2. (30%) In the following system, tn A/D ZOH tipl = u(nT), yin] = y(nT), T...
--2-11x(t)+は111(t) 2. (10 pts.) If X(t) and the sample period. T. is selected to equal T-0. I, find Ф and Г in the ZOH equivalent discrete-time, state space representation. y(t)=[-1 1]x(t) , --2-11x(t)+は111(t) 2. (10 pts.) If X(t) and the sample period. T. is selected to equal T-0. I, find Ф and Г in the ZOH equivalent discrete-time, state space representation. y(t)=[-1 1]x(t) ,
r[n] + K(z) D/A with ZOH G(s) A/D Here the sampling period T = 0.5 sec and G(s) = FT K(z) = 30 (i) Find the ZOH discrete equivalent of the system and determine if it is stable. For this problem, you are NOT allowed to use the table of z-transforms.
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...
Feedback u(t) u1(t) y1(t) System 1 y(t) System 2 y2(t) u2(t) Please find the final equivalent state space representation. Note: the state space representation of Systi is: Sii = AjX; + B;Ui Yi = Cixi (i.e. D;=0)
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...
Show all steps and solution clearly: 2. For the following system: T-13 1 07 x(t) = -30 0 1 x(t) + Ou(t) 10 00 y(t) = [1 0 0] x(t) 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: • %PO = 1.5% . Ts = 0.667 sec
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t) r*(t ZOH Process zero-order hold, and the process are given by 2s +1 Go(s) =--s G(s) = There parameter a is some real number, and T is the sampling time. (a) (15 points) Determine the discrete-time transfer function G(z). 4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y...
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...
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...