Modern Control Engineering
30 Chapter 2 / Mathematical Modeling of Control Systems leastnvariablesx 1 ,x 2 ,p,xnare needed to completely describe the behav ...
Section 2–4 / Modeling in State Space 31 The outputs y 1 (t), y 2 (t),p,ym(t)of the system may be given by (2–9) If we define ym ...
32 Chapter 2 / Mathematical Modeling of Control Systems m k b u(t) y(t) Figure 2–15 Mechanical system. u(t) D(t) B(t) A(t) C(t) ...
In a vector-matrix form, Equations (2–17) and (2–18) can be written as (2–20) The output equation, Equation (2–19), can be writt ...
34 Chapter 2 / Mathematical Modeling of Control Systems wherexis the state vector,uis the input, and yis the output. The Laplace ...
Section 2–5 / State-Space Representation of Scalar Differential Equation Systems 35 Note that (Refer to Appendix C for the inver ...
36 Chapter 2 / Mathematical Modeling of Control Systems State-Space Representation of nth-Order Systems of Linear Differential E ...
Section 2–5 / State-Space Representation of Scalar Differential Equation Systems 37 The output can be given by or (2–32) where [ ...
38 Chapter 2 / Mathematical Modeling of Control Systems where are determined from (2–35) With this choice of state variables the ...
Section 2–6 / Transformation of Mathematical Models with MATLAB 39 or (2–37) (2–38) where In this state-space representation, ma ...
40 Chapter 2 / Mathematical Modeling of Control Systems Let us write the closed-loop transfer function as Once we have this tran ...
Section 2–6 / Transformation of Mathematical Models with MATLAB 41 (2–41) MATLAB transforms the transfer function given by Equat ...
42 Chapter 2 / Mathematical Modeling of Control Systems EXAMPLE 2–4 Obtain the transfer function of the system defined by the fo ...
Section 2–7 / Linearization of Nonlinear Mathematical Models 43 2–7 Linearization of Nonlinear Mathematical Models Nonlinear Sys ...
44 Chapter 2 / Mathematical Modeling of Control Systems where the derivatives are evaluated at If the variation is small, we may ...
Section 2–7 / Linearization of Nonlinear Mathematical Models 45 where The linearization technique presented here is valid in the ...
46 Chapter 2 / Mathematical Modeling of Control Systems Example Problems and Solutions A–2–1. Simplify the block diagram shown i ...
Example Problems and Solutions 47 G 1 G 2 R(s) C(s) G 2 R(s) C(s) G 1 + 1 R(s) C(s) G 1 G 2 +G 2 + 1 (a) (b) (c) + + + + + + Fig ...
48 Chapter 2 / Mathematical Modeling of Control Systems G 1 G 1 G 2 H 3 G 4 G 3 G 4 H 1 H 2 + + ++ +– +– R(s) R(s) C(s) C(s) H 3 ...
Example Problems and Solutions 49 By substituting Equation (2–47) into Equation (2–48), we get (2–50) By substituting Equation ( ...
«
1
2
3
4
5
6
7
8
9
10
»
Free download pdf