Can someone please explain how to solve the problem below?
Can someone please explain how to solve the problem below? 6. State Space Systems: a. (5...
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...
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...
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...
could you please answer this question QUESTION 2 Consider a system with an open-loop trans fer function given by Y(s) s+7 U(s) s2 +3s-8 (a) (8 marks) Derive a state-space model for the system in canonical form. (b) (4 marks) Check the observability of the system. (c) 8 marks) Design a suitable full-order state observer for the system. Explain your choice of the observer's poles. d) (10 marks) Design a PI controller for the system so the output of the...
i dont understand this problem. please show how to solve all parts using MATLAB. thank you. State-Space Representation and Analysis csys canon(sys,type) compute a canonical state-space realization type 'companion': controllable canonical form type modal: modal canonical form poles of a system controllability matrix observability matrix eig(A) ctrb(A,B) obsv(A,C) -7 L-12 0 EX A 2C-ioD0 uestions () Define the system in the state-space form (2) Determine the stability of the system (3) Determine the controllability and the observability of the system....
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...
The transfer function of a linear system is G(s) = Y(s) S-1 U(s) 5? + 4s +3 a. Express this system in the modal form. b. Express this system in the standard controllable form (SCF). (Parts d, e, f, and g use this system) c. In the standard controllable form, suppose the output is replaced by y=[-1 a] | [x2] Give a value for a which makes the system unobservable. d. What is y(t) if y(0-)=-3, ay = 6 and...
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...
please answer all ELE480/580: Control Systems II Homework #6 Due: 4/29/2019 1. Consider a state equation with 0 0-2 B 1C [0 0 1] A1 0 1 0 1 -3 0 Find the observer gain matrix L that places all three observer eigenvalues at -5. Write the state equation that defines the observer 2. For the state equation defined by the following state matrices x(t) 1 01x,(t)[1 h(t) | = | 0 0 111X2(t) | + | | | u(t)...
6. (15 points) The EoM of a system is given below. The inputs are u(t) and u2(t the outputs are x1, , x2. Write the state space representation of the system.X AX+BU and Y = CX + DU) 2x1 + 4x1-2x2 + 8x1-2X2 = 24(t) + 6u2(t) 3X2ー6x1 + 3x2-3x1 + 9X2-u2(t)