make1DOF

Convert 2-DOF PID controller to 1-DOF controller

Syntax

C1 = make1DOF(C2)

Description

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.

Examples

Convert 2-DOF PID Controller to 1-DOF

Design a 2-DOF PID controller for a plant.

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.

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.

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--')

Input Arguments

C2 — 2-DOF PID controller

pid2 object | pidstd2 object

2-DOF PID controller, specified as a pid2 object or a pidstd2 object.

Output Arguments

C1 — 1-DOF PID controller

pid object | pidstd object

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:

$$u=K_p\left(br-y\right)+\frac{K_i}{s}\left(r-y\right)+\frac{K_{d}s}{T_{f}s+1}\left(cr-y\right)$$

Then C1 is a parallel-form 1-DOF pid controller of the form:

$$C_1=K_p+\frac{K_i}{s}+\frac{K_{d}s}{T_{f}s+1}.$$

The PID gains K_p, K_i, and K_d, and the filter time constant T_f 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.

Version History

Introduced in R2015b