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(6) 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, 0v i.e. V s vu t T ( ) ( ) = L{ } 0 where u t( ) is the unit step function. K is the controller parameter to be tuned in order to achieve the control objective. (a) Derive the final transfer function ( ) ( ) Φ T s V s , of the crane cart plus controller shown in Figure 2. (b) Design a suitable value of K such that the resulting response of the rope sway is nonoscillatory. (c) Sketch the trajectory of the rope sway when the cart is driven at a constant velocity of 0v = 2 m s. You may assume that the initial angle of the rope is zero. (d) Explain qualitatively how the control system works. How does the control parameter K affect the quality of control? (12 marks)

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