C1 = make1DOF(C2)
converts the two-degree-of-freedom PID controller C2 to one
degree of freedom by removing the terms that depend on coefficients
b and c.
G = tf(1,[1 0.5 0.1]);
C2 = pidtune(G,'pidf2',1.5)
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 = 0.664, c = 0.0136
Continuous-time 2-DOF PIDF controller in parallel form.
Model Properties
Convert the controller to one degree of freedom.
C1 = make1DOF(C2)
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.
Model Properties
The new controller has the same PID gains and filter constant. However, make1DOF removes the terms involving the setpoint weights b and c. Therefore, in a closed loop with the plant G, the 2-DOF controller C2 yields a different closed-loop response from C1.
CM = tf(C2);
T2 = CM(1)*feedback(G,-CM(2));
T1 = feedback(G*C1,1);
stepplot(T2,T1,'r--')
1-DOF PID controller, returned as a pid or
pidstd object. C1 is in
parallel form if C2 is in parallel form, and standard
form if C2 is in standard form.
For example, suppose C2 is a continuous-time,
parallel-form 2-DOF pid2 controller. The relationship
between the inputs, r and y, and the
output u of C2 is given by:
Then C1 is a parallel-form 1-DOF
pid controller of the form:
The PID gains
Kp,
Ki, and
Kd, and the filter time
constant Tf are unchanged.
make1DOF removes the terms that depend on the
setpoint weights b and c. 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.
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