Control Engineering Basics
A plant that contains no integrator (a type 0 system) is under proportional (P) control. Which of the following correctly describes the general change when the proportional gain Kp is increased?
- AThe steady-state error becomes smaller but not zero, and too large a gain makes the response oscillatory or unstable
- BThe steady-state error becomes exactly zero, and the response always stays stable without any oscillation, however large the gain is made
- CThe speed of response does not change, and only the steady-state error grows
Show answer and explanation
Answer: A. The steady-state error becomes smaller but not zero, and too large a gain makes the response oscillatory or unstable
Proportional control is the most basic control, producing a manipulated variable proportional to the error. Increasing Kp makes the response faster and reduces the steady-state error to a step, 1/(1 + Kp·K) where K is the steady-state gain of the plant, but with no error the manipulated variable would also be zero, so the error does not reach zero (offset). Raising the gain also reduces the phase margin and increases the overshoot, and a plant with a large lag becomes unstable. Integral action is added to remove the steady-state error.
- A. Correct. Speed and steady-state error improve, at the cost of stability.
- B. Proportional control alone leaves a steady-state error (offset), and too much gain makes it unstable.
- C. Increasing the gain makes the response faster and the steady-state error smaller.