Hello dear academicians,
I control my system with a LQR . My input (u) is torque produced by 3 reaction wheels. These wheels are connected to DC Motors. Reaction wheels inertias are already added as a B matrix without motors. I want to integrate the wheel's DC Motor's dynamic model into the system. But I am confused a lot. You can see my system's Simulink diagram below.
Can you help me please?
Sincerely.
Ali Abdul Razzaq Altahir Sheyhi , I already use MATLAB. I curious that how can I integrate DC Motor characteristics into MATLAB Simulink Environment that I attach above.
Dear Abdurrahim Bilal,
I suggest you to see links and attached files on topic.
https://www.mathworks.com/help/control/examples/dc-motor-control.html
https://www.academia.edu/35770071/Comparison_of_Performance_Measures_of_Speed_Control_for_a_DC_Motor_using_Fuzzy_Logic_Controller_and_Optimal_LQR_Controller
http://tudr.thapar.edu:8080/jspui/bitstream/10266/1271/3/1271.pdf
https://pdfs.semanticscholar.org/a2fa/973a6d0debe877aa8991c78e644722213d9b.pdf
Best regards
Thank you @Mohamed-Mourad Lafifi , articles you sent are not about my question, but the first attached article is useful for my Kalman filter problem :). Thank you so much.
V: motor voltage
E: back emf
R: armature resistance
I: armature current
Kv: motor velocity constant
Kt: motor torque constant
w: motor speed
Now, neglecting the electrical dynamics (since I assume your system is much slower than electrical dynamics), the motor dynamics can be expressed as:
V = R*I + E
T = Kt*I
E = Kv*w
V = R*T/Kt + Kv*w. (1)
Or:
T = Kt*V/R - Kt*Kv*w/R. (2)
Add equation (2) into your model and redesign the controller using V as control variable.
Or since I think you have an estimation or measure of the motor speed, you could use equation (1) and directly set a value for V, compensating for the term Kv*w.
Hope this is useful.
Sir Simone Pozzoli , thank you so much. But, a reaction wheel is connected to DC motor (Look at pic.: https://directory.eoportal.org/documents/163813/202216/STRaND1_Auto5 )
Overall torque can be calculated by this formula : T=I * d(w)/dt (w: Angular velocity of DC motor. I: Inertia of reaction wheel)
For my LQR controller, B matrix is attached below. Torque of Reaction Wheel (T_RW) is my input. Your interpretation is very good. I consider it. But,
I ask to produced torque by reaction wheel by adding DC Motor's model into the system.
For example;
If my input become Voltage (V), I would calculate produced torque according to this Voltage value. How?
If my input become angular velocity (w) of DC motor, I would calculate produced momentum (I*w=H) according to this angular velocity value. How can I reach to the moment from this angular momentum (H) value?
Thank you again.
Dear Abdurrahim,
Could you please provide the entire set of equation you used to model the system, it would be much easier to understand your problem and help you.
The motor and the reaction wheel have a transmission in between?
In any case the fastest way to solve the problem I think is using a PI to control the current in the DC motor. Since I = T/k, the reference value for the current is easy to obtain from the torque set point.
The motor armature voltage is given by:
V = R*I + L*(dI/dt) + E
You could notice that in the current control loop there is a disturbance term given by E = k*w, but the dynamics of the disturbance are as fast as the mechanical system, so the current controller should be able to filter it if it's fast enough. If you don't know the value of the armature inductance (L) just tune the regulator to be ~10 times faster than the outer closed loop (your LQR).
Simone Pozzoli Sir,
I realized PID control and published it in this link :
Article ATTITUDE CONTROL OF SATELLITE TEST SETUP USING REACTION WHEELS
Now, I linearized my system because it is nonlinear and I want to control my system with linear controllers. LQR is the first controller that I intend.
Hi Abdurrahim Bilal Özcan
Most likely you have solved this problem few months ago. I guess you were confused because the flywheel is driven by the DC motor and both have different inertias. So, you were unsure of how to unify the dynamics for the LQR design. I have uploaded a method. If you are interested, you can find it here:
Method How to Obtain A State Space Model from Two Cascaded Blocks f...
Yew-Chung Chak Sir, thank you for your detailed answer/paper. I have not solved yet. I will investigate the background of "series" and I will let you know when I realise the total solution.
Sincerely,
Please see
https://www.mathworks.com/help/control/examples/dc-motor-control.html
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