All questions in this assignment concern the following typical unity-feedback control system with a proportional-gain controller,...

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All questions in this assignment concern the following typical unity-feedback control system with a proportional-gain controller, where K is any real number: r K P(s) s-1 s+2 1. Draw (by hand) and fully label a Nyquist plot for K = 1 when P(s) = 1. Show all your work. Use the Nyquist Stability Test to determine all values of K (if any) for which the closed-loop system is stable. 2. Suppose the plant transfer function is P(s) = (s+1)(s+2) $2 (a) Draw and label a Nyquist plot for K = 1. Show all your work. (b) Using your answer to part (a), draw and label a Nyquist plot for K = -1. (c) Based on your answers to parts (a) and (b), use the Nyquist Stability Test to determine all values of K (if any) for which the closed-loop system is stable. (d) Check your answer to part (c) using the Routh-Hurwitz Stability Test. All questions in this assignment concern the following typical unity-feedback control system with a proportional-gain controller, where K is any real number: r K P(s) s-1 s+2 1. Draw (by hand) and fully label a Nyquist plot for K = 1 when P(s) = 1. Show all your work. Use the Nyquist Stability Test to determine all values of K (if any) for which the closed-loop system is stable. 2. Suppose the plant transfer function is P(s) = (s+1)(s+2) $2 (a) Draw and label a Nyquist plot for K = 1. Show all your work. (b) Using your answer to part (a), draw and label a Nyquist plot for K = -1. (c) Based on your answers to parts (a) and (b), use the Nyquist Stability Test to determine all values of K (if any) for which the closed-loop system is stable. (d) Check your answer to part (c) using the Routh-Hurwitz Stability Test.