Getting started
Let's begin with some information about you| Variable name | Description |
|---|---|
| FbMmMeasAct | Actual meassured height in mm |
| FbMmCtrlSetp | Setpoint (height) sent to controller in mm |
| FbPWMCtrlOut | Controller output |
Critical Gain
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 (\(T_u\)).
Run the experiment
- Set a suitable setpoint height to be applied to the FloatingBall Experiment (between 100 and 800 mm) and load the values.
- Make sure the controller is on with a \(K_p\) of around 0.05.
- Run the experiment... and steadily increase \(K_s\) until you find a steady oscillation. Repeat if necessary
- Determine \(K_{krit}\) and \(T_u\)
Document your results
Is \(K_{krit}\) dependent on the setpoint you defined?
Applying the critical stability method per Ziegler & Nichols
The controller setting rules per Ziegler-Nichols [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
Controller gains
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:
\(R(s) = K_P + K_I \cdot \frac{1}{s} + K_D \cdot s\)
Run the experiment
- Please write your calculated values of \(K_P\), \(K_I\) and \(K_D\) in the controller dashboard or use the button to transfer the values automatically
- Turn controller and Anti-windup on and set a suitable setpoint.
- For each set of controller parameters, run the experiment (for the same setpoint). After each experiment you should take a look at the step response and the disturbance response. Before changing the parameters make a snapshot of your findings.
| 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 |
|
|
Anti-Windup
In this section you will look at the windup effect and see the change in the response of a controller with an anti-windup feature. For this you will need the best controller parametrization you got from the previous section.
Run the experiment
- Verify that:
- Controller is turned on
- Anti-windup is turned off
- Setpoint is set to 0 mm
- Turn the experiment on and immediately set a suitable setpoint.
- Look carefully at the controller output FbPWMCtrlOut and the controlled output value FbMmMeasAct. Take a snapshot of your results.
- Repeat the first two points but with Anti-Windup on
| Case | Anti-windup OFF | Anti-windup ON |
|---|---|---|
| Result |
|
|
Please explain in your own words what the wind-up effect is and the difference between the experiment without anti-windup mechanism and with anti-windup mechanism.
Dashboard
| Setpoint/controller output | Value |
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