Variable name  Description 

FbMmMeasAct  Actual meassured height in mm 
FbMmCtrlSetp  Setpoint (height) sent to controller in mm 
FbPWMCtrlOut  Controller output 
In order to identify the plant, we need to get the system to steadily oscillate. After this we shall note the critical gain (\(K_{krit}\)) and the oscillation period (\(T_u\)).
Is \(K_{krit}\) dependent on the setpoint you defined?
The controller setting rules per ZieglerNichols [1] give you a simple yet powerful way to paramatrize your controller (see Theory). Now you may calculate and set the gain partameters of the proportional, integral and derivative parts of the controller \(R(s)\) in the ideal form:
\(R(s) = K_r \left( 1 + \frac{1}{T_N \cdot s} + T_v \cdot s\right)\)
PI  PID  

Controller gain (\(K_r\))  \(K_r = 0.45 \cdot K_{krit}\)  \(K_r = 0.6 \cdot K_{krit}\) 
Integral time (\(T_N\))  \(T_N = 0.85\cdot T_u\)  \(T_N = 0.5\cdot T_u\) 
Derivative time (\(T_v\))  \(T_N = 0.12\cdot T_u\) 
[1] Kun Li Chien, J. A. Hrones, J. B. Reswick: On the Automatic Control of Generalized Passive Systems. In: Transactions of the American Society of Mechanical Engineers., Bd. 74, Cambridge (Mass.), USA, Feb. 1952, S. 175–185
In this phase you will set up the controller. You have two possible optimizations in the Chien, Hrones & Reswick method: Setpoint tracking and disturbance rejection
Write the required \(K_P\) and \(K_I\) for each optimization in the parallel form of the controller:
\(R(s) = K_P + K_I \cdot \frac{1}{s} + K_D \cdot s\)
Controller  PI  PID 

Proportional gain \(K_P\) 
4.1
\(K_P\)

4.4
\(K_P\)

Integral gain \(K_I\) 
4.2
\(K_I\)

4.5
\(K_I\)

Derivative gain \(K_D\) 
4.3
\(K_D\)

4.6
\(K_D\)

Document your result 
In this section you will look at the windup effect and see the change in the response of a controller with an antiwindup feature. For this you will need the best controller parametrization you got from the previous section.
Case  Antiwindup OFF  Antiwindup ON 

Result 
Please explain in your own words what the windup effect is and the difference between the experiment without antiwindup mechanism and with antiwindup mechanism.
Setpoint/controller output  Value 
 