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Problem 1: Common rules of thumb for controller discretization is to have "6 samples per rise time" in order to achieve a reasonable approximation of the CT controller, without wasting computing resources. Derive the effect on PM that this choice will have.
Problem 2: A motor position control system has transfer function
P(s) = 1/s2(s + 1)
Design a PID controller to approximately maximize its BW, keeping the PM above 40deg.
Problem 3: Consider the system with transfer function P(s) = 1/s which is to be controlled by a strictly causal DT-PI controller of the form C(z) = K(z-a)/z(z-1) so that the loop crossover frequency is 1 rad/s and the phase margin is 45o.
1. Discuss the selection of a suitable sampling time for the controller.
2. Use Ts = 0.3(sec) to design a DT-PI to meet the specifications by designing the controller in CT first, and then discretizing it.
3. Use Ts = 0.3(sec) and design the DT-PI to meet the specifications in DT entirely.
Calculate the reciprocal lattice of the body-centred cubic and Show that the reciprocal of the face-centred cubic (fcc) structure is itself a bcc structure.
How much gasoline do vehicles with the following fuel efficiencies consume in one year? Calculate the gasoline savings, in gallons per year, created by the following two options. Show all your work, and draw boxes around your answers.
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How did this procedure affect the signal observed from the electrode and the electrode impedances?
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