systems problem 6. Suppose you are to design a unity feedback controller for a first-order plant...
Problem 5: Suppose that you are to design a unity gain feedback controller for a first order plant. The plant and controller respectively take the form ,s+ p where K> 0, p. z are parameters to be specified. (a) Using root-locus methods, specify some p and z for which it is possible to make the closed-loop system strictly stable. Include a sketch of the closed-loop root locus, as well as the corresponding range of gains K for which the system...
Consider a unity-feedback control system with a PI controller Gpr(s) and a plant G(s) in cascade. In particular, the plant transfer function is given as 2. G(s) = s+4, and the PI controller transfer function is of the forrm KI p and Ki are the proportional and integral controller gains, respectively where K Design numerical values for Kp and Ki such that the closed-loop control system has a step- response settling time T, 0.5 seconds with a damping ratio of...
Q-2 Suppose a system, as shown in the block diagram of a unity feedback loop, below, has a transfer function, P(S) = . We want to stabilize this system with a proportional integral (PI) controller, such that the poles of the characteristic equation are to be: s, = s2 = S3 = -1. If we let the controller, C(s) = , determine all parameters (a, a, b , K, and K) in the following transfer function in order to satisfy...
6 and controller C(s), as shown in the Consider a unity-feedback control system with plant G(s)- following figure. Reference Error Controller Plant r(t) e(t) u(t) y(t) C(s) G(s) [5] (a) Determine the poles, zeros, order, type, relative degree, and de gain of the plant G(s) and show [5] (b) Can a P controller C(s)Kp stabilize the plant G(s)? If so, find the values of Kp that are [4] (c) Show using the Final Value Theorem that the system with the...
The Nyquist plot of a plant P in a unity feedback system is shown below. It is know that P has one pole with a non-negative real part. 6.13 The Nyquist plot of a plant P in a unity feedback system is shown below. It is known that P has one pole with non-negative real part 1. What is the number of poles of P with zero real part? 2. What is the number of unstable poles of P? 3....
Problem 3: Consider a unity feedback system with a plant model given by 10(s- 5) and a controller given by s + p for K 0 and some real z and p. a) Use the root-locus technique to determine the sign of z and p so that the closed-loop system is stable for all K E (0, K) for some Ku> 0. b) Sketch the possible forms of the root-locus in terms of the pole and zero locations of Ge(s)....
PROBLEM 4 A unity feedback closed loop control system is displayed in Figure 4 (a) Assume that the controller is given by G (s)-2. Based on the lsim function of MATLAB, calculate and obtain the graph of the response for 0,(1)-a. Here a ; 0.5%, Find the height error after 10 seconds, (b) In order to reduce the steady-state error, substitute G. (s) with the following controller: K2 This is a Proportional-Integral (PI) controller. Repeat part (a) in the presence...
Implement a PID controller to control the transfer function shown below. The PID controller and plant transfer function should be in a closed feedback loop. Assume the feedback loop has a Gain of 5 associated with it i.e. . The Transfer function of a PID controller is also given below. Start by: 6. Implement a PID controller to control the transfer function shown below. The PID feedback loop has a Gain of 5 associated with it i.e. (HS) = 5)....
Consider the following controller in a unity feedback configuration: (s + 10) C(s) = k· (s + 5) (a) (by hand) Using an approximation for the plant P(s) a 11 S +2)(s2 + 5s + 25) determine the proper L(s) and sketch an accurate Root Locus plot (b) (by hand) Once you have established the Root Locus, determine the range of k values that guarantees closed-loop stability using the L(jw) method along with the Root Locus plot.
Problem 6 Design a PI controller to drive the step-response error to zero for the negative unity feedback system shown in Fig. 1, where G(s) = (s+1)(s + 3)(s+ io). The system operates with a damping factor of 0.4 Design a PI controller whose compensator zero located at-0.1 Use MATLAB or any other computer program to simulate the step response to closed-loop system Problem 6 Design a PI controller to drive the step-response error to zero for the negative unity...