Compensator Design and parameters modification using Bode plot and root locus
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The document outlines a compensator design experiment using Bode plots and root locus techniques in the context of modern control systems. It details the objectives, theoretical background, and practical steps for tuning compensators to meet specified performance criteria through MATLAB's Control System Designer. The experiment includes specific design requirements such as rise time, steady-state error, overshoot, and stability margins for different tasks.
![Objective:
• Compensator design using Bode plot and root locus
• Modification of root locus using control system designer
• Observing parameters for different root locus points
Theory:
Bode diagram design is an interactive graphical method of modifying a compensator to achieve a
specific open-loop response (loop shaping). To interactively shape the open-loop response using
Control System Designer, use the Bode Editor. In the editor, you can adjust the open-loop
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 the tuning methods available in Control System
Designer, see Control System Designer Tuning Methods.
Tuning Compensator for Desired Response:
For this example, the design requirements are:
• Rise time of less than 0.5 seconds
• Steady-state 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:](https://image.slidesharecdn.com/moderncontrollab9-220408213732/85/Compensator-Design-and-parameters-modification-using-Bode-plot-and-root-locus-2-320.jpg)
Compensator Design and parameters modification using Bode plot and root locus
- 1. Department of Avionics Engineering AE-3452 Modern Control Systems Experiment No. 9 Compensator Design and parameters modification using Bode plot and root locus Prepared for By: Name: ID: Section: Semester: Total Marks: ________________ Obtained Marks: _____________ Signature: __________________ Date: _____________________
- 2. Objective: • Compensator design using Bode plot and root locus • Modification of root locus using control system designer • Observing parameters for different root locus points Theory: Bode diagram design is an interactive graphical method of modifying a compensator to achieve a specific open-loop response (loop shaping). To interactively shape the open-loop response using Control System Designer, use the Bode Editor. In the editor, you can adjust the open-loop 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 the tuning methods available in Control System Designer, see Control System Designer Tuning Methods. Tuning Compensator for Desired Response: For this example, the design requirements are: • Rise time of less than 0.5 seconds • Steady-state 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:
- 3. • Open-loop Bode Editor for the LoopTransfer_C response. This response is the open-loop transfer function GC, where C is the compensator and G is the plant. • Step Response for the IOTransfer_r2y response. This response is the input-output transfer function for the overall closed-loop system. To view the open-loop frequency response and closed-loop step response simultaneously, click and drag the plots to the desired location. The app displays the Bode Editor and Step Response plots side-by-side. Adjust Bandwidth Since the design requires a rise time less than 0.5 seconds, set the open-loop DC crossover frequency to about 3 rad/s. To a first-order 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. Right-click 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.
- 4. View Step Response Characteristics To add the rise time to the Step Response plot, right-click the plot area, and select Characteristics > Rise Time. To view the rise time, move the cursor over the rise time indicator. To increase the stability margins, add a lead network to the compensator. In the Bode Editor, right-click 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. 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 (left-most) pole of the DC motor plant. In the Real Pole text box, specify a value of -28, and press Enter. Task 01:
- 5. For this transfer function, the design requirements are: • Rise time of less than 0.8 seconds • Steady-state error of less than 5% • Overshoot of less than 8% • Gain margin greater than 25 dB • Phase margin greater than 40 degrees Task 02: E= 7 2𝑠215𝑠+10∗𝑛 Where n is your roll number, the design requirements are: • Rise time of less than 1 seconds • Steady-state error of less than 5% • Overshoot of less than 20% • Gain margin greater than 20 dB • Phase margin greater than 40 degrees Find bode plot, root locus and Step plot for all these given transfer function.