3. For the system given by 1 0 (a) Determine Ф(s) and Ф(t). (b) Determine x(t)...
20 points] Q1. The Stately State Transition Matrix, Ф 16 2 3 13 Consider a state transition matrix, Ф, for a SISO LTI system A1. A- 5 11 10 8 9 76 12 Please determine and justify: (a) Ф(t) for this system A 4 14 15 1 ] (b) Ф(s) for this system A (c) System A's characteristic polynomial (d) Ф(z) for this system A via Tustin's method (ie, trapazoid-rule) (e) A difference equation assuming: (1) a step input at...
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?
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no? c) H HG) were modified as follows. Determine the system stability as a function of parameter k, i.e, what is the minimal value of k required to keep the system stable? d) Sketch Bode the plot for T(s) including data 'k, derived from...
Consider the state equation 3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and the state vector x(t) for t 2 0 when the input is u(t) 1 for t 20. 3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and the state vector x(t) for t 2 0 when the input is u(t) 1 for t 20.
Consider the LTI system described by the following information X(s) = 2. S-2 where x(t) = 0 for t > 0, and y(t) = -e2'u(-t) + e-t u(t). 3 Determine H(s), and its region of convergence. (5 points). Determine h(t). (5 points). a. b. Using the system function found in part(a), determine the output y(t) if the - o <t < + o. ( 10 points). c. input is given by: est,
For the following system: -13 1 0 x(t)30 01x(t)u(t) y(t)=[1 이 x(t) 0 a. Determine if the system is completely controllable. b. If the system is completely controllable, design a state feedback regulator of the form u(t)-Kx(t) to meet the following performance criteria: %10 1.5% · T, = 0.667 sec For the following system: -13 1 0 x(t)30 01x(t)u(t) y(t)=[1 이 x(t) 0 a. Determine if the system is completely controllable. b. If the system is completely controllable, design a...
5. Consider the system given in (a) is marginally stable. X + 4. 10/( s (0.1 s +1) 1/s G(s) (a) Find G(s) (b) Determine Y(s)/X(s) in terms of G(s). (c) If the error E(s)-X(s)-Y (s) determine E(s)/Y(s). (d) Determine the steady-state value of e(t) given that s(t): u(t) 6. Consider the system given in (a) is marginally stable. X+ G(s) (a) Determine the transfer function (s)/X(s). (b) If the error e()-x(0)-y() determine a G(s) such that e(oo) -1/2 when...
Ill): The system shown in Fig. 3 is in equilibrium when ф 0°. Knowing that initially °,-150° and that block C is given a slight nudge when the system is in that position, determine the speed of the block as it passes through the equilibrium position ф-0. Neglect the weight of the rod. (20 points) .В i b 35 2 Fig. 3 5.3 Ill): The system shown in Fig. 3 is in equilibrium when ф 0°. Knowing that initially °,-150°...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
I need a Matlab code example plz 1. Suppose x(t) -3u(t+3) - u(t)+ 3H(t-3) - 5H(t-6) a. Sketch x(t). b. For the signal x(t) given, determine and sketch the following signals: ,g(t) x(t-6) g2(t) - x(3t-6) ii. s(t) x(3t-6) +2 c. Create a MATLAB script that uses a function to express x(t), and plots x(t) in the time interval- 5 < t < 8s, using a time increment of At= 0.01s. Next, use the function to graph each of the...