Variable name | Description |
---|---|
VtgMeasAct | Actual voltage |
VtgCtrlSetp | Setpoint sent to controller |
VtgCtrlOut | Controller output |
In order to identify the plant, we need to get its step response. After this we shall draw the inflectional tangent of the response and read the delay time (\(T_u\)) and the compensation time (\(T_g\)) as well as the static gain (\(K_s\))of the plant.
\(T_u\) is related to the electrical properties, measurement, anti-aliasing filter and sample time. It is possible to measure it and in this case it should be very near the sampling time of the experiment, which is \(T_a=5\,\mathrm{ms}\). You can zoom-in to determine the values
How did you calculate the static gain \(K_s\) from the values you obtained from the graph? Is \(K_s\) dependent on the setpoint you defined?
The controller setting rules per Chien, Hrones and Reswick [1] give you a simple yet powerful way to paramatrize your controller (see Theory). Now you may turn on your controller and set the gain partameters of the proportional and integral parts of the controller \(R(s)\) in the ideal form:
\(R(s) = K_r \left( 1 + \frac{1}{T_N \cdot s}\right)\)
Controller without overshoot | Setpoint tracking optimization | Disturbace rejection optimization |
---|---|---|
Controller gain (\(K_r\)) | \(K_r = 0.35 \frac{T_g}{K_S\cdot T_u}\) | \(K_r = 0.6 \frac{T_g}{K_S\cdot T_u}\) |
Integral time (\(T_N\)) | \(T_N = 1.2\cdot T_g\) | \(T_N = 4\cdot T_u\) |
[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:
\(R(s) = K_P + K_I \cdot \frac{1}{s}\)
Optimization | Setpoint tracking | Disturbance rejection |
---|---|---|
Proportional gain \(K_P\) |
4.1
\(K_P\)
|
4.3
\(K_P\)
|
Integral gain \(K_I\) |
4.2
\(K_I\)
|
4.4
\(K_I\)
|
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 anti-windup feature. For this you will need the best controller parametrization you got from the previous section.
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.
Control Value in V | |
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Set Value in rpm | |
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