tailieunhanh - Control Systems Simulation using Matlab and Simulink

Control Systems Simulation Using Matlab and Simulink | 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 i .lx2 1 d . -i 2 .2a 2 .lu at 2 and transfer function G s .01 s2 3s .02 3 Y s G s U s Here u is the input y is the output and xi and x- 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. 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 y t were 1 Figure 1 fluid system Load the simulink file . 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. Continuous Time . 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 Ki C s Kp - Kds U s C s E s . In the time domain the PID control action can be described by d d Up Kpe Ui Kie ud Kd e dl dt u up ui ud where e r y and the reference input is a unit-step r t Notice that pure D action is unrealizable and must be approximated by numerical differentiation. Using simulink modify the system in the file so that the continuous time . PID control block is connected in the feedback loop. Run simulations of the closed loop unit-step input response of this system for