PID Tuning of Joint Position for a Two-Degree-of-Freedom Robot Arm under Varying Payload

Project info

• Field of studyRobotics and Mechatronics
• LevelMaster's thesis (S2)
• Method typeControl Systems
• Estimated build time± 5 working days
• Toolspidtune, pid, feedback, step, stepinfo (Control System Toolbox)
• PriceUS$25 - US$159

Research goal

Design and simulate PID control so that the joint angle tracks its target through the motor torque, accounting for the payload mass.

Variables

Example result

• 1.033Kp
• 0.408Ki
• 0.542Kd
• 5.114Overshoot (%)
• 9.269Settling time (s)
• 1.717IAE

The tuned PID controller (Kp=1.03, Ki=0.41, Kd=0.54) makes Joint angle follow the reference with 5.1% overshoot and 9.3 s settling time; its IAE of 1.72 is lower than P-only control.

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

About PID Controller Tuning

A PID controller uses proportional, integral, and derivative actions to reduce system error. It is used to control temperature, motor speed, level, and other processes whose models can be approximated by a transfer function.

Steps

1. 1Build the plant model (transfer function or identified model)
2. 2Set performance criteria (overshoot, settling time)
3. 3Tune the PID with pidtune or the Ziegler-Nichols method
4. 4Form the closed loop with feedback
5. 5Simulate step and disturbance responses
6. 6Compare P, PI, and PID performance with stepinfo

Assumptions to check

• The plant model represents the real system well
• The actuator does not saturate in the operating range (or is modelled)
• The closed loop is stable with adequate margins

Reading and reporting the results

Report Kp, Ki, Kd, plus rise time, overshoot, settling time, and steady-state error. Include stability margins and a discussion of actuator saturation.

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');
joint_angle = 1 / ((s + 1) * (0.5*s + 1) * (0.2*s + 1));      % plant
motor_torque = 0:0.01:15;                                      % time vector

Cp   = pidtune(joint_angle, 'P');
Cpi  = pidtune(joint_angle, 'PI');
Cpid = pidtune(joint_angle, 'PID');
ctrls = {Cp, Cpi, Cpid};
names = {'P', 'PI', 'PID'};

figure; hold on;
for k = 1:3
    T = feedback(ctrls{k} * joint_angle, 1);
    [yt, t] = step(T, motor_torque);
    info = stepinfo(T);
    ess = abs(1 - dcgain(T));
    fprintf('%-4s Tr=%.2f Ts=%.2f OS=%.1f %% Ess=%.3f\n', names{k}, ...
        info.RiseTime, info.SettlingTime, info.Overshoot, ess);
    plot(t, yt, 'DisplayName', names{k});
end
hold off; grid on; legend show;
xlabel('Time (s)'); ylabel('Output');
fprintf('PID gains: Kp=%.3f Ki=%.3f Kd=%.3f\n', Cpid.Kp, Cpid.Ki, Cpid.Kd);

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