Getting Started

Nichols Plot Design

An alternative method for designing compensators is to use the Nichols plot, which combines gain and phase information in a single plot. The combination of the two is useful when you are designing to gain and phase margin specifications.

You can design compensators with the SISO Design Tool by using Nichols plot techniques. This section repeats the DC motor compensator design presented in Example: DC Motor, only this time the focus is on Nichols plot techniques. The design strategy, however, is the same:

1. Adjust the compensator gain to improve the rise time.
2. Add an integrator to eliminate steady-state error.
3. Add a lead network to further improve the rise time while minimizing overshoot.

DC Motor Example

From "SISO Example: the DC Motor" on page 2-4, the transfer function of the DC motor is

• Transfer function:
         1.5
  ------------------
  s^2 + 14 s + 40.02
  

This example uses the design criteria specified in Design Specifications:

• Rise time of less than 0.5 second
• Steady-state error of less than 5%
• Overshoot of less than 10%
• Gain margin greater than 20 dB
• Phase margin greater than 40 degrees

Opening a Nichols Plot

To open the SISO Design Tool with a Bode diagram and a Nichols plot, use these commands.

• load ltiexamples
  sisotool({'bode','nichols'},sys_dc)
  

This figure opens.

Figure 4-42: SISO Design Tool with a Bode Diagram and a Nichols Plot

Storing and Retrieving Intermediate Designs

Adjusting the Compensator Gain