2- Solve for y(t) for the following system 1 01 -3 represented in state space, where...
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54 +52 +7 Convert the following state space into a transfer function. (Marks 5) x = 11 * = x + ( u 21 y = [02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) i [ 10] [21. *= 15 2]* +11 y = [ 02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) -1 0x+lu x =...
An LTI system, with an input g(t) and an output y(t), is represented with the following state and output matrices. Assuming a zero-state condition, identify the steady state error if the system is subject to a unit step function. [x1 [x2. ) = [] : [22] + [3] AND y = [2 -1) [x3] + [2]g 4. 0 2 1 3 5
A system (a plant) is represented as a state-space model in the form: dt (1) Deduce and draw a simulation diagram for the system. Implement it afterwards in Simulink. For a unit stepin- put, simulate and plot the trajectories in the state space, and the output y(t) of the system, for a set of four different initial conditions: x(0)-[0 ofT,x(0-[1 o, x(0-0 IT,x(0-[0 I]T
A system (a plant) is represented as a state-space model in the form: dt (1) Deduce...
(1 point) Use the Laplace transform to solve the following initial value problem: y" +12y' 85y (- 6 (0) 0, y(0)0 Use step(t-C) for ue(t). y(t) = (1/49jeAqt-6))sin(7)step(t-6)
(1 point) Use the Laplace transform to solve the following initial value problem: y" +12y' 85y (- 6 (0) 0, y(0)0 Use step(t-C) for ue(t). y(t) = (1/49jeAqt-6))sin(7)step(t-6)
Use the Laplace transform to solve the given initial-value problem. 0 st<1 t 1 y' y f(t), y(0) 0, where f(t) (4, ae-1 -(1-1) 4 y(t) X
Use the Laplace transform to solve the given initial-value problem. 0 st
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 + 4y = u(t) dt dt where y(t) is the output of the system and u(t) is the input. This is an Initial Value Problem (IVP) with initial conditions y(0) = 0, y = 0. Also by setting u(t) = (t) an input 8(t) is given to the system, where 8(t) is the unit impulse function. a. Write a function F(s) for a function f(t)...
Consider the following nonhomogeneous system for 2-dimensional vector X(t), t 2 0. 0 x(0)1 2 -1 where A- 5 -2 (a) Use the Laplace transform to compute eAt. (b) Using eAt of (a), find the solution of the above nonhomogeneous system
Consider the following nonhomogeneous system for 2-dimensional vector X(t), t 2 0. 0 x(0)1 2 -1 where A- 5 -2 (a) Use the Laplace transform to compute eAt. (b) Using eAt of (a), find the solution of the above...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...
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%...