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Control Systems Simulation using Matlab and Simulink

# Control Systems Simulation using Matlab and Simulink - 1 0...

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UNIVERSITY OF CALIFORNIA AT BERKELEY Department of Mechanical Engineering ME134 Automatic Control Systems Spring 2002 Report Due: Tuesday, February 26 One report per group is required. Control Systems Simulation Using Matlab and Simulink 1 Introduction In ME134, we will make extensive use of Matlab and Simulink in order to design, analyze and simulate the response of control systems. 2 Control of Second Order System We will simulate the open loop and closed loop step response of the dynamic system described by the state and output equations d dt x 1 = - . 1 x 1 + . 1 x 2 (1) d dt x 2 = - . 2 x 2 + . 1 u y = x 1 (2) and transfer function G ( s )= . 01 s 2 + . 3 s + . 02 (3) Y ( s G ( s ) U ( s ) Here u is the input, y is the output, and x 1 and x 2 are the two states of the system. The two tank fluid system shown in Fig. 1 can be modeled by the above state and output equations and/or transfer function. 2.1 Open loop unit-step response Consider the open loop unit-step input response of this system. The unit-step input is given by u ( t μ ( t ), were μ ( t ):= 0i f t< 0 1i f t 0 1

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Figure 1: fluid system Load the simulink file tank open.m . Using simulink, modify the system to the obtain the open loop unit-step input response of this system. Plot the open loop response on a plot. 2.2 Continuous Time (C.T.) closed loop unit-step response Consider now the closed loop unit-step input response of this system. The control system is described by the block diagram in Fig. 2 where the controller is a PID type controller given by the Figure 2: feedback control system transfer function C ( s )= K p + K i s + K d s U ( s C ( s ) E ( s ) . In the time domain the PID control action can be described by u p = K p e, d dt u i = K i e, u d = K d d dt e u = u p + u i + u d where e = r - y and the reference input is a unit-step r ( t μ ( t ). (Notice that pure D action is unrealizable and must be approximated by numerical differentiation.) Using simulink, modify the system in the file tank continuous.m so that the continuous time (C.T.) PID control block is connected in the feedback loop. Run simulations of the closed loop unit-step input response of this system for different combinations of the PID gains. Try first P action only (i.e. K i = 0) and observe how the response of the closed loop system varies when K p is increased. Subsequently analyze the effect of introducing the I and D actions in the feedback control system. Try at least the following cases: 2
K p K i K d controller 1 100 controller 2 10 0 0 controller 3 20 0 0 controller 4 20 1 0 controller 5 20 1 20 Plot all the unit-step output (y(t) vs. t) responses of the system in one plot. Indicate which response corresponds to which feedback gain selection. Comment on your results and on the effect that each feedback action has on the response of the control system. Plot all the unit-step control input (u(t) vs. t) responses of the system in one plot. Indicate which response corresponds to which feedback gain selection. Comment on your results and on the effect that each feedback action has on the control input, u . What do you think would occur if the input u , saturates?

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Control Systems Simulation using Matlab and Simulink - 1 0...

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