Simulink Control Design™ - MathWorks

Interpret Numeric Tuning Results

When you tune a control system with systune or Control System Tuner, the software

provides reports that give you an overview of how well the tuned control system meets

your design requirements. Interpreting these reports requires understanding how the

tuning algorithm optimizes the system to satisfy your tuning goals. (The software also

provides visualizations of the tuning goals and system responses to help you see where

and by how much your requirements are not satisfied. For information about using these

plots, see “Visualize Tuning Goals” on page 10-187.)

Tuning-Goal Scalar Values

The tuning software converts each tuning goal into a normalized scalar value which it

then constrains (hard goals) or minimizes (soft goals). Let fi(x) and gj(x) denote the scalar

values of the soft and hard goals, respectively. Here, x is the vector of tunable parameters

in the control system to tune. The tuning algorithm solves the minimization problem:

Minimize max

i

fix subject to max

j

gjx < 1, for xmin<x<xmax.

xmin and xmax are the minimum and maximum values of the free parameters of the control

system. (For information about the specific functions used to evaluate each type of

requirement, see the reference pages for each tuning goal.)

When you use both soft and hard tuning goals, the software solves the optimization as a

sequence of subproblems of the form:

min

x

maxαfx,gx.

The software adjusts the multiplier α so that the solution of the subproblems converges to

the solution of the original constrained optimization problem.

The tuning software reports the final scalar values for each tuning goal. When the final

value of fi(x) or gj(x) is less than 1, the corresponding tuning goal is satisfied. Values

greater than 1 indicate that the tuning goal is not satisfied for at least some conditions.

For instance, a tuning goal that describes a frequency-domain constraint might be

satisfied at some frequencies and not at others. The closer the value is to 1, the closer the

tuning goal is to being satisfied. Thus these values give you an overview of how

successfully the tuned system meets your requirements.

10 Control System Tuning