a) The dynamics of a discrete-time system are determined by the difference equation; 8yk+2 –6y+1 +yk=9 Determine the response of the system given that y0=1 and y1=1.5 b) Find the state transition matrix for the digital system given by X (k+1) = [ -1 0] x (k) [ 1 3] c) Obtain Z-transform of (1-e-Ts )/s(1/s+1) d) The z-transform X (z) of a function X (k), is given by; X (z) =z(0.1065z +0.09021)/(z-1)(z2-1.5z+0.6967)

a) The dynamics of a discrete-time system are determined by the difference equation; 8yk+2 –6y+1 +yk=9 Determine the response of the system given that y0=1 and y1=1.5 b) Find the state transition matrix for the digital system given by X (k+1) = [ -1 0] x (k) [ 1 3] c) Obtain Z-transform of (1-e-Ts )/s(1/s+1) d) The z-transform X (z) of a function X (k), is given by; X (z) =z(0.1065z +0.09021)/(z-1)(z2-1.5z+0.6967)

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.16P

See similar textbooks

Similar questions

Given an RC circuit in Figure 1 is modelled by the differential equation written as, ????+1???(?)=1???(?).If the input, ?(?)=0.8?−??(?) with initial condition ?(0−)=3?, by using the Laplace transform approach determine,a) overall output response, ?(?)b) zero input responsec) zero state response
Q1. Solve the sequence x[n]={3, 4, 1, 1, 1} into a sum of weighted impulse δ[n], and unit step u[n] sequences.
For a particular digital processing system, inputting the finite sequence x[n]= (1,-1) results in the finite output sequence of (1, 2, - 1, - 2 ) . Determine the z-transforms for the two signals and give the transfer function for the processing system
Suppose that: H(z) = (z^2 − 1)(z ^2 − 2z + 5) / (25z^2 + 25z + 6) is the transfer/system function of a DT LTI system. Assuming that the impulse response h[n] is right-sided, draw the pole-zero diagram, including the ROC. Find an appropriate partial fractions expansion for inverting the z-transform and use the tables of z-transform properties and pairs to find the impulse response h[n], assuming h[n] is right-sided. Thank you for the help on this problem. I got poles at -3/5 and -2/5 and zeros at 1, 1+- j2 I'm not sure that is right and I'm not exactly sure if my pole diagram is correct. for the partial fractions and invert z transfom i got 3/5e^-30 and 2/5e^-20 u(n). I 'm not exactly sure all this is right though and was hoping for a second opinion. Thanks again for your time and energy.
Given the following ordinary differential equation describing the dynamics of a system y'''+17y''+80y'+100y=3(u''+5u'+4u) Here, y(t) is the output and u(t) is the input. Laplace table is given below. Find the transfer function G(s) [=Y(s)/U(s)] by applying Laplace transform (all initial valus are zero) Find the poles and zeros of the system. Is the system stable or unstable? Which pole(s) is/are slow and which ones is/are fast? Find Y(s) if input is unit step function. Find initial and final values of the system by applying the theorems.
17.3) Using K – map, simplify the following Boolean expression. Y = ∑ m ( 0, 1, 2, 4, 5, 6, 8, 10, 11, 13, 15)
the following statements given, write if each statement is true or false. a. If the complex frequency domain function, F(s), is derived using a “One-sided” Laplace Transform, the inverse of that function, f(t), is only valid for t ≥ 0. b. When using an ideal transformer, if voltage increases from primary side to secondary side, current also increases from primary side to the secondary side. c. Initial value theorem states that the initial value of a time function f(t) can be obtained from its Laplace Transform F(s) by multiplying the transform by s and letting s approach zero. ..
Determine the Total Response when x(n)=4(0.5)nu(n)+3(0.75)nu(n) using the Z-transform, given the system described below and its initial conditions.Then considering the given input, what are the energies of the input and the resulting output of the system?
a) State the order of this ODE. Use the ODE and a Laplace transform table to derive the open-loop(or forward-path) transfer function, H(s) = Y(s)/U(s) = Θ(?)/Δ(?)(b) Compute the finite zeros and finite poles of H(s) and state the number of infinite zeros ofH(s). Is the transfer function H(s) stable, marginally stable, or unstable?
Given J(a,b,c,d) = Σm(0,1,2,3,7,8,10) + Σd(5,6,11,15) 1. Determine the minimal Sum of Products (SOP) expression using a Karnaugh Map. 2. Determine the minimal Product of Sums (POS) expression using a Karnaugh Map.
Transfer function ? (?) = 2/1 + 2 ∗ 0.5?-1 + 0.52 ?-2, steady state response for unit step function input… ..
a) Y(ω) = 1/(5+jω) The expression above defines the frequency domain signal Y(ω) from a time domain signal y(t) i) Determine the imaginary & real parts of Y(ω). ii.Determine the signal y(t) that produced the signal Y(ω). b)What are the 3 areas of application of i.Signals ii.Systems c) Briefly summarise with explanation the difference between discrete & continuous time signal and also write an expression that describes each signal type.