Time Domain Design Project Instructions (revised 10/28/2025)
Each student will be provided a unique system, G(s), and unique specifications to meet in the design
of the controller, GP(s). Students should follow the outline at the end of the document to complete
each section of the report. Your grade will be affected by the presentation of your work.
Problem Statement:
Consider a closed loop unity feedback system with the system transfer function, G(s), below. Use
time domain controller design methodologies (i.e. with root locus) to design a controller, G P(s), to
meet the specifications given.
Submission Instructions:
For each section, submit the following on Blackboard:
 one pdf with required information as a formal report,
 Simulink models, and
 one .m file.
The design project will be submitted in stages and worth the following points:
Section I: Uncompensated System
Section II: Derivation of Controller – PD, PI, PID
Section III: Derivation of Controller – Lead, Lag, Lead-lag
Section IV: Conclusions
Percentage
Value
15%
40%
40%
5%
All sections of the project are due by 10:59 PM (CST), 11/3/25. Late submissions will be penalized
10% per hour. every 12 hours.
It is suggested that you meet the following milestones in the submission of your project:
Section I
Section II
Section III
Section IV
Suggest Submission
10/13
10/27
11/3
11/3
Due Date
11/3
11/3
11/3
11/3
Time Domain Design Project Outline
Section 1: Uncompensated System Response
A. Simulink model displaying output on scope
B. Root Locus showing the value of K that will cause instability (MATLAB)
C. Calculated steady-state error for step, ramp, and parabolic input
D. Time response including the rise time, peak time, settling time, percent overshoot (MATLAB)
Section 2: Derivation of Controller – PD, PI, PID
A. Statement of system specifications (given system and requirements)
B. Controller Design
1. Discussion of controller type chosen (PD, PI, PID)
2. Design the controller using Time Response (root locus) methods (show
calculations). Show the calculation of the sum of angles of poles and zeros if
appropriate.
3. Clearly specify your controller including the gain K, poles, and zeros.
C. Proof of design
1. Fulfillment of design requirements include time response including the rise time, peak
time, settling time, percent overshoot and any other design requirements.
2. Root Locus showing the value of K that will cause instability
3. Calculated steady-state error for step, ramp, and parabolic input
4. Simulink model displaying output on scope
Section 3: Derivation of Controller – Lead, Lag, Lead-lag
A. Statement of system specifications (given system and requirements)
B. Controller Design
1. Discussion of controller type chosen (lead, lag, or lead-lag)
2. Design the controller using Time Response (root locus) methods (show
calculations). Show the calculation of the sum of angles of poles and zeros if
appropriate.
3. Clearly specify your controller including the gain K, poles, and zeros.
C. Proof of design
1. Fulfillment of design requirements include time response including the rise time, peak
time, settling time, percent overshoot and any other design requirements.
2. Root Locus showing the value of K that will cause instability
3. Calculated steady-state error for step, ramp, and parabolic input
4. Simulink model displaying output on scope
Section 4: Conclusions
A.
Discussion of uncompensated system performance
B.
Discussion and comparison of system performance with PD/PI/PID controller (Part II) and
Lead/Lag/Lead-lag controller (Part III)