TAILIEUCHUNG - Ebook Analysis and design of control systems using Matlab: Part 2
(BQ) Part 2 book "Analysis and design of control systems using Matlab" has contents: Transientresponse analysis, response to initial condition, second order systems, root locus plots, bode diagrams, transformation of system models, nyquist plots of a system defined in state space,. and other contents. | Chapter 3 MATLAB TUTORIAL INTRODUCTION MATLAB has an excellent collection of commands and functions that are useful for solving control engineering problems. The problems presented in this chapter are basic linear control systems and are normally presented in introductory control courses. The application of MATLAB to the analysis and design of control systems is presented in this chapter with a number of illustrative examples. The MATLAB computational approach to the transient response analysis, steps response, impulse response, ramp response, and response to the simple inputs are presented. Plotting root loci, Bode diagrams, polar plots, Nyquist plot, Nichols plot, and state space method are obtained using MATLAB. TRANSIENT RESPONSE ANALYSIS Transient responses include the step response, impulse response, and ramp response. They are often used to investigate the time-domain characteristics of control systems. Transient response characteristics including the rise time, peak time, maximum overshoot, settling time, and steady state error can be obtained from the step response. When the numerator and denominator of a closed-loop transfer function are known, the commands step (num, den), step (num, den, t) in MATLAB can be used to generate plots of unit- step responses. Here, t is the user specified time. RESPONSE TO INITIAL CONDITION Case 1: State Space Approach Consider a system defined in state-space given by & x = Ax () x(0) = xo Assuming that there is no external input acting on the system, the response x(t) knowing the initial condition x(0) and that x is an n-vector, is obtained as follows: Taking Laplace transform of both sides of Eq. (), we obtain s x(s) – x(0) = AX (s) Equation () can be rearranged as s x (s) = AX (s) + x(0) () () 126 ANALYSIS AND DESIGN OF CONTROL SYSTEMS USING MATLAB Taking inverse Laplace transform of Eq. (), we get & x = A x + x(0) δ (t) () & Defining z = x, Eq. () can be written .
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