Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y +...
answer ASAP 2. (20 points) Consider the following unity-feedback system. Suppose G(s) sis+45+6s+4) R) Ets) G(s) A. Check the stability of the closed-loop system by using Routh-Hurwitz Criterion. B. Find the steady-state error when the input is a unit step function.
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...
4) A unity feedback control system shown in Figure 2 has the following controller and process with the transfer functions: m(60100c Prs(s +10(s+7.5) a) Obtain the open- and closed-loop transfer functions of the system. b) Obtain the stability conditions using the Routh-Hurwitz criterion. e) Setting by trial-and-error some values for Kp, Ki, and Ko, obtain the time response for minimum overshoot and minimum settling time by Matlab/Simulink. Y(s) R(s) E(s) Fig. 2: Unity feedback control system 4) A unity feedback...
(10 points) For the differential equation y(6) - 2y (5) – 3y(4) + 2y(3) + 10y" – 8y = 0. Find the fundamental solution set to the DE if the characteristic equation in factored form is given by (r – 2) (r2 + 2r + 2) (r - 1) (r + 1) = 0
The Class Name is: MAE 318 System Dynamics and Control I Problem 1: Steady-state error analvsis (a) A block diagram of a feedback control system is given below. Assuming that the tunable constant Khas a value that makes this closed-loop system stable, find the steady-state error of the closed-loop system for (a a step reference input with amplitude R, r(t)- R u(t) (ii) a ramp reference input with slope R, r(t) = Rt-us(t) R(s) Y(s) (s+2)(s +5) (b) A block...
Q2 (a) List down THREE (3) important requirements to design a control system. (3 marks) State the possible consequence when a physical system becomes unstable. (2 marks) (6) (c) Consider the following characteristic Equation shown below: P(s) = 55 +683 + 582 +8s + 20 (1) Construct Routh table for the characteristic Equation. (6 marks) (ii) Using the Routh – Hurwitz criterion, determine the stability of the system. (2 marks) (ii) Determine the numbers of roots on the right half-plane,...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control input is defined as u- -Kx + r, with r(t) a reference input. This results in a closed-loop system x (A-BK)x(t)+ Br(t) = with matrices 2 -2 K=[k1 K2 For this type of controller, ki, k2 ER do not need to be restricted to positive numbers - any real number is fine (a) What is the characteristic equation of the closed-loop system, in terms...
pleas show all work thank you Disturbance D(s) Reference Control Output Input Error Input t US) Y(s) Plant Given the above closed loop block diagram: Let aundl s) KK (a) Show that the above system will have zero steady state error for step reference input (when D(s)-0) as well as for step disturbance input (when R(s)-0). (b) LetJ B K1 and Kp0, what about the stability of the closed loop system? Disturbance D(s) Reference Control Output Input Error Input t...
Please code on MATLAB and explain D) only. Thank you The block diagram of a linear control system is shown in the Fig., where r(t) is the reference input and n(t) is the disturbance. (a) Find the steady-state value of e(t) when n(t) = 0 and r(t) tuz(t). Find the conditions on the values of a and K so that the solution is valid. N(s) R(S) E(S) S + a K(s + 3) Y(s) S (5² - 1) Controller Process...