The Design and Application of Control Using Dynamic Grey Prediction System Chapter 1 Introduction .................................. 1 1.1 Background .......................................... 1 1.2 Motivation........................................... 2 1.3 Organization ........................................ 3 Chapter 2 Grey Prediction .......................................... 4 2.1 Introduction .......................................... 4 2.2 The Mapped Generating and its Inverse Operator (MGO and IMGO) ........ 4 2.3 The Complete Prediction Process .......................................... 5 Chapter 3 Genetic Algorithm .......................................... 8 3.1 Introduction .......................................... 8 3.2 The Basic Operators in GA .......................................... 8 3.2.1 Reproduction .......................................... 9 3.2.2 Crossover .......................................... 9 3.2.3 Mutation .......................................... 10 3.3 Elite Method .......................................... 10 3.4 Reinforced Search Method .......................................... 11 Chapter 4 Application of a Dynamic Grey Prediction System Using Fuzzy Logic to Switch the Prediction Modes ........................... 13 4.1 Introduction .......................................... 13 4.2 Grey Prediction Controller .......................................... 14 4.3 Genetic-based and Fuzzy-switching GPC ................................... 17 4.4 Simulation and Discussion .......................................... 20 4.5 Conclusion .......................................... 25 Chapter 5 An Alternative Approach for the Switching Grey Prediction Controller .............. 26 5.1 Introduction .......................................... 26 5.2 Problem Formulation .......................................... 26 5.3 The Proposed Method .......................................... 29 5.4 Simulation .......................................... 31 5.5 Conclusion .......................................... 33 Chapter 6 Conclusions and Recommendations .............................. 34 References .......................................... 36 List of Figures Fig. 2.1 The prediction procedure of a simple grey predictor ............. 6 Fig. 3.1 The complete flow chart of the genetic algorithm ................. 12 Fig. 4.1 The framework of a simple grey prediction controller ............ 14 Fig. 4.2 The output response of G(s) using a positive step in GPC ...... 15 Fig. 4.3 The output response of G(s) using a negative-step in GPC ....... 15 Fig. 4.4 The framework of the switching grey prediction PID controller ...... 16 Fig. 4.5 The Block Diagram of the Genctic-based and Fuzzy-switching GPC controller .......................................... 17 Fig. 4.6 The fuzzy sets in the premise part of the fuzzy inference scheme ....18 Fig. 4.7 The fuzzy sets in the consequence part of the fuzzy inference scheme .........18 Fig. 4.8 The step response of Gp(s) using GB-FSGPC method (9 parameters in searching .......................................... 20 Fig. 4.9 The step response with kp in [5,15] ......................... 22 Fig. 4.10 The step response with wn=1 and wp=1 ............................ 23 Fig. 4.11 The system response with Ziegler-Nichols PID rules .............. 25 Fig. 5.1 The results of feeding Unit step signal into the stable plant Gp(s) (Eq. 4.9 ) .......................................... 27 Fig. 5.2 The results of feeding Unit step signal into the unstable plant Gu(s) ...................28 Fig. 5.3 The results of feeding an Inverse Unit step input signal into the unstable plant .......................................... 29 Fig. 5.4 An Alternative Approach of the SGPC controller ................ 29 Fig. 5.5 The output response of controlling the Gp(s) by the proposed method .......... 32 Fig. 5.6 The output response of controlling the unstable plant G2(s) ...... 33 List of Table Table 4.1 The code length of the searched arguments in the proposed method (GB-FSGPC) .......................................... 20 Table 4.2 The system parameters of Gp(s) using GB-FSGPC method .......... 21 Table 4.3 The performance indices of the system Gp(s) using GB-FSGPC design .............. 21 Table 4.4 The searched results with kp in [5,15] ......................... 21 Table 4.5 The performance indices with kp in [5,15] ..................... 22 Table 4.6 The searching results with wn=1 and wp=1 ..................... 22 Table 4.7 The performance indices with wn=1 and wp=1 .................... 23 Table 4.8 The Ziegler-Nichols PID rules ................................ 24 Table 4.9 The system arguments with the Ziegler-Nichols rules .............. 24 Table 4.10 The performance indices with the Ziegler-Nichols rules ........... 25 Table 5.1 The system parameters of the design to control Gp(s) (a third-order stable plant) .......................................... 31 Table 5.2 The performance indices of Gp(s) (a third-order stable plant) .... 31 Table 5.3 The system parameters of controlling the unstable plant G2(s) ( a third-order unstable plant ) ............................. 32 Table 5.4 The performance indices of controlling G2(s) ( a third-order unstable plant ) .................................. 32