# Documentation

## Automated Tuning Design

### Supported Automated Tuning Methods

The SISO Design Tool simplifies the task of designing and tuning compensators. There are five automated tuning methods in the SISO Design Tool to help you design an initial stabilizing compensator for a SISO loop on-the-fly or refine existing compensator design so that it satisfies a certain user-defined design specification.

The available design methods are:

• Optimization-based tuning

• PID tuning

• Internal Model Control (IMC) tuning

• LQG synthesis

• Loop shaping

For a detailed discussion of these, see Automated Tuning.

Follow these steps to load and display the DC Motor example for automated tuning:

1. If you have not yet built the DC Motor example, type

```load ltiexamples ```

2. To open the SISO Design Tool and import the DC motor, type

```controlSystemDesigner(sys_dc) ```

at the MATLAB® prompt. This opens both the SISO Design Task node on the Control and Estimation Tools Manager and the Graphical Tuning window with `sys_dc` loaded.

3. Click the Analysis Plots tab to set the analysis plots. Select the plot type as `Step` for Plot 1. Then, check the box for plot 1 to the left of ```Closed-Loop r to y```, as shown in the following figure, to open a linked Linear System Analyzer with the closed-loop step response from reference signal r to output signal y.

4. In the Linear System Analyzer that appears, use the right-click menu to add rise time and steady state values to your plot.

Step Response When Compensator = 1

Note that by default, the compensator is 1 and unit negative feedback is used (see Architecture). When a unit step is applied to the setpoint change, the steady state value of the system output is 0.0361, which is far from the setpoint, and its rise time is 0.589.

### Applying Automated PID Tuning

1. Click the Automated Tuning tab.

2. Select `PID tuning` from the Design method list.

3. Leave `C` as the default compensator.

#### Design a Proportional-Only Controller

1. In the Tuning method menu, select ```Classical design formulas```.

2. In the Design options area, select P for proportional-only control (C = Kp).

3. In the Formula menu, select `Ziegler-Nichols step response`.

4. Click Update Compensator. The Linear System Analyzer is updated with the application of PID automated tuning with a proportional-only compensator. The compensator value is now 203.75.

Note that the rise time is reduced to 0.0769 seconds, compared with 0.589 when C = 1. However, the steady state value of 0.885 can still be improved by setting the automated tuning controller type to `PI`.

#### Designing a Proportional-Integral Controller

1. In the Design options area, select PI for proportional-integral control ($C={K}_{p}+\frac{{K}_{I}}{s}$).

2. In the Formula menu, select `Ziegler-Nichols step response`.

3. Click Update Compensator. The Linear System Analyzer is updated with the application of PID automated tuning with a proportional-integral compensator. The compensator value is now $1448.8×\frac{\left(1+0.13s\right)}{s}$.

Now the steady state value is 1. Applying automated tuning using PID tuning set to `PI` guarantees zero offset.

This compensator design has a high degree of overshoot and ringdown. For further improvements on the result, try the ```Robust response time``` tuning method.