Hello !...I need this problem to be solved as soon as possible. Tonight at 10 pm is the deadline. Kindly solve it. I'll be grateful to you . And this question is an Complex Engineering Problem from , Complex Variables Transforms subject. Please help me.

Q: The location of poles and their significance in simple feedback control systems in which the plant contains a dead-time lag are treated. Such control systems have an infinite number of poles. If a system is designed by assuming that one pair of complex conjugate poles dominates, in certain cases real poles or low frequency complex poles occur which also contribute significantly to the closed- loop dynamic behavior. The transfer function of the controller system is given by G(S) = - k(1+3(1+45) 1+ms (1) Where k, T, q and n are constant The plant is represented by second order transfer function with dead-time F (S) =- ws #2dws+1 (2) Where w and d are constant and r is dead-time constant. Task: (a) Find Inverse Laplace of G(s) with k=4, T=1, q=2 and n=4. (b) Find inverse Loplace of F(s) with w=2, d=1 and r = 5. (c) What is significant role of negative poles and positive poles in control system and plant so that system remains stable. Explain in one paragraph. (d) What are your suggestions for improving control system? Only 3-5 bullets