A First Course in FUZZY and NEURAL CONTROL

1.4. A LOOK AT CONTROLLER DESIGN 11 specific plant outputyby manipulating a plant inputuin such a way to achieve somecontrol obj ...

12 CHAPTER 1. A PRELUDE TO CONTROL THEORY wherex(t)denotes the carís position. The velocity is described by the equationy(t)=dx( ...

1.4. A LOOK AT CONTROLLER DESIGN 13 In the case of linear and time-invariant systems, the mathematical model can be converted to ...

14 CHAPTER 1. A PRELUDE TO CONTROL THEORY In summary, standard control theory emphasizes the absolute need to have a suitable ma ...

Chapter 2 MATHEMATICAL MODELS IN CONTROL In this chapter we present the basic properties of control and highlight significant de ...

16 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL form, the mathematical model of the motion of a pendulum, which is derived from mec ...

2.1. INTRODUCTORY EXAMPLES: PENDULUM PROBLEMS 17 In this example, we concentrate on answering thefirst question. When we attempt ...

18 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL Now back to our control problem. Having simplified the original dynamics, Equation ...

2.1. INTRODUCTORY EXAMPLES: PENDULUM PROBLEMS 19 like a brake. In technical terms, we need to adddampingto the system. The modif ...

20 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL Let us further pursue our problem of controlling an inverted pendulum. The lineariz ...

2.1. INTRODUCTORY EXAMPLES: PENDULUM PROBLEMS 21 position then even the smallest external disturbance on the cart would make the ...

22 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL Figure 2.4. Free-body diagrams of the cart and the pendulum By summing the forces a ...

2.1. INTRODUCTORY EXAMPLES: PENDULUM PROBLEMS 23 represents small deviations around the vertical position. For this situation, w ...

24 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL in state-space form as     x ̇ 1 (t) x ̇ 2 (t) φ ̇ 1 (t) φ ̇ 2 (t)     =  ...

2.1. INTRODUCTORY EXAMPLES: PENDULUM PROBLEMS 25 b = 0.1; i = 0.006; g = 9.8; l = 0.3; r = (M+m)(i+mll)-(ml)(ml); numplant = [ml ...

26 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL C=[1000; 0010] D = [0; 0] The output gives the following state-space model     ...

2.1. INTRODUCTORY EXAMPLES: PENDULUM PROBLEMS 27 vertical reference set to a zero value. Hence, the control structure may be red ...

28 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL we can easily manipulate the transfer function inMatlabfor various numerical values ...

2.2. STATE VARIABLES AND LINEAR SYSTEMS 29 2.2 Statevariablesandlinearsystems.................. We now begin to formalize the ge ...

30 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL The system is calledtime invariantif the response tou(t−τ)isy(t−τ), that is, g(x(t− ...