurrent neural network

in discrete sliding-mode controlrdquo in Proc Inst Electr Eng Control

Theory Appl vol 146 Jan 1999 pp 84ndash90

[3] R M Sanner and J J E Slotine ldquoGaussian networks for direct adaptive

controlrdquo IEEE Trans Neural Networks vol 3 pp 837ndash863 Nov 1992

[4] F P Da andW Z Song ldquoSliding mode adaptive control based on fuzzy

neural networksrdquo Control and Decision vol 13 no 4 pp 301ndash305

1998 in Chinese

[5] C T Chen andW D Chang ldquoA feedforward neural network with function

shape autotuningrdquo Neural Netw vol 9 no 4 pp 627ndash641 1996

[6] W D Chang R C Hwang and J G Hsieh ldquoAdaptive control of multivariable

dynamic systems using independent self-tuning neuronsrdquo in

Proc 10th Int Conf Tools with Artificial Intelligence Taipei Taiwan

ROC 1998 pp 68ndash73

[7] L X Wang A Course in Fuzzy Systems and Control Englewood


Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)


ILLUSTRATIVE EXAMPLES (2)

CONCLUSION

REFERENCES

Slide 13

Outline

Abstract

Introduction


CONCLUSION

REFERENCES

Abstract


Introduction





Introduction


Introduction


Introduction


Introduction



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13

Abstract


Introduction





Introduction


Introduction


Introduction


Introduction



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13

Introduction





Introduction


Introduction


Introduction


Introduction



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13


Introduction


Introduction


Introduction


Introduction



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13


Introduction


Introduction


Introduction



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13


Introduction


Introduction



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13


Introduction



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13



these simulations


as [7]






CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13




CONCLUSION





REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13

REFERENCES










1998 in Chinese









Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13

Thanks for watching


Outline

Abstract

Introduction

Introduction (2)

Introduction (3)

Introduction (4)

Introduction (5)



CONCLUSION

REFERENCES

Slide 13

Introduction to Motion Control Application of an Auto-Tuning Neuronto Sliding Mode Control Wei-Der...

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