Thailand Excellence Community
อาจารย์ผู้สอน/อาจารย์ที่ปรึกษา ผู้ช่วยศาสตราจารย์ ดร.กิตติพงษ์ เยาวาจา (Kittipong Yaovaja)
หัวหน้ากลุ่มวิจัยวิทยาการหุ่นยนต์และระบบอัตโนมัติขั้นสูง และผู้รับผิดชอบหลักสูตรหุ่นยนต์และระบบอัตโนมัติ (นานาชาติ) ม.เกษตรศาสตร์ วิทยาเขตศรีราชา คณะวิศวกรรมศาสตร์ศรีราชา
% Define the parameters for the mobile robot’s motion
mass = 5; % Mass of the robot in kg
b = 0.3; % Damping coefficient in Nms
K = 2; % Driving force coefficient in N*m
% Define the transfer function for the robot’s linear motion
% Assuming a simple second order system: masss^2 + bs + K
numerator = [K];
denominator = [mass, b, K];
sys = tf(numerator, denominator);
% Frequency Domain Analysis
figure;
bode(sys); % Bode plot to show frequency response
title(‘Frequency Domain Analysis of Mobile Robot’);
% Convert the continuous time transfer function to Z domain using Tustin’s method
Ts = 0.05; % Sampling time
sys_z = c2d(sys, Ts, ‘tustin’);
% Z Domain Analysis
figure;
impulse(sys_z); % Impulse response in the Z domain
title(‘Z Domain Analysis – Impulse Response of Mobile Robot’);
% Time Domain Analysis
figure;
step(sys); % Step response in the time domain
title(‘Time Domain Analysis – Step Response of Mobile Robot’);
% Display the system in Zero-Pole-Gain format for further insight
figure;
pzmap(sys); % Pole-Zero map of the system
title(‘Pole-Zero Map of the Mobile Robot’);
Summary
For a practical tank level control system, these analyses help in:
• Designing the controller (choosing the right type of controller like PID, determining tuning parameters).
• Predicting how the system will behave under different conditions and inputs.
• Ensuring that the system will be stable and meet performance specifications under both continuous and digital control schemes.
Each type of analysis contributes to a comprehensive understanding of the system, enabling the design of efficient and reliable control strategies tailored to the specific needs and characteristics of the tank level control system.
% System parameters
A = 10; % Cross-sectional area of the tank (square meters)
tau = 5; % Time constant of the system (seconds)
% Transfer function
s = tf(‘s’);
G = 1/(taus + 1); % Transfer function G(s) = 1/(taus + 1)
% Time Domain Analysis
figure;
step(G);
title(‘Step Response of the Tank Level System’);
xlabel(‘Time (seconds)’);
ylabel(‘Tank Level (meters)’);
% Frequency Domain Analysis
figure;
bode(G);
grid on;
title(‘Bode Plot of the Tank Level System’);
% Z-Domain Analysis
Ts = 0.5; % Sampling time in seconds
Gz = c2d(G, Ts, ‘zoh’); % Convert to discrete-time system using zero-order hold
figure;
step(Gz, 50*Ts);
title(‘Step Response of the Discrete Tank Level System’);
xlabel(‘Time (seconds)’);
ylabel(‘Tank Level (meters)’);
% Define system parameters
tau = 500; % Time constant in seconds
K = 0.1; % Gain
T_ambient = 20; % Ambient temperature in degrees Celsius (not used in TF directly)
% Define the transfer function for the heating system
% The transfer function is K/(tau*s + 1)
sys = tf(K, [tau 1]);
% Frequency response – Bode Plot
figure;
bode(sys);
title(‘Bode Plot of the Thermostat-Controlled Heating System’);
grid on;
% Time domain response – Step Response
figure;
step(sys);
title(‘Step Response of the Thermostat-Controlled Heating System’);
ylabel(‘Temperature Change (°C)’);
xlabel(‘Time (seconds)’);
grid on;
Conclusion
Summary of Findings:
Theoretical Validation: The simulation results validate the theoretical models of dynamic behavior in the Series RLC circuit.
Implications for Robotics: The insights gained from the RLC circuit study can be applied to more complex systems in robotics, helping in the design of more efficient and robust control systems.
Future Work:
Model Refinement: Incorporating non-linear elements or considering more complex circuit arrangements.
Advanced Control Techniques: Exploring state-space control or adaptive control strategies for enhanced performance in variable conditions.
References:
MATLAB and Simulink Resources: Comprehensive documentation and user guides.
Control Systems Textbooks: Standard texts that provide foundational theories and practical applications in control engineering.
Balancing robots represent a remarkable convergence of mechanics, electronics, and control systems engineering. Their ability to maintain dynamic stability while maneuvering through various terrains highlights the effectiveness of advanced control algorithms and sensor integration. These robots are not only valuable educational tools but also serve as platforms for research and development in autonomous systems, AI, and robotics.
The compact and efficient design, combined with their versatility and robustness, makes balancing robots suitable for a wide range of applications, from personal transportation to industrial automation. Their impact on promoting STEM education and inspiring future innovations is significant. As technology advances, balancing robots will continue to evolve, offering new possibilities and addressing real-world challenges in innovative ways.
Implementation using Simulink involves converting the controller design into a form that can be tested and then deployed either as simulation or to real-time systems using automatic code generation tools. Simulink supports integration with hardware through features like Simulink Hardware Support Packages, which allows for direct deployment and testing on hardware platforms.
Simulation Results Simulation results are crucial for validating the performance of the designed controller against the expected outcomes. In Simulink, results can be visualized using scopes and displays or analyzed with MATLAB functions to evaluate system performance metrics such as settling time, overshoot, and stability
Implementation and Tuning:Implement the designed controller in the real system and fine-tune its parameters based on practical observations.•Real-time Tuning: Adjust the PID gains based on the system’s response in real-time to achieve optimal performance.By following these steps, a robust PID controller can be designed for liquid or water tank level control, ensuring accurate and stable regulation of the tank level. Each design approach offers unique insights and tools for controller development, catering to different system requirements and constraints.
Example Code% Parameters of the tank systemA = 1; % Cross-sectional area of the tank (m^2)k = 0.1; % Valve constant (m^3/s/V)% Transfer function of the tank systemnumerator = k;denominator = [A, 0]; % First-order systemG = tf(numerator, denominator);% Create a figure with subplotsfigure;% Plot Bode diagramsubplot(2, 2, 1);bode(G);title(‘Bode Diagram’);% Plot pole-zero mapsubplot(2, 2, 2);pzmap(G);title(‘Pole-Zero Map’);% Calculate step responset_step = 0:0.1:20;
r_step = ones(size(t_step)); % Step input[y_step, t_step] = step(G, t_step);% Plot step responsesubplot(2, 2, 3);plot(t_step, y_step);xlabel(‘Time (s)’);ylabel(‘Tank Level (m)’);title(‘Step Response’);% Plot Nyquist diagramsubplot(2, 2, 4);nyquist(G);title(‘Nyquist Diagram’);
อาจารย์ผู้สอน/อาจารย์ที่ปรึกษา ผู้ช่วยศาสตราจารย์ ดร.กิตติพงษ์ เยาวาจา (Kittipong Yaovaja)
หัวหน้ากลุ่มวิจัยวิทยาการหุ่นยนต์และระบบอัตโนมัติขั้นสูง และผู้รับผิดชอบหลักสูตรหุ่นยนต์และระบบอัตโนมัติ (นานาชาติ) ม.เกษตรศาสตร์ วิทยาเขตศรีราชา คณะวิศวกรรมศาสตร์ศรีราชา