Simulink Control Design™ - MathWorks

Specify PI-D and I-PD Controllers

About PI-D and I-PD Controllers

PI-D and I-PD controllers are used to mitigate the influence of changes in the reference

signal on the control signal. These controllers are variants of the 2DOF PID controller.

The general formula of a parallel-form 2DOF PID controller is:

u=P(br−y)+I

1

s

(r−y)+D

N

1+N

1

s

(cr−y).

Here, r and y are the reference input and measured output, respectively. u is the

controller output, also called the control signal. P, I, and D specify the proportional,

integral, and derivative gains, respectively. N specifies the derivative filter coefficient. b

and c specify setpoint weights for the proportional and derivative components,

respectively. For a 1DOF PID, b and c are equal to 1.

If r is nonsmooth or discontinuous, the derivative and proportional components can

contribute large spikes or offsets in u, which can be infeasible. For example, a step input

can lead to a large spike in u because of the derivative component. For a motor actuator,

such an aggressive control signal could damage the motor.

To mitigate the influence of r on u, set b or c, or both, to 0. Use one of the following

setpoint-weight-based forms:

• PI-D (b = 1 and c = 0) — Derivative component does not directly propagate changes in
  r to u, whereas the proportional component does. However, the derivative component,
  which has a greater impact, is suppressed. Also referred to as the derivative of output
  controller.

The general formula for this controller form is:

u=P(r−y)+I

1

s(r−y)−D

N

1+N^1 s

y.

• I-PD (b = 0 and c = 0) — Proportional and derivative components do not directly
  propagate changes in r to u.

The general formula for this controller form is:

7 PID Controller Tuning