Modern Control Engineering
70 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems To derive the equations of motion for the syst ...
Section 3–2 / Mathematical Modeling of Mechanical Systems 71 Equation (3–20) was obtained by eliminating from Equations (3–18) a ...
72 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems In terms of vector-matrix equations, we have ( ...
Section 3–3 / Mathematical Modeling of Electrical Systems 73 Equations (3–24) and (3–25) give a mathematical model of the circui ...
74 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems It will be shown that the second stage of the ...
Section 3–3 / Mathematical Modeling of Electrical Systems 75 Complex Impedances. In deriving transfer functions for electrical c ...
76 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems EXAMPLE 3–7 Consider again the system shown in ...
Section 3–3 / Mathematical Modeling of Electrical Systems 77 Transfer Functions of Nonloading Cascaded Elements. The transfer fu ...
78 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems Operational Amplifiers. Operational amplifiers ...
Section 3–3 / Mathematical Modeling of Electrical Systems 79 The equation for this circuit can be obtained as follows: Define Si ...
80 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems EXAMPLE 3–8 Figure 3–16 shows an electrical ci ...
Section 3–3 / Mathematical Modeling of Electrical Systems 81 Impedance Approach to Obtaining Transfer Functions. Consider the op ...
82 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems Lead or Lag Networks Using Operational Amplifi ...
where Notice that This network has a dc gain of Note that this network, whose transfer function is given by Equation (3–36), is ...
84 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems we have (3–37) Notice that the second operatio ...
Section 3–3 / Mathematical Modeling of Electrical Systems 85 1 2 3 4 5 6 7 P I PD PI PID Lead or lag Lag–lead Control Action G(s ...
86 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems Example Problems and Solutions A–3–1. Figure 3 ...
Example Problems and Solutions 87 A–3–2. Obtain the transfer function Y(s)/U(s)of the system shown in Figure 3–21. The input uis ...
88 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems A–3–3. Obtain a state-space representation of ...
Example Problems and Solutions 89 Solution.In Figure 3–23(a) we assume that displacements xi, xo,andyare measured from their res ...
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