True/false: derivative controllers always used with others

True. A derivative (D) controller is never used alone; it is always combined with a proportional and/or integral controller, as PD or PID.

Justification

A derivative controller gives an output proportional to the rate of change of the error:

$$u(t)=K_d\frac{de(t)}{dt},\qquad G_c(s)=K_ds$$

1. No action on constant error: if the error is constant (even large), $de/dt=0$, so the controller output is zero. A steady error is never corrected, so D alone cannot hold the output at the set point.
2. Blocks DC signals: $G_c(0)=0$. In the loop it acts like a zero at the origin, which can cancel the plant's integrator and reduce the system type, so the steady-state error grows.
3. Noise amplification: $|G_c(j\omega)|=K_d\omega$ rises with frequency, so high-frequency noise is amplified strongly. With a P term the useful low-frequency action dominates.
4. Anticipatory, not corrective: D action predicts the error trend and adds damping; it only improves the transient part of the response.

How it is used

With proportional action (PD):

$$G_c(s)=K_p+K_ds=K_p(1+T_ds)$$

• The P part removes and holds the error.
• The D part adds a zero, increases damping, reduces overshoot and settling time, and improves stability.

Example: in a position servo, a PD controller lets the motor slow down as it nears the target (D) while still pushing it there (P). A pure D controller would stop acting once the motor is at rest away from the target.