EGR 345 (Practice) Final ExamName:1. For the following control system select a controller transfer function, Gc, that will make the overall system performance match the desired transfer function. Controller MotorPotentiometer+-s 1+s 0.25+-------------------s 1+s 0.25+-------------------100s20.1+------------------1s---θdθaωVseVaVdGcθaθd-----1s222()10()s 102++---------------------------------------------------=desired transfer functionEGR 345 (Practice) Final ExamName:2. Write a C program for an ATMega microcontroller to implement the control system in the dashed line below with an update time of 10ms. Controller ActuatorSensor+-s0.25----------s0.25----------s2KdsKpKi++s---------------------------------------100ss 0.1+()-----------------------1s---QdθVseVaVdEGR 345 (Practice) Final ExamName:3. (NOTE: this would be a multi-page problem) A feedback control system is shown below. The system incorporates a PID controller. The closed loop transfer function is given. a) Develop the transfer function for the system.b) Select controller values that will result in a response that includes a natural fre-quency of 2 rad/sec and damping factor of 0.5. Verify that the controller will be stable.c) If the values of Kp = Ki = Kd = 1 find the response to a unit ramp input as a function of time using LaPlace Transforms.d) Find the response in part c) using numerical methods.e) Find the system response to an input of X = 5sin(100t + 1)f) If the input X is a trapezoidal motion profile with an acceleration time of 2 sec-onds, and a maximum velocity of 5, what would the response Y look like.KpKis----- Kds++3s 6+s29s 91++-----------------------------4+-XYEGR 345 (Practice) Final ExamName:4. Write the differential equations AND state equations for the systems below.
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