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5. Given: Y(s) U(s) Find: The state-space representation. 3s + 2 5+65 +9
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input
4. Given: 92 + 5s - 5 53 +852 +8s +6 U(s) Find: The state-space representation.
this problem needs to be done using SciLab 9. A control system is given by the following state-space representation -8 101 [2 dt 1-6 00 y [1 0 0]x Please do the following: a. Find its transfer function representation. b. Calculate its zeros and poles c. Write a Scilab program to draw the step response and impulse response graphs in the same window with the step response graph in the upper half the window and the impuise response graph in...
Test 1 2: A state space representation of a system is given by: -2 011 y=[0 1]x 1. Design a state variable feedback control to place the closed-loop poles s =-3 ±j2. Assume that the complete state vector is available for feedback.。 Find the resulted close loop transfer function.
Q3. The state-space representation of a dynamical system is given as follows: (2) (y = 2 x 1. By finding the eigenvalues, eigenvectors of the A matrix, compute el via the diagonal transformation. 2. Assume that the control input is u(t) = 0, compute x(1) and y(t). 3. Assume that the input is u(t) = 1 + 2e-21, compute x(t) and y(t). 4. Given your answers to the previous question, compute x(t) when 1 00
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54 +52 +7 Convert the following state space into a transfer function. (Marks 5) x = 11 * = x + ( u 21 y = [02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) i [ 10] [21. *= 15 2]* +11 y = [ 02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) -1 0x+lu x =...
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...
2. Find the state space representation of the system represented by the following transfer function: (s +1.2) (s 15.8) (s +23) s(S 1.3) (s +7.2) (s + 47) G(s)- 3. Find the transfer function of the system with the following state space representation: 1 3.2 1.6 1(01) [-1 e) -7.4 2.4 -9.1l(O You may use your calculator, Matlab, or calculate by hand to find the following transfer functions: G1(s) 0,() R(S) G3(s) s) R(
Given a linear time-invariant system in state-space representation: -100 5*+u(t) y=[1 0]x (i) Determine the transfer function of the system. (ii) Build an equivalent mechanical system showing all the parameters. (ii) Derive an expression x(t) for this system for step input. Is the mechanical system over damped, under damped or critically damped system?
9. For the transfer function: Find its state space representation. 10. A system is described by the following differential equations: Find its state space representation.