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 () = (1+ T )(1+) 1+ , (1) Where k, T, q and n are constant. The plant is represented by second order transfer function with dead-time () = − 2+2+1 , (2) Where w and d are constant and 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 Laplace of F(s) with w=2, d=1 and = 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.
