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Question: engr46206620 quiz 1 quiz 1 closed control loop amp static...

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ENGR4620/6620: Quiz 1 Quiz 1: Closed Control Loop & Static Response In this quiz, you will examine the behavior of a simple motor speed con trol system. Figure 1 shows the block diagram of the entire control loop Without covering the details, the motor is approximated by two equations First, the current through the motor coils (IM) creates a magnetic torque TM. We consider an external load D(s) (i.e., the disturbance) that subtracts from this torque. The difference accelerates the rotational inertia J of the rotor, and the relationship between torque and rotational speed w can be approximated by Js+ R where R is a combination of friction and reverse electromagnetic force that increases with increasing speed.1 D(s) Controller Armature coil LM(s) Rotor E(S) ω(s) H(s) R(s) Sensor Voitage Figure 1: Block diagram of the motor speed control system. The control system is based on a tachometer (sensor) that provides a linearly scaled voltage. To simplify the tasks, we simply assume ks 1 The controller itself subtracts the sensor output from the setpoint R(s) to provide the control deviation e(s). The motor drive current is then obtained as IM(s) H(s) e(s) Note that the motor transfer function bears close similarity to the transfer function of the waterbath. Similar to the waterbath, the output variable, here, w(t) has only one derivative, ω(t)-r(t)/J. Therefore, this is a first-order system, and it has only one pole in the Laplace domainENGRA620/6620: Quiz I 1, where is the open-loop pole of the control system, i.e., the location of the one system pole in the Laplace-domain when H(s)- 0? (Score: 3 points) 2. Determine the transfer functions of the closed-loop system, i.e., deter- mine the output w(s) as a function of the two inputs R(s) and D(s) in the form w(s) G1 (s) . R(s) + G2(s) . D(s) Note that Gı(s) and G2(s) must have the same denominator poly- normal, which is the systems characteristic polynomial. (Score: γ points) 3. When we use a simple P-controller H(s)-kp and both the setpoint and disturbance are constant over time (r and TD, respectively), pro- vide the steady-state rotational speed woo. (Score: 5 points) Hints: e Remember the steps we need to take to resolve a feedback control loop: Collect and remove all dependent variables with the exception of the output variable -Arrive at an expression that contains only the output variable and the independent input variables (and, of course, process con stants) Rearrange the equation to have all terms with the output variable on the left-hand side, and all terms with independent variables on the right-hand side -Factor out the output variable and isolate it by dividing both sides with its multiplicative function For the steady-state speed, use step inputs and the final value theorem e No initial conditions were given, so none need to be considered

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