Modern Control Engineering
50 Chapter 2 / Mathematical Modeling of Control Systems Solution.From the figure, we obtain (2–52) (2–53) By substituting Equati ...
Example Problems and Solutions 51 +– R 1 C 1 R 1 C 1 1 – G 1 G 2 G 3 G 4 G 1 G 1 G 3 G 4 – G 2 +– R 1 C 2 G 3 G 1 –G 2 G 4 = +– ...
52 Chapter 2 / Mathematical Modeling of Control Systems and Solution.From the definition of state variables x 2 andx 3 ,we have ...
Example Problems and Solutions 53 we find Referring to Equation (2–35), we have Referring to Equation (2–34), we define Then ref ...
54 Chapter 2 / Mathematical Modeling of Control Systems A–2–8. Obtain a state-space model of the system shown in Figure 2–26. So ...
Example Problems and Solutions 55 which can be rewritten as By taking the inverse Laplace transforms of the preceding four equat ...
56 Chapter 2 / Mathematical Modeling of Control Systems Taking the inverse Laplace transforms of the preceding three equations, ...
Example Problems and Solutions 57 Rewriting gives Notice that the output of the integrator and the outputs of the first-order de ...
58 Chapter 2 / Mathematical Modeling of Control Systems Hence A–2–12. Consider a system with multiple inputs and multiple output ...
Example Problems and Solutions 59 A–2–13. Linearize the nonlinear equation in the region defined by 8x10, 2y4. Solution.Defi ...
60 Chapter 2 / Mathematical Modeling of Control Systems Thus Hence a linear approximation of the given nonlinear equation near t ...
Problems 61 C(s) D(s) R(s) +– Gc(s) Gp(s) + + Figure 2–32 Controller Plant Closed-loop system. B–2–4.Consider industrial automat ...
62 Chapter 2 / Mathematical Modeling of Control Systems B–2–8.Obtain a state-space representation of the system shown in Figure ...
3 63 Mathematical Modeling of Mechanical Systems and Electrical Systems 3–1 Introduction This chapter presents mathematical mode ...
64 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems EXAMPLE 3–1 Let us obtain the equivalent sprin ...
Section 3–2 / Mathematical Modeling of Mechanical Systems 65 (a) The force fdue to the dampers is In terms of the equivalent vis ...
66 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems EXAMPLE 3–3 Consider the spring-mass-dashpot s ...
Section 3–2 / Mathematical Modeling of Mechanical Systems 67 Next we shall obtain a state-space model of this system. We shall f ...
68 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems EXAMPLE 3–4 Obtain the transfer functions and ...
only a two-dimensional problem in which the pendulum moves only in the plane of the page. The control force uis applied to the c ...
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