make2DOF
Convert 1-DOF PID controller to 2-DOF controller
Description
Examples
Convert 1-DOF PID Controller to 2-DOF
Design a 1-DOF PID controller for a plant.
G = tf(1,[1 0.5 0.1]);
C1 = pidtune(G,'pidf',1.5)
C1 = 1 s Kp + Ki * --- + Kd * -------- s Tf*s+1 with Kp = 1.12, Ki = 0.23, Kd = 1.3, Tf = 0.122 Continuous-time PIDF controller in parallel form.
Convert the controller to two degrees of freedom.
C2 = make2DOF(C1)
C2 = 1 s u = Kp (b*r-y) + Ki --- (r-y) + Kd -------- (c*r-y) s Tf*s+1 with Kp = 1.12, Ki = 0.23, Kd = 1.3, Tf = 0.122, b = 1, c = 1 Continuous-time 2-DOF PIDF controller in parallel form.
The new controller has the same PID gains and filter constant. It also contains new terms involving the setpoint weights b
and c
. By default, b
= c
= 1. Therefore, in a closed loop with the plant G
, the 2-DOF controller C2
yields the same response as C1
.
T1 = feedback(G*C1,1);
CM = tf(C2);
T2 = CM(1)*feedback(G,-CM(2));
stepplot(T1,T2,'r--')
Convert C1
to a 2-DOF controller with different b
and c
values.
C2_2 = make2DOF(C1,0.5,0.75)
C2_2 = 1 s u = Kp (b*r-y) + Ki --- (r-y) + Kd -------- (c*r-y) s Tf*s+1 with Kp = 1.12, Ki = 0.23, Kd = 1.3, Tf = 0.122, b = 0.5, c = 0.75 Continuous-time 2-DOF PIDF controller in parallel form.
The PID gains and filter constant are still unchanged, but the setpoint weights now change the closed-loop response.
CM_2 = tf(C2_2);
T2_2 = CM_2(1)*feedback(G,-CM_2(2));
stepplot(T1,T2_2,'r--')
Input Arguments
C1
— 1-DOF PID controller
pid
object | pidstd
object
1-DOF PID controller, specified as a pid
object or a
pidstd
object.
b
— Setpoint weight on proportional term
1 (default) | real nonnegative scalar
Setpoint weight on proportional term, specified as a real, nonnegative,
finite value. If you do not specify b
, then
C2
has b
= 1.
c
— Setpoint weight on derivative term
1 (default) | real nonnegative scalar
Setpoint weight on derivative term, specified as a real, nonnegative,
finite value. If you do not specify c
, then
C2
has c
= 1.
Output Arguments
C2
— 2-DOF PID controller
pid2
object | pidstd2
object
2-DOF PID controller, returned as a pid2
object or
pidstd2
object. C2
is in
parallel form if C1
is in parallel form, and standard
form if C1
is in standard form.
For example, suppose C1
is a continuous-time,
parallel-form pid
controller of the form:
Then C2
is a parallel-form 2-DOF
pid2
controller, which has two inputs and one
output. The relationship between the inputs, r and
y, and the output u of
C2
is given by:
The PID gains Kp,
Ki, and
Kd, and the filter time
constant Tf are unchanged. The
setpoint weights b and c are specified
by the input arguments b
and c
, or
1 by default. For more information about 2-DOF PID controllers, see Two-Degree-of-Freedom PID Controllers.
The conversion also preserves the values of the properties
Ts
, TimeUnit
, Sampling
Grid
, IFormula
, and
DFormula
.
Version History
Introduced in R2015b
See Also
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