# Experiment 1 Dashboard (Preparation)

## Getting started

Let's begin with some information about you
1.1 Registration ID
1.2 Name
1.3 Test bench
Throughout this experiment the following IEC-conform software variables are in use:

## 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 $$T_u$$

2.1 $$K_{krit}$$
2.2 $$T_u$$

Is $$K_{krit}$$ dependent on the setpoint you defined?

2.3

## 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.

## 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.

5.3

## Dashboard

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