Suppose a crane controller is designed as shown in Figure 2, to automatically modulate the cart velocity in a manner which ensures that the load does not swing wildly when the cart is driven at the constant velocity, vo i.e. Vr(s)=L{vou(t)} where u(t) is the unit step function. K is the controller parameter to be tuned in order to achieve the control objective. V₁ (s) = L{v₁u(t)} — + Crane Cart D(s) Vr(s) from Part (1) s+ K Controller Figure 2: Control Configuration for the Crane. S 10+305² → Þ(s) Design a suitable value of K such that the resulting response of the rope sway is non- oscillatory. Sketch the trajectory of the rope sway when the cart is driven at a constant velocity of % = 2 m/s. You may assume that the initial angle of the rope is zero. Explain qualitatively how the control system works. How does the control parameter K affect the quality of control?

Electrostatic levitation in comb-drives: Movable fingers in comb-drive actuators/sensors can experience a levitation effect when the plane underneath the structure is biased at the same potential as the fingers, shown by Zo in figure below. Explain qualitatively why such a levitation happens in the freestanding structure. Fixed electrode Vp Movable finger -Zo ↑ GND Fixed electrode V₂ GND Plane N Out of plane

A shunt generator supplies a current of 1.2 Q2 at 240 V to a load. Find the emf generated if the shunt field and armature resistance are 120 2 and 0.08 2 respectively.

Question-1: The induced magnetic force, given by Find = i (Lx B), is called motor action and the induced magnetic force, given by eina = (V × B). L, is called generator action. a) Explain the role of induced forces in generators when we expect generators to be all about induced voltages and not induced forces? b) Explain the role of induced voltages in motors when we expect motors to be all about induced forces and not induced voltages?