Feedback Control and Proportional Action

Robotics and Automation · CHAPTER 3 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Explain error, feedback and actuator saturation.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

A feedback controller compares a reference with a measured output. Proportional control multiplies the error by a gain. Larger gain increases corrective action but can worsen oscillation or amplify noise. Actuators have limits, and a static proportional law alone does not describe full closed-loop dynamics.

2. Write the model

e=r−y; u=Kp e

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

With target 100 units and Kp=2, measured outputs 80,90,100 produce commands 40,20,0 before actuator limits. If the actuator limit is 30, the first command saturates.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Measured output	Raw command	Command limited to ±30
80	40	30
90	20	20
100	0	0

Sweep measured output and compare raw with saturated commands. Do not interpret this static table as a stability test.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

What command follows when y=105?

Reveal the answer and check your work

−10 before limits.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

Controller tuning requires a plant model or controlled experimental validation.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.