piddata

Access coefficients of parallel-form PID controller

Syntax

[Kp,Ki,Kd,Tf] = piddata(sys) [Kp,Ki,Kd,Tf,Ts] = piddata(sys) [Kp,Ki,Kd,Tf,Ts] = piddata(sys,J1,...,JN)

Description

[Kp,Ki,Kd,Tf] = piddata(sys) returns the PID gains Kp,Ki, Kd and the filter time constant Tf of the parallel-form controller represented by the dynamic system sys.

[Kp,Ki,Kd,Tf,Ts] = piddata(sys) also returns the sample time Ts.

[Kp,Ki,Kd,Tf,Ts] = piddata(sys,J1,...,JN) extracts the data for a subset of entries in sys, where sys is an N-dimensional array of dynamic systems. The indices J specify the array entry to extract.

Input Arguments

`sys`	SISO dynamic system or array of SISO dynamic systems. If `sys` is not a `pid` object, it must represent a valid PID controller that can be written in parallel PID form.
`J`	Integer indices of N entries in the array `sys` of dynamic systems. For example, suppose `sys` is a 4-by-5 (two-dimensional) array of `pid` controllers or dynamic system models that represent PID controllers. The following command extracts the data for entry (2,3) in the array. [Kp,Ki,Kd,Tf,Ts] = piddata(sys,2,3);

Output Arguments

`Kp`	Proportional gain of the parallel-form PID controller represented by dynamic system `sys`. If `sys` is a `pid` controller object, the output `Kp` is equal to the `Kp` value of `sys`. If `sys` is not a `pid` object, `Kp` is the proportional gain of a parallel PID controller equivalent to `sys`. If `sys` is an array of dynamic systems, `Kp` is an array of the same dimensions as `sys`.
`Ki`	Integral gain of the parallel-form PID controller represented by dynamic system `sys`. If `sys` is a `pid` controller object, then the output `Ki` is equal to the `Ki` value of `sys`. If `sys` is not a `pid` object, then `Ki` is the integral gain of a parallel PID controller equivalent to `sys`. If `sys` is an array of dynamic systems, then `Ki` is an array of the same dimensions as `sys`.
`Kd`	Derivative gain of the parallel-form PID controller represented by dynamic system `sys`. If `sys` is a `pid` controller object, then the output `Kd` is equal to the `Kd` value of `sys`. If `sys` is not a `pid` object, then `Kd` is the derivative gain of a parallel PID controller equivalent to `sys`. If `sys` is an array of dynamic systems, then `Kd` is an array of the same dimensions as `sys`.
`Tf`	Filter time constant of the parallel-form PID controller represented by dynamic system `sys`. If `sys` is a `pid` controller object, the output `Tf` is equal to the `Tf` value of `sys`. If `sys` is not a `pid` object, `Tf` is the filter time constant of a parallel PID controller equivalent to `sys`. If `sys` is an array of dynamic systems, `Tf` is an array of the same dimensions as `sys`.
`Ts`	Sample time of the dynamic system `sys`. `Ts` is always a scalar value.

Examples

Extract the proportional, integral, and derivative gains and the filter time constant from a parallel-form pid controller.

For the following pid object:

sys = pid(1,4,0.3,10);

you can extract the parameter values from sys by entering:

[Kp Ki Kd Tf] = piddata(sys);

Extract the parallel form proportional and integral gains from an equivalent standard-form PI controller.

For a standard-form PI controller, such as:

sys = pidstd(2,3);

you can extract the gains of an equivalent parallel-form PI controller by entering:

[Kp Ki] = piddata(sys)

These commands return the result:

Kp =

     2


Ki =

    0.6667

Extract parameters from a dynamic system that represents a PID controller.

The dynamic system

$H (z) = \frac{(z - 0.5) (z - 0.6)}{(z - 1) (z + 0.8)}$

represents a discrete-time PID controller with a derivative filter. Use piddata to extract the parallel-form PID parameters.

H = zpk([0.5 0.6],[1,-0.8],1,0.1);  % sample time Ts = 0.1s
[Kp Ki Kd Tf Ts] = piddata(H);

the piddata function uses the default ForwardEuler discrete integrator formula for IFormula and DFormula to compute the parameter values.

Extract the gains from an array of PI controllers.

sys = pid(rand(2,3),rand(2,3)); % 2-by-3 array of PI controllers
[Kp Ki Kd Tf] = piddata(sys);

The parameters Kp, Ki, Kd, and Tf are also 2-by-3 arrays.

Use the index input J to extract the parameters of a subset of sys.

[Kp Ki Kd Tf] = piddata(sys,5);

Tips

If sys is not a pid controller object, piddata returns the PID gains Kp, Ki, Kd and the filter time constant Tf of a parallel-form controller equivalent to sys.

For discrete-time sys, piddata returns the parameters of an equivalent parallel-form controller. This controller has discrete integrator formulas IFormula and DFormula set to ForwardEuler. See the pid reference page for more information about discrete integrator formulas.

Documentation