Determine the state-variable model for a system with the following difference equation y(k+2)-y(k+1)+2y(k)=u(k)
Determine the state-variable model for a system with the following difference equation y(k+2)-y(k+1)+2y(k)=u(k)
1- A system has a block diagram as shown. Determine a state variable representation (model) and state transition matrix Φ(s) R(s) + 25 Y(s) 25 2- A system has the following differential equation: 2 -3 Determine Ф(t) and its transform D(s) for the system
For a system with the difference equation: y[n] = -2y[n-1] + x[n] + 2x[n-2], find a.The impulse response b.The step response
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation by H(s) a) D, and find the transfer function for the system above. (5 marks) Sketch the Bode plot. b) (5 marks)
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation...
2) An LTI DT system is defined by the difference equation: y[n] = -0.4yIn - 1] + x[n]. a) Derive the impulse response of the system. (2 pt) b) Determine if the system is BIBO stable. (1 pt) c) Assuming initial conditions yl-1) = 1, derive the complete system response to an input x[n] = u[n] - u[n-2), for n > 0.(2 pt) d) Derive the zero-state system response to an input z[n] = u[n] - 2u[n - 2] +...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
1.3. Assume a discrete-time system with input u(k) and output y(k). The system has a constant input disturbance d. Find the augmented state-space model with input Au(k) and output y(k) for the plant model given as below: Im(k +1) = AmIm (k) + Bmu(k) + Bad; y(k) = Cmlm (k) (1.82) [10.5 0 ] [ 0.51 where Am = 0.1 -0.1; Bm = 1 ; Cm = [101]; Ba= 100 0.8 -0.6 1. Calculate the plant transfer function that relates...
Please help me with QUESTION 2.
1. Consider the electrical system shown below, for which the input variable u, the output variable y, and the state variables xi and x2 have been specified. R L + C (a) Determine the state-space model of the system (b) Show that the transfer function (from u to y) has the form bis H(s)=2+ajs+ a0 by relating (ao, ai, bi) to (R, L, C) (c) Show that the frequency response function (from u to...
6. Find the particular part of the solution of the difference equation y(n+2) – 2y(n+1)+y(n) = 4 for n <0.
For an LTID system described by the difference equation y[k + 2]-0.5ylk +1]-0.24 3flk + 2lFind the zero-input response if yI-1] 0 and y[-2] 4) 100 72"