Entire system

Select this option to constrain the locations of closed-loop poles of the control system.

Specific feedback loop(s)

Select this option to specify one or more feedback loops to constrain. Specify a feedback loop by selecting a signal location in your control system. Poles Goal constrains the dynamics of the sensitivity function measured at that location. (See getSensitivity for information about sensitivity functions.)

To constrain the dynamics of a SISO loop, select a single-valued location. For example, to constrain the dynamics of the sensitivity function measured at a location named 'y', click Add signal to list and select 'y'. To constrain the dynamics of a MIMO loop, select multiple signals or a vector-valued signal.

Compute poles with the following loops open

Select one or more signal locations in your model at which to open a feedback loop for the purpose of evaluating this tuning goal. The tuning goal is evaluated against the open-loop configuration created by opening feedback loops at the locations you identify. For example, to evaluate the tuning goal with an opening at a location named 'x', click Add signal to list and select 'x'.

Minimum decay rate

Enter the target minimum decay rate for the system poles. Closed-loop system poles that depend on the tunable parameters are constrained to satisfy Re(s) < -MinDecay for continuous-time systems, or log(|z|) < -MinDecay*Ts for discrete-time systems with sample time Ts. This constraint helps ensure stable dynamics in the tuned system.

Enter 0 to impose no constraint on the decay rate.

Minimum damping

Enter the target minimum damping of closed-loop poles of tuned system, as a value between 0 and 1. Closed-loop system poles that depend on the tunable parameters are constrained to satisfy Re(s) < -MinDamping*|s|. In discrete time, the damping ratio is computed using s = log(z)/Ts.

Enter 0 to impose no constraint on the damping ratio.

Maximum natural frequency

Enter the target maximum natural frequency of poles of tuned system, in the units of the control system model you are tuning. When you tune the control system using this requirement, closed-loop system poles that depend on the tunable parameters are constrained to satisfy |s| < MaxFrequency for continuous-time systems, or |log(z)| < MaxFrequency*Ts for discrete-time systems with sample time Ts. This constraint prevents fast dynamics in the control system.

Enter Inf to impose no constraint on the natural frequency.

Enforce goal in frequency range

Limit the enforcement of the tuning goal to a particular frequency band. Specify the frequency band as a row vector of the form [min,max], expressed in frequency units of your model. For example, to create a tuning goal that applies only between 1 and 100 rad/s, enter [1,100]. By default, the tuning goal applies at all frequencies for continuous time, and up to the Nyquist frequency for discrete time.

The Poles Goal applies only to poles with natural frequency within the range you specify.

Apply goal to

Use this option when tuning multiple models at once, such as an array of models obtained by linearizing a Simulink model at different operating points or block-parameter values. By default, active tuning goals are enforced for all models. To enforce a tuning requirement for a subset of models in an array, select Only Models. Then, enter the array indices of the models for which the goal is enforced. For example, suppose you want to apply the tuning goal to the second, third, and fourth models in a model array. To restrict enforcement of the requirement, enter 2:4 in the Only Models text box.

For more information about tuning for multiple models, see Robust Tuning Approaches (Robust Control Toolbox).

f(x) = 1 means the smallest damping among the constrained poles is ζ = 0.5 exactly.

f(x) = 1.1 means the smallest damping ζ = 0.5/1.1 = 0.45, roughly 10% less than the target.

f(x) = 0.9 means the smallest damping ζ = 0.5/0.9 = 0.55, roughly 10% better than the target.