ENJ331 CONTROL SYSTEMS ENGINEERING: Simulation laboratory
ENJ331 CONTROL SYSTEMS ENGINEERING
Simulation laboratory
Instructions:
- You are welcomed to use any software to develop and simulate your solutions.
- A compressed file containing Matlab scripts called “simulation lab” is available to assist with drawing the figures and simulating the system.
- Note it is highly unlikely that students will develop similar systems, please ensure you work on your own as it will prepare you for the exam.
- Ensure you upload you answer sheet by the due date in PDF format .
Question
A negative unity feedback system has a feedforward function defined as
𝐺(s)=10𝐾(2𝑠+5)(𝑠2 +6𝑠+34) (𝑠+7)(50𝑠4+644 𝑠3+996 𝑠2−739 𝑠−3559 )
The input to the system is r(t) = u(t). Answer all the questions below and only submit the answer sheet for assessment.
a) Derive the transfer function for the system .
b) Derive a Routh table and calculate for which values of K the system will be stable?
c) Sketch the root locus for the given system. Refine the sketch to include all asymptotes, break points and jω -crossings . Ensure all calculated values are present on the sketch.
d) Find the gain K and closed loop pole locations that will provide output response with a 41% overshoot, motivate if a second order approximation is acceptable?
e) For the system specified in (d), please complete the corresponding column of table 1 in the answer sheet.
f) Design an ideal PD which will have less than one-fifth of the settling time of the system specified in (d). Complete the corresponding column of table 1 in the answer sheet.
g) Design an ideal PID which will reduce the steady state error of the system of question (f) to have error less than 0.01 . Complete the corresponding column of table 1 in the answer sheet.
h) Plot output responses for all 3 systems over time. These outputs include the uncompensated, ideal PD and ideal PID system.
i) Design a passive PD which will have less than one -fifth of the settling time of the system specified in (d). Complete the corresponding column of table 1 in the answer sheet.
j) Design a passive PID which will reduce the steady state error of the system of question ( i) to have error less than 0.01. Complete the corresp onding column of table 1 in the answer sheet.
k) Plot output responses for all 3 systems over time . These outputs include the uncompensated, passive PD and passive PID.
