Please help me with QUESTION 2.
Please help me with QUESTION 2. 1. Consider the electrical system shown below, for which the input variable u, the out...
control system with observer Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is...
Please only solve part C Assume the following state space representation of a discrete-time servomotor system. (As a review for the Final Exam, you might check this state space representation with the difference equation in Problem 1 on Homework 2. This parenthetical comment is not a required part for Homework 8.) 2. 0.048371 u(n) 1.9048x(n) lo.04679 [1,0]x(n) y(n) Compute the open-loop eigenvalues of the system. That is, find the eigenvalues of Ф. Check controllability of the system. Or, answer the...
Problem 1 Given the transfer function from input u(t) to output y(t), s2-4s +3 Y(s) U(s) (s2 + 6s + 8)(82 + 25) (a) Develop a state space model for this transfer function, in the standard form y=Cx + Du (b) Suppose that zero input is applied, such that u 0. Perform a modal analysis of the state response for this open-loop system. Your analysis should include the nature of the time response for each mode, as well as how...
Question 4 (a) A feedback control system with a proportional controller is shown in Figure Q4 (a). (i) Sketch the root locus of the system, (ii) Design the proportional controller (choose the value of K) such that the damping ratio does not exceed 0.5 and the time constant is less than 1 second. [All necessary steps of root locus construction and controller design must be shown). C(s) R(S) + s(s+4)(s + 10) Figure Q4 (a). A feedback control system [11...
Problem 6. Consider the system *1 = x1 + u iz = -x1 + x2 (a) Determine the stability of the open-loop system by checking the eigenvalues of the above system. (b) Define the output to be y = X1. Use the MATLAB command “Iqr” to find the constant optimal feedback control law gains by solving the infinite-horizon output regulator problem with Q=1 and R=0.1. (c) Determine the closed-loop stability by calculating the eigenvalues of the closed- loop system when...
a-represent system in state space form? b-find output response y(t? c-design a state feedback gain controller? 3- A dynamic system is described by the following set of coupled linear ordinary differential equations: x1 + 2x1-4x2-5u x1-x2 + 4x1 + x2 = 5u EDQMS 2/3 Page 1 of 2 a. Represent the system in state-space form. b. For u(t) =1 and initial condition state vector x(0) = LII find the outp (10 marks) response y(t). c. Design a state feedback gain...
Problem 1: Given the transfer function from input u(t) to output y(t), Y (s) U(s) = s 2 − 4s + 3 (s 2 + 6s + 8)(s 2 + 25) (a) Develop a state space model for this transfer function, in the standard form x˙ = Ax + Bu y = Cx + Du (b) Suppose that zero input is applied, such that u = 0. Perform a modal analysis of the state response for this open-loop system. Your...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Consider the sontrol system shown in the figure below: R(S) + E(s) C(s) K (s + 4)(s + 6) g) Sketch the uncompensated system root locus showing all details. (5 Points) h) Find the dominant closed loop poles of the uncompensated system to operate with a 16.3% overshoot and peak time tp = 0.7255 (make sure to show this point on the Root Locus) (5 Points) (s+z) Now we want to design a PI compensator of the form to increase...