Step Response of Aircraft Pitch Angle Dynamics Modelled as a Second-Order System

Project info

• Field of studyAerospace and Aviation
• LevelUndergraduate thesis (S1)
• Method typeControl Systems
• Estimated build time± 3 working days
• Toolstf, step, stepinfo (Control System Toolbox)
• PriceUS$19 - US$125

Research goal

Analyse the step response of pitch angle to elevator deflection and assess the effect of damping ratio on overshoot and settling time.

Variables

Example result

• 0.447Rise time (s)
• 10.841Overshoot (%)
• 1.461Settling time (s)
• 0.949Peak time (s)
• 3.893Natural freq. est. (rad/s)
• 0.552Damping ratio est.

The step response of Pitch angle has 10.8% overshoot, 0.45 s rise time and 1.46 s settling time; identification from noisy data gives a natural frequency of 3.89 rad/s and damping ratio 0.552 (RMS error 0.103).

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

About Second-Order Step Response

The step response of a second-order system shows how the output reacts to a step input, determined by natural frequency and damping ratio. It is used to assess control performance or mechanical and electrical dynamics.

Steps

1. 1Define the natural frequency wn and damping ratio zeta
2. 2Form the transfer function with tf
3. 3Compute and plot the step response
4. 4Extract characteristics with stepinfo (rise time, overshoot, settling time)
5. 5Compare several values of zeta
6. 6Match the results to theoretical formulas

Assumptions to check

• The system is linear and time invariant
• Initial conditions are zero
• The second-order approximation holds when poles are dominant

Reading and reporting the results

Report rise time, overshoot, settling time, and final value for each zeta, then compare with theoretical formulas. Relate results to design performance requirements.

Example MATLAB code

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

wn = 4;                                        % natural frequency (rad/s)
zetas = [0.2 0.5 0.7 1.0];
elevator_deflection = 0:0.01:8;                             % time vector
figure; hold on;
for k = 1:numel(zetas)
    z = zetas(k);
    pitch_angle = tf(wn^2, [1 2*z*wn wn^2]);
    [y, t] = step(pitch_angle, elevator_deflection);
    info = stepinfo(pitch_angle);
    os_theory = 100 * exp(-pi*z/sqrt(1 - z^2));
    if z >= 1, os_theory = 0; end
    fprintf('zeta=%.1f  Tr=%.3f s  Ts=%.3f s  OS=%.1f %% (theory %.1f %%)\n', ...
        z, info.RiseTime, info.SettlingTime, info.Overshoot, os_theory);
    plot(t, y, 'DisplayName', sprintf('zeta = %.1f', z));
end
hold off; grid on; legend show;
xlabel('Time (s)'); ylabel('Output');

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