Bode diagram design is an interactive graphical method of modifying a compensator to achieve a specific openloop response (loop shaping). To interactively shape the openloop response using Control System Designer , use the Bode Editor. In the editor, you can adjust the openloop bandwidth and design to gain and phase margin specifications.
To adjust the loop shape, you can add poles and zeros to your compensator and adjust their values directly in the Bode Editor, or you can use the Compensator Editor. For more information, see Edit Compensator Dynamics.
For information on all of the tuning methods available in Control System Designer, see Control System Designer Tuning Methods.
This example shows how to design a compensator for a DC motor using Bode diagram graphical tuning techniques.
Plant Model and Requirements
The transfer function of the DC motor plant, as described in SISO Example: The DC Motor, is:
$$G=\frac{1.5}{{s}^{2}+14s+40.02}$$
For this example, the design requirements are:
Rise time of less than 0.5 seconds
Steadystate error of less than 5%
Overshoot of less than 10%
Gain margin greater than 20 dB
Phase margin greater than 40 degrees
Open Control System Designer
At the MATLAB^{®} command line, create a transfer function model of the plant, and open Control System Designer in the Bode Editor configuration.
G = tf(1.5,[1 14 40.02]);
controlSystemDesigner('bode',G);
The app opens and imports G
as the plant
model for the default control architecture, Configuration
1.
In the app, the following response plots open:
Openloop Bode Editor for the LoopTransfer_C
response.
This response is the openloop transfer function GC,
where C is the compensator and G is
the plant.
Step Response for the IOTransfer_r2y
response.
This response is the inputoutput transfer function for the overall
closedloop system.
Tip
To open the openloop Bode Editor when Control
System Designer is already open, on the Control System tab,
in the Tuning Methods dropdown list, select Bode
Editor. In the Select Response to Edit dialog box, select
an existing response to plot, or create a 
To view the openloop frequency response and closedloop step response simultaneously, on the Views tab, click Left/Right.
The app displays the Bode Editor and Step Response plots sidebyside.
Adjust Bandwidth
Since the design requires a rise time less than 0.5 seconds, set the openloop DC crossover frequency to about 3 rad/s. To a firstorder approximation, this crossover frequency corresponds to a time constant of 0.33 seconds.
To make the crossover easier to see, turn on the plot grid. Rightclick the Bode Editor plot area, and select Grid. The app adds a grid to the Bode response plots.
To adjust the crossover frequency increase the compensator gain. In the Bode Editor plot, in the Magnitude response plot, drag the response upward. Doing so increases the gain of the compensator.
As you drag the magnitude plot, the app computes the compensator gain and updates the response plots.
Drag the magnitude response upward until the crossover frequency is about 3 rad/s.
View Step Response Characteristics
To add the rise time to the Step Response plot, rightclick the plot area, and select Characteristics > Rise Time.
To view the rise time, move the cursor over the rise time indicator.
The rise time is around 0.23 seconds, which satisfies the design requirements.
Similarly, to add the peak response to the Step Response plot, rightclick the plot area, and select Characteristics > Peak Response.
The peak overshoot is around 3.5%.
Add Integrator To Compensator
To meet the 5% steadystate error requirement, eliminate steadystate error from the closedloop step response by adding an integrator to your compensator. In the Bode Editor rightclick in the plot area, and select Add Pole/Zero > Integrator.
Adding an integrator produces zero steadystate error. However, changing the compensator dynamics also changes the crossover frequency, increasing the rise time. To reduce the rise time, increase the crossover frequency to 3 rad/s.
Adjust Compensator Gain
To return the crossover frequency to 3 rad/s, increase the compensator gain further. Rightclick the Bode Editor plot area, and select Edit Compensator.
In the Compensator Editor dialog box, in the Compensator section,
specify a gain of 99
, and press Enter.
The response plots update automatically.
The rise time is around 0.4 seconds, which satisfies the design requirements. However, the peak overshoot is around 32%. A compensator consisting of a gain and an integrator is not sufficient to meet the design requirements. Therefore, the compensator requires additional dynamics.
Add Lead Network to Compensator
In the Bode Editor, review the gain margin and phase margin for the current compensator design. The design requires a gain margin greater than 20 dB and phase margin greater than 40 degrees. The current design does not meet either of these requirements.
To increase the stability margins, add a lead network to the compensator.
In the Bode Editor, rightclick and select Add Pole/Zero > Lead.
To specify the location of the lead network pole, click
on the magnitude response. The app adds a real pole (red X
)
and real zero (red O
) to the compensator and to
the Bode Editor plot.
In the Bode Editor, drag the pole and zero to change their locations. As you drag them, the app updates the pole/zero values and updates the response plots.
To decrease the magnitude of a pole or zero, drag it towards the left. Since the pole and zero are on the negative real axis, dragging them to the left moves them closer to the origin in the complex plane.
Tip As you drag a pole or zero, the app displays the new value in the status bar, on the right side.

As an initial estimate, drag the zero to a location around 7
and
the pole to a location around 11
.
The phase margin meets the design requirements; however, the gain margin is still too low.
Edit Lead Network Pole and Zero
To improve the controller performance, tune the lead network parameters.
In the Compensator Editor dialog box, in the Dynamics section, click the Lead row.
In the Edit Selected Dynamics section,
in the Real Zero text box, specify a location
of 4.3
, and press Enter. This
value is near the slowest (leftmost) pole of the DC motor plant.
In the Real Pole text box, specify
a value of 28
, and press Enter.
When you modify a lead network parameters, the Compensator and response plots update automatically.
In the app, in the Bode Editor, the
gain margin of 20.5
just meets the design requirement.
To add robustness to the system, in the Compensator Editor dialog
box, decrease the compensator gain to 550
, and
press Enter. The gain margin increases to 21.8
,
and the response plots update.
In Control System Designer, in the response plots, compare the system performance to the design requirements. The system performance characteristics are:
Rise time is 0.445 seconds.
Steadystate error is zero.
Overshoot is 3.39%.
Gain margin is 21.8 dB.
Phase margin is 65.6 degrees.
The system response meets all of the design requirements.
bodeplot
 Control System Designer