# Control System Assignment

Any attempt to prove/solve the problem will be considered as added value such as: 0) Troubleshooting (it) Possible constraints Idea (lb) Evidence of team works Assignment Problem 1 In many mechanical positioning systems, the movement of a large unwieldy object is enthroned by manipulating a much smaller object that is mechanically coupled with It. The figure below depicts such a situation, where a force u Is applied to a small mass ms in order to position a larger mass MBA.

The coupling between the objects is modeled by a spring constant k with a damping coefficient b. Denote x and y to be the displacements of the small and large masses respectively. (l) Write the equations of motion for the entire system. Assume Ideal conditions and neglect all effects of friction or gravity. (ii) Find the transfer function. Hint – read the question properly to figure out what is the input and output of the system. (ill) Draw the block diagram.

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Question 2 a) Construct the root locus for for the transfer function: (I) the open loop poles and zeros, (it) the asymptotes, the centre of asymptotes, (iii) section(s) of the root locus on the real axis, (v) the breakaway and break in points (if any), (v) the departure and arrival angles (if applicable), (vi) the intersection points with the imaginary axis (if applicable) (vii) the value of gain K when the root locus intersects the imaginary axis, Leary show the direction of “flow’ in each of the root locus branch as the gain K goes from O to infinity b) Consider the system in question 1 and let it be connected in a unity negative feedback configuration with K = 10. (I) If the reference input is a unit step, calculate the steady-state error. Verify your answer using Mutual. (it) If the reference input is a unit ramp, calculate the steady state error. Verify your answer using Mutual. (iii) If the reference input is a unit acceleration, calculate the steady state error. Verify your answer using Mutual.