Control Engineering Basics
In a unity-feedback system with a stable closed loop, the forward transfer function G(s) contains one integrator 1/s (a type 1 system). Which of the following correctly describes the steady-state error?
- AThe steady-state error to a step setpoint is zero, while a constant error remains for a ramp setpoint that increases at a constant rate
- BA constant steady-state error remains even for a step setpoint, and for a ramp setpoint the error keeps growing larger and larger with time
- CThe steady-state error is zero for all of a step, a ramp and a setpoint increasing with constant acceleration
Show answer and explanation
Answer: A. The steady-state error to a step setpoint is zero, while a constant error remains for a ramp setpoint that increases at a constant rate
The number of integrators in the forward path is called the type of the system. In a type 1 system, any remaining error keeps the integrator changing the manipulated variable, so the steady-state error to a step is zero. To keep following a ramp setpoint, a constant error is needed, of size 1/Kv, where Kv = lim[s→0] sG(s) is the velocity error constant. For example, G(s) = 2/(s(s + 1)) has Kv = 2, and the steady-state error to a unit ramp is 0.5.
- A. Correct. One integrator removes the error to a step.
- B. This is the behavior of a type 0 system, which has no integrator.
- C. Following a setpoint increasing with constant acceleration without error needs two integrators (type 2).