By the end of the activity, the student should be able to:
1) Translate damping ratio and natural frequency requirements into a desired pole location;
2) Use root-locus angle and magnitude conditions to design lead/lag compensators;
3) Verify a design with MATLAB;
4) Compare transient performance and implementation burden; and
5) Justify a design recommendation using engineering evidence.

This activity is intended for a feedback controls course after students have learned the root-locus angle and magnitude conditions and have been introduced to lead and lag compensation. Students should be comfortable using MATLAB transfer functions and rlocus, but the Live Script provides the computational structure needed for the activity.
The activity can replace a traditional homework assignment or be used as an in-class application after compensator design has been introduced. A 50–60 minute class works well if students have already seen the design procedure. A 75–90 minute class allows additional time for interpretation, robustness discussion, and short group presentations.
Recommended group structure:
- Individual prediction: 5–10 min
- Expert groups: 20–25 min
- Jigsaw groups: 15–20 min
- Client recommendation/share-out: 5–10 min

The student Live Script guides students through five phases.
1. Individual prediction: Students locate the desired pole from the damping-ratio and natural-frequency requirements, inspect the uncompensated root locus, and estimate the phase deficiency/excess at the target location.
2. Expert-group design: Each student is assigned to one expert group. The group designs only one of the three controller architectures and uses MATLAB to determine compensator parameters, calculate the gain, and verify the closed-loop response.
3. Implementation analysis: Students identify the order and fastest pole of their controller. The shortest controller time constant is used as a simple proxy for how demanding the design may be to simulate or implement digitally. This is intentionally presented as an implementation indicator rather than a complete processor-load model.
4. Jigsaw comparison: Students reorganize into mixed groups containing experts from Designs A, B, and C. Each expert teaches the other students how the assigned controller works and presents the MATLAB evidence. The group builds a common comparison table containing:
- compensator structure/order,
- dominant closed-loop poles,
- rise time,
- 2% settling time,
- percent overshoot,
- fastest controller pole magnitude,
- shortest controller time constant,
- implementation concerns, and
- robustness concerns.
5. Client-value recommendation: The mixed group recommends a design for the client. The client values meeting the transient-response target, fast response with limited overshoot, practical implementation, and reasonable robustness to modeling error. No numerical weighting is prescribed, so students must state their assumptions and explain the gains and sacrifices associated with each design.
Student Activity Guidelines (MATLAB Live Script 105kB Sep28 26)
Instructor Solution (MATLAB Live Script 709kB Sep28 26)

Students often focus immediately on the controller with the smallest settling time. Before the jigsaw discussion, remind them that controller design is a multi-objective engineering problem. A faster response can come with additional controller states, faster internal dynamics, numerical demands, or robustness concerns.

A suggested rubric is:
- Technical controller design (40%): correct use of root-locus conditions, compensator construction, gain calculation, and closed-loop verification.
- MATLAB analysis and evidence (25%): clear root-locus/step-response plots and accurate tabulation of performance metrics.
- Tradeoff analysis (20%): meaningful discussion of controller order, fastest dynamics, implementation demands, and robustness.
- Client-value recommendation (15%): recommendation is supported by numerical evidence, acknowledges tradeoffs, and states assumptions.

A short individual exit question can be added after the group work: Which piece of evidence changed your view of the three designs the most, and why?