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Engineering
Electrical Engineering
in this quiz you will examine the behavior of a...

Question: in this quiz you will examine the behavior of a...

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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 where R is a combination of friction and reverse electromagnetic force that increases with increasing speed.1 D(s) Controller Armature coil Rotor s)H(S) w(s) ly(s) R(s) Js +R Torque Sensor Votage ks 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) (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, (t) has only one derivative, ot)OJ Therefore, this is a first-order system, and it has only one pole in the Laplace domain.

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. (Scoe: 5 points)

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