# 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:

## Step response

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

### Run the experiment

• Set a suitable voltage to be applied to the DC-Machine (between 0 and 9V) and load the values.
• Make sure the controller is off (direct feedthrough of setpoint voltage).
• Run the experiment...
• Determine $$T_0$$, $$T_u$$, $$T_g$$ and $$K_s$$

### Document your results

2.1 $$T_0$$
2.2 $$T_u$$
2.3 $$T_g$$
2.4 $$K_s$$

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?

2.5

## Applying the empirical method per Chien, Chrones & Reswick

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

## 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:

$$R(s) = K_P + K_I \cdot \frac{1}{s}$$

## Run the experiment

• Please write your calculated values of $$K_P$$ and $$K_I$$ 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 V
• Turn the experiment on and immediately set a suitable setpoint.
• Look carefully at the controller output VtgCtrlOut and the controlled output value VtgMeasAct. 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

6.1 Date
6.2 Key