Control System

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For each of the transfer functions shown below, find the locations of the poles and zeros, plot them on the s-plane, and then write an expression for the general form of the step response without solving for the inverse Laplace transform. State the nature of each response (overdamped, underdamped, and so on). [Sections: 4.3, 4.4]s


a) Find the state-space representation in phase-variable form for the transfer function


2. For the unity feedback system above, let: G(s)= K(s + 4) / s(s+1.2) (s + 2) Find the following: a. The range of K that keeps the system stable. b. The value of K that makes the system oscillate. c. The frequency of oscillation when K is set the value that makes the system oscillate.


1. Consider the unity feedback closed-loop control system shown below, with G(s) = 100 / s(s² + 20s +10) a. Determine the transfer function 7 (s) = C(s) / R (s) b. Determine the poles and zeros of I(s) c. Use a unit step input, R(s)=1/s, and obtain the partial fraction expansion for C(s) and the value of the residues.


Q4) answer the followings: 4.1 Given the following forward transfer function: G(P) = 2 / (s + 3) Assume that you have introduced proportional plus integral controller (G(c)) with gains of Kcp and Kci respectively within the closed loop system. Workout the values for Kcp and Kci so that the peak time Tp is 0.2 sec and the settling time Ts is less than 0.4 sec. 4.2 Complete the empty fields within the table below in reflecting the effect of each of the PID controller gains on the closed loop control system performance factors.


Consider the differential equation d²x / dt² + 3dx / dt + 2x = f(x) where f(x) is the input and is a function of the output, x. If f(x) = sinx, linearize the differential equation for small excursions. [Section: 2.10] Where x = π


Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions:


Write the differential equation that is mathematically equivalent to the block diagram shown in Figure P2.2. Assume that r(t) = 3r³.


For each of the following transfer functions, write the corresponding differential equation.


. A system is described by the following differential equation: Find the expression for the transfer function of the system, Y(s)/X(s).


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