ELE 639 Study Guide - Midterm Guide: Settling Time, Step Response, Ryerson University

• School: Ryerson University
• Department: Electrical Engineering
• Course: ELE 639
• Professor: Gosha Zywno

Document Summary

Ele639/bme639: control systems test # 2, march 11, 2014 - solutions. Note: full solutions are derived for version a, and the final results are provided for all remaining versions - they differ only by numerical values. Consider the closed loop control system with a relatively slow hydraulic process under a modified pid control, with rate feedback replacing the derivative term: The desired step response specifications are as follows: percent overshoot, (cid:1)(cid:2)=20%,(cid:8)settling time within 2% of the steady state value, (cid:9)(cid:10)(cid:11)(cid:12)(cid:12)(cid:13)(cid:11)( (cid:16)%)=10 seconds, steady state error, (cid:19)(cid:10)(cid:10)%=0. Your task is to calculate the pid controller parameters, (cid:20)(cid:21),(cid:20)(cid:22)(cid:8)and (cid:20)(cid:23) so that the: find the closed loop transfer function, (cid:24)(cid:25)(cid:13)((cid:26)), in terms of controller gains(cid:8)(cid:20)(cid:21),(cid:8)(cid:20)(cid:23)(cid:8)and (cid:20)(cid:22). above specifications are met. Let"s first find the minor feedback loop transfer function with the rate feedback, (cid:24)#((cid:26)): (cid:26)(cid:16)+(0. 2+2(cid:20)(cid:22))(cid:26)+0. 01 ((cid:26)+0. 1)(cid:16)+2(cid:20)(cid:22)(cid:26)= Next, find the open loop transfer function, (cid:24)%(cid:21)(cid:11)&((cid:26)): (cid:24)%(cid:21)(cid:11)&((cid:26))="(cid:20)(cid:21)+(cid:20)(cid:23)(cid:26)( (cid:26)((cid:26)(cid:16)+(0. 2+2(cid:20)(cid:22))(cid:26)+0. 01) (cid:26)(cid:16)+(0. 2+2(cid:20)(cid:22))(cid:26)+0. 01=