Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems

1. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems

2. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems Abstract: - Rule-based fuzzy control, in which the plant model is replaced by a number of control rules, provides an alternative approach and has been developed significantly. On the other hand, the potential benefits of neural networks extend beyond the high computation rates provided by the massive parallelism to provide a greater degree of robustness. integrating these two approaches brings what is so-called neurofuzzy system which gives rise to gain the merits of both approaches. Structural and functional mapping from a fuzzy logic-based algorithm to the neural network-based approach has been considered with a thorough design procedures for SISO control systems. Simulation technique will be implemented through out this research using C++ programming language to verify the proposed controller capabilities. Keywords: - Functional Neurofuzzy Controller (FNFC), Multi-Layer Perceprtron Neural Networks (MLP NN)

3. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems Simulation has many advantages, and even some disadvantages. These are listed by Pegden, Shannon, and Sadowski [1]. The advantages are:- 1.New policies, operating procedures, decision rules, information flows, organizational procedures, and so on can be explored without disrupting ongoing operations of the real system. 2. New hardware designs, physical layouts, transportation systems, and so on, can be tested without committing resources of their acquisition. 3. Hypotheses about how or why certain phenomena occur can be tested for feasibility.

4. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems 4. Time can be compressed or expanded allowing for a speed up or slow down of the phenomena under investigation. 5. Insight can be obtained about the interaction of variables. 6. Insight can be obtained about the importance of variables on the performance of the system. 7. A simulation study can help in understanding how the system operates rather than how individuals think the system operates. 8. "What if" questions can be answered? This is particularly useful in the design of new systems.

5. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems While the disadvantages are:- 1- Simulation results may be difficult to interpret. 2- Simulation modeling and analysis can be time consuming and expensive

6. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems A classical 49-fuzzy rule as in table (1) below, with triangular fuzzifier of 7-fuzzy sets for each controller input error and its rate of change and center of gravity defuuzifier a fuzzy logic controller of Mamdani style is designed. Table (1): 49-fuzzy production rule

7. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems (1) (2) Where and are the maximum elements in and respectively, while & are the maximum measured error and change-in-error. With regard to the output (control action) scaling factor GU, it is simply set to

8. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems (3) For the next instructions:- (4) A stopping iteration criterion is taken based on minimizing a Performance Index of the form: (5)

9. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems

10. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems Fig. (2) Controlled & uncontrolled responses of the underlying unstable system

11. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems Fig.(5) Effect of steady-state disturbance imposed on the controlled response Fig. (6) Generalization feature to track stair case input signal

12. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems Fig. (8): Uncontrolled unity feedback response of the underlying non-linear system

13. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems Fig. (9): Controlled response of the underlying non-linear system Fig. (10) Generalization to track ramp input

14. Simulation of Neurofuzzy Controller Design for Unstable and Non-linear Control Systems Conclusion:- - The merits of linking both fuzzy logic and neural network approaches are obvious, confirmed through the comprehensive knowledge extraction, robustness, adaptivity and generalization characteristics offered by the neurofuzzy system. - Simulation gives a very good insight view to the underlying system before implementation which yields to less cost and efforts. - Simulation results in this research showed the good capability of the proposed controller when used to control unstable and non-linear systems.

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