1.3. Assume a discrete-time system with input u(k) and output y(k). The system has a constant...
The output of a discrete-time system is related to the input by Y(n) x(n is 1 1) = - a. Find the transfer function of the system. b. If the input X(n) is stationary with E(X(n)) = 0 Rxx(k) = { 1, for k = 0 for k 0 0 find Sy(f) and EfY'(n) γγ
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...
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
Bonus Question) A discrete-time LTI system with a sampling frequency of Ukm2 is shown in the following Figure. The rectangular boxes with the label z provide one sample period delay to their input signals. The circular components are adders or subtractors. The triangular components provide linear vain factors of ar or bi where i is 0,1 or 2. i) Derive the system transfer function H(2). ü) Find the difference equation relating the output y[n] and input x[n]. iii) Given that...
Problem 2. A signal flow graph for a system with input (k) and output y(k) is shown in Figure 1. 0.005 r(k) ei(k) z1v2(k) Vk) 0.03 0.1 0.05 e2(k) y(k) 0.07 e2(k) 11 0.7 0.2 V4(k) y(k) 0.9 0.4 Figure 1. Signal flow graph of a system. e) Find a state-space representation of the system in Figure 1 with state variables Find the transfer functionusing using Mason's gain rule and one other technique to verify the R(E) result g) Suppose...
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
control system with observer Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
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...
For this problem we consider a radiant heat transfer system commonly found in space/room heaters. The input to the plant is (heat) energy q(Watts) and the output of the system is its temperature (K). The ODE that describes the system is given below Where, 8a is the ambient temperature (27°C), b-91.6 is an input constant, m 0.1 kg is the mass, C 420 J/Kg.K is the specific heat of the heater and a-AEo. A0.25 m2 is the surface area of...
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function...