Control system of rotary motor
Description of the problemThis paper describes linearization and controlling of a system using the method of static characteristic. The system has a pressure valve, proportional flow valve and the controlled motor. In order to control our system, we need to watch how the system works, find the linearization, the transfer function and finally a proper PID controller.
Figure 1: System
Measurement DataBefore we start with static characteristic, we record the pneumatic pressure, the voltage and the engine speed. We import the data in Matlab, after processing this data we can understand how the system works right know. The pressure starts at 0.1 (MPa) till 0.4(Pa). The voltage depends on the motor speed, so the measurement is between 6 (V) till 10 (V). And the speed from 0(rpm) to almost 1400(rpm).
Figure 2: Static characteristicThe engine works faster when the pressure is higher and giving more voltage. When the pressure is high we will have some problems with the peak speed limit of our motor. In order to figure correctly the limits of the motor, we have to understand the function between motor speed and pressure
Figure 3: Max speed of working pressureStatic CharacteristicNow in order to found the transfer function, first we should check the output of system based on input.
Figure 4: Dynamic characteristicWe can saw that our output (green line) isnt higher than the system input (blue line) but as time goes, approaching the input. Thats why we need a PI controller so that our machine will work correctly. Transfer FunctionBefore finding the PI parameters we need the systems transfer function. Using equations on Matlab we found the transfer function.
PI ControllerBy using the method of Ziegler-Nichols, the PI parameters are:For Pkp= 1.7889For I ti= 1.0187
The block diagram for the PI and transfer function is:
Figure 5: Block diagram of modelFinally, the systems diagram with PI controller.
Figure 6: PI ControllerOur motor has a small disturbance till the 7sec, but after that the output tends to reach the input. There will be no problem on our motor its never going to be higher than the input.
PID ControllerAlso, I created another one controller but this time I add the D parameter.With the same method of Ziegler-Nichols the PID parameters are:
For Pkp= 2.3150For I ti= 0.6112For D td= 0.1528The block diagram its the same as before with the only difference, in PID controller block added the td. The new diagram is:
Figure 7: PID ControllerThe difference between PI and PID controller for this problem, is in disturbance. With the PID Controller the disturbance stops at 4(sec). If we change the I parameter in PI controller, the disturbance will be softer but if we change it at PID controller, the disturbance will be softer and slower. I changed the parameters of PID into For Pkp= 2.3150For I ti= 1.5For D td= 2
The new diagram is:
Figure 8: PID Controller
Now with the new I and D parameters, the output has a small disturbance and is going faster to reach the input. So the system has a very good function with no error.
Conclusion We need to create linearization of the system, we design PID parameters. We saw that in PI controller we need a lot of time to stabilize our engine and we have some error on the beginning. Finally, with PID controller, the stabilize is better and the error is smaller than with PI controller.ReferencesR. Gayakwad, L. Sokoloff, Analog and Digital Control Systems, Prentice Hall, GB, 1988, ISBN 978-01-303-3028-4H. Khalil, Nonlinear systems, 3rd ed. Upper Saddle River, Prentice Hall, 2002, ISBN 01-306-7389-7.S. Samarasinghe, Neural networks for applied sciences and engineering, 2nd ed. Auerbach, Boca Raton, 2007, ISBN 978-084-9333-750.A. Ralston, P. Rabinowitz, A first course in numerical analysis, 2nd ed. New York, Dover Publications, 2001, ISBN 04-864-1454-X. O. L. R. Jacobs, Introduction to Control Theory, Clarendon Press, 2nd ed. Oxford GB, 1974, ISBN 978-0-19-856249-8.