Simulink Control Design™ - MathWorks

Hs =

K

T 1 s+1

.

This model is defined by the parameters K, the gain, and T 1 , the first time constant. The

most complex process-model structure choose has three poles, an additional integrator, a

zero, and a time delay, such as the following model, which has one real pole and one

complex conjugate pair of poles:

Hs =K

Tzs+1

sT 1 s+1 Tω^2 s^2 +2ζTωs+1

e−τs.

In this model, the configurable parameters include the time constants associated with the

poles and the zero, T 1 , Tω, and Tz. The other parameters are the damping coefficient ζ, the

gain K, and the time delay τ.

When you select a process model type, PID Tuner automatically computes initial values

for the plant parameters and displays a plot showing both the estimated model response

and your measured or simulated data. You can edit the parameter values graphically

using indicators on the plot, or numerically using the Plant Parameters editor. For an

example illustrating this process, see “Interactively Estimate Plant Parameters from

Response Data” (Control System Toolbox).

The following table summarizes the various parameters that define the available types of

process models.

Parameter Used By Description

K — Gain All transfer functions Can take any real value.

In the plot, drag the plant

response curve (blue) up or

down to adjust K.

T 1 — First time constant Transfer function with one

or more real poles

Can take any value between

0 and T, the time span of

measured or simulated data.

In the plot, drag the red x

left (towards zero) or right

(towards T) to adjust T 1.

7 PID Controller Tuning