Root Locus and Bode Plot Analysis of Stability Margins in servo position on an actuator node

Project info

• Field of studyIoT and Embedded Systems
• LevelMaster's thesis (S2)
• Method typeControl Systems
• Estimated build time± 5 working days
• Toolsrlocus, bode, margin, allmargin, rlocfind (Control System Toolbox)
• PriceUS$22 - US$147

Research goal

Assess the stability and the gain and phase margins of servo position on an actuator node through root locus and Bode plots.

Variables

Example result

• 4.911Gain margin (dB)
• 15.198Phase margin (deg)
• 2.289Gain crossover (rad/s)
• 3.092Phase crossover (rad/s)
• 37.747Loop gain K
• 0.117Dominant damping ratio

At gain K=37.7 the Servo position loop has a 4.9 dB gain margin and 15.2 degree phase margin with a dominant-pole damping ratio of 0.117; the critical gain before instability is about 66.4.

Computed from illustrative synthetic data, not from a real study.

About Root Locus and Bode Plot

The root locus shows the closed-loop pole paths as gain varies, while the Bode plot shows frequency response and stability margins. They are used to analyse stability and design compensators in control systems.

Steps

1. 1Define the open-loop transfer function
2. 2Plot the root locus and choose a gain that meets specifications
3. 3Plot the Bode diagram
4. 4Compute gain and phase margins with margin
5. 5Check the closed-loop step response at the chosen gain
6. 6State conclusions on stability and margins

Assumptions to check

• The system is linear time invariant
• Unity negative feedback
• The model is accurate near the crossover frequency

Reading and reporting the results

Report pole locations, chosen gain, gain and phase margins (with units), and crossover frequency. Relate margins to robustness against model uncertainty.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

s = tf('s');
servo_position = 10 / (s * (s + 2) * (s + 5));          % open-loop transfer function
proportional_gain = 0:0.01:10;                            % time vector

figure;
subplot(1,2,1); rlocus(servo_position); grid on;
subplot(1,2,2); bode(servo_position); grid on;

[Gm, Pm, Wcg, Wcp] = margin(servo_position);
fprintf('Gain margin: %.2f (%.1f dB) at %.2f rad/s\n', Gm, 20*log10(Gm), Wcg);
fprintf('Phase margin: %.1f deg at %.2f rad/s\n', Pm, Wcp);

T = feedback(servo_position, 1);
fprintf('Closed-loop poles:\n'); disp(pole(T));
info = stepinfo(T);
fprintf('Overshoot %.1f %%, settling time %.2f s\n', info.Overshoot, info.SettlingTime);

figure;
step(T, proportional_gain); grid on; title('Closed-loop step response');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions