A First Course in FUZZY and NEURAL CONTROL

2.6. STATE-VARIABLE FEEDBACK CONTROL 51 Example 2.6Consider an unstable third-order system given by the set of state and output ...

52 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL From this, we can determine the desired characteristic matrix as Acf=   010 001 − ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 53 This computation showingRank< 2 implies the system is not fully controllable ...

54 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL 2.18. Using Newtonís law of motion, the model equations for this system are m dv dt ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 55 Performing partial fractions expansion, we obtain Y(s)= 10 s − 10 s+0. 05 The i ...

56 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL The objective in the controller design then is to select the appropriate parame- te ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 57 Let us selectKP = 100as a start and see what happens. Substituting values forKP ...

58 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL However, the response continues to exhibit the small steady-state error of 10 − 9 . ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 59 we obtain a relationship between system state and inputF(s),andchoosing Y(s) Q( ...

60 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL Figure 2.23. Simulation diagram The closed-loop transfer function therefore is give ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 61 0 2 4 6 8 10 (^2468101214161820) t Figure 2.25.y(t)=10u(t)− 10 e−^0.^8 tu(t) 2. ...

62 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL ter time constant is usually very small, so its effects will be assumed to be negli ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 63 and results in a high average power consumption. It is for this reason that we ...

64 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL Figure 2.29. Response to PD control Proportional + integral + derivative control Al ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 65 Proportional + integral control Sometimes derivative action can cause the heate ...

66 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL a largeKpwill have the effect of reducing the rise time and will reduce (but never ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 67 Figure 2.32. Step response of the open-loop transfer function As outlined previ ...

68 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL Figure 2.34. Step response withKd= 500 the uncontrolled function. We now take the l ...

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 69 Figure 2.35. Step response withKp= 500andKd=10 Figure 2.36. Step response withK ...

70 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL sysclosedloop=feedback(sysopenloop,sysfeedback); %Closed-loop TF step(sysclosedloop ...