ENGR398 Laboratory Project II

Laboratory description: The speed control of a high-speed train is represented by the system shown in Figure 1. The transfer function of the train dynamics is as follows.

1

G(s)  

s

Laboratory assignment: 

Part A. For the open-loop system described by the following block diagram, assume that the input r(t) is a unit step. (1) Calculate the steady-state system output y_ss . (2) Find the steady-state error e_ss . (3) Make a plot for the system output y(t) by using MATLAB/SIMULINK.

            ry

Figure 1 A high speed train system

Part B. Consider the closed loop control system shown below

Figure 2 PID closed loop control system

where D(s) is a PID controller. Assume that the input r(t) is a unit step. Determine the steady-state error and use MATLAB/SIMULINK to plot the response of the system output y(t) for each of the following cases:

(1) Use P control, let D(s) K_P , in which (a)  K_P 30, (b) K_P 300, and (c) K_P 1000.

K ^I , in which (a) K_P 300 and K_I 10, (b) (2) Use PI control, let D(s) K_P

s

K_P 300 and K_I 100, and (c) K_P 300 and K_I 300.

3. Use PD control, let D(s) K_P  K_Ds , in which (a) K_P 300 and K_D 10, (b) K_P 300 and K_D 500, and (c) K_P 300 and K_D 1000.
4. Use PID control, let D(s) K_P  K ^I  K_Ds , in which (a) K_P 30, K_I 10,

s

and K_D 10, (b) K_P 300, K_I 100, and K_D 500, and (c) K_P 1000, K_I 300, and K_D 1000.

Part C. Compare all results in Part A and Part B, what are your conclusions? After you complete the above three parts, please write and submit an individual lab report in two weeks.

Explanation about this laboratory: this project is designed to aid students in understanding and mastering the important concepts, and acquiring the corresponding skills as listed below:

x Be familiar with the PID controller, which is a key element of many feedback control systems used today.

x Understand the differences between the transient response and the steady-state response for a dynamic system.

10. Know how to obtain transient responses by using computer-aided design tool.