Project: Consider the position control problem of a DC motor using PID control. The system can be represented using the following block diagram: + и у K(s) G(s) where r is the reference position signal, e is the error signal, u is the control effort signal and y is the measured position signal. The transfer function G(s) is the DC motor plant given as follows: y(s) (s) к G(s) u(s) (s) s [mLas? + (b La +R2Jm)s +(K_Ke +bR)] sec where o(s) is the DC-motor's shaft angle and V(s)is the input voltage to the motor's circuit. The system parameters are given by Jm = 1.13 x 10-2 N. m. sece, b = 0.028 N.m. La 10-1H, Ra = 0.45 12, K+ = 0.067 N., K = 0.067 v. Sec rad amp rad The controller K(s) is a continuous PID controller with a low-pass filter. The controller is given as follows: u(s) kas? + kps + ki = K(s) = e(s) s(ts + 1) where ka = 0.466, kp = 0.379, ki = 0.0457 and 1 = 1. 2 Requirements: a) Discretize the controller K(s) for an arbitrary sample time T using the Forward rectangular rule. b) Compare between controllers discretized using the forward rectangular rule and the zero- order hold (ZOH) for different sample times (T = 0.05, 0.5 and 2.5 seconds). Comment on the results. (Hint: you may use software to help you in the ZOH discretization) (Hint: use pole-zero maps and bode plots) c) For a sample time of (T = 0.2 seconds), design a controller for the DC motor using direct digital control design. (Hint: you may use SISOTOOL to help you in the design) d) Simulate the DC motor's response for a step reference of magnitude pi/4 using the ZOH controller with a T = 0.05 seconds as designed in b) e) Derive the difference equation for the controller used in part d). 1) Write C-code for ATmega328P to implement the controller in part e). Make sure that your code satisfies the following points: 1. The code should measure the current position of the motor. 2. The code should keep the sampling time fixed as required by the controller using an interrupt service routine (ISR). g) Implement your code practically and plot your experimental results for the motor position as a function of time. (You may need to adjust your controller gains according to the DC motor you are using). Note that: You should show all your steps clearly, submit all the codes used and the results.
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I would love to complete your Matlab Project. I am a electrical engineer with more than 5 years eperience. I have done many proects. Waiting for your response for further discussion