- Please Use Matlab 1 (42.17 KiB) Viewed 52 times
Please use MATLAB
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answerhappygod
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Please use MATLAB
Please use MATLAB
The dynamics of a turret actuated about its azimuth axis by a hydraulic motor can be linearized and modeled by θ˙=ωω˙=pp˙=−ωmp+JKmq−JKmωq˙=−Kvq+KvKdJp+Kvu where θ (in rad) is the azimuth angle, ω (in rad/s) is the angular speed p and q are states of the actuator dynamics. u is the control input to the motor. ωm=45.9 rad s is the motor's natural frequency. Km=8.46×106 is the motor gain. J=7900 kg⋅m2 is the load inertia. Kv=94.3 is the servo valve gain. Kd=6.33×10−6 is ∣ the differential pressure feedback coefficient. (a) Design a state feedback control system satisfying the following specifications: It should be able to track a train of steps (desired azimuth angle) that alternates between −1 and 1 radians, at a frequency of 1 Hz. The settling time should be at most 0.25 seconds (using the 98% criterion). Show your tracking performance via a plot of the step train reference and the actual angle θ superimposed. Show two full periods. (b) Now let the azimuth reference be a sawtooth signal, also with frequency of 1 Hz. Your control system should be able to track this reference, where the steady-state error when tracking the ramp parts of the sawtooth should be less than 0.2 rad. Demonstrate the performance of your design by providing a corresponding plot, and make sure you show a zoom of the plot that allows one to verify that the steady-state error requirement has been met.
The dynamics of a turret actuated about its azimuth axis by a hydraulic motor can be linearized and modeled by θ˙=ωω˙=pp˙=−ωmp+JKmq−JKmωq˙=−Kvq+KvKdJp+Kvu where θ (in rad) is the azimuth angle, ω (in rad/s) is the angular speed p and q are states of the actuator dynamics. u is the control input to the motor. ωm=45.9 rad s is the motor's natural frequency. Km=8.46×106 is the motor gain. J=7900 kg⋅m2 is the load inertia. Kv=94.3 is the servo valve gain. Kd=6.33×10−6 is ∣ the differential pressure feedback coefficient. (a) Design a state feedback control system satisfying the following specifications: It should be able to track a train of steps (desired azimuth angle) that alternates between −1 and 1 radians, at a frequency of 1 Hz. The settling time should be at most 0.25 seconds (using the 98% criterion). Show your tracking performance via a plot of the step train reference and the actual angle θ superimposed. Show two full periods. (b) Now let the azimuth reference be a sawtooth signal, also with frequency of 1 Hz. Your control system should be able to track this reference, where the steady-state error when tracking the ramp parts of the sawtooth should be less than 0.2 rad. Demonstrate the performance of your design by providing a corresponding plot, and make sure you show a zoom of the plot that allows one to verify that the steady-state error requirement has been met.
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