UestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Fin...
Q1, pease help asap, please write clearly. Thanks in advance. 1. Given the transfer function of the control system. (60%) G(s) S) 5s+13 R(s) +6s+13 Y (1) Sketch the state diagram in the form of signal flow graph. (2) Find the state equations. (3) Find the output equation. (4) Find the fundamental matrix 2(t). (5) Find the state-transition matrix D(t) (6) Find the state vector x(t) if the input r(t) 2 and y(0)= (0) = 0 . 1. Given the...
1. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01 (1) 60 = {1, 1421 a) Find the state transition matrix and the impulse response matrix of the system. b) Determine whether the system is (i) completely state controllable, (ii) differentially control- lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. c) Repeat part (b) for to = 1. d) Determine whether the system is (i) observable, (ii) differentially observable, (iii) instanta-...
The transfer function of a linear system is G(s) = Y(s) S-1 U(s) 5? + 4s +3 a. Express this system in the modal form. b. Express this system in the standard controllable form (SCF). (Parts d, e, f, and g use this system) c. In the standard controllable form, suppose the output is replaced by y=[-1 a] | [x2] Give a value for a which makes the system unobservable. d. What is y(t) if y(0-)=-3, ay = 6 and...
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...
please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system. 5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F,...
Consider the system. (1) M →1.0) M +0.1 kg, B=0.2 N-s/m Mv(1) + By(t) = 1,01) Consider a system described by the following differential equation: 0.1"WX2 +0.2v(t) = .0), where y(t) and 4.0) are the output and the input of the system. dt (la) Convert the above differential equation into the form of the typical first-order dynamic system: + ) = ), and explain the physical meaning of the two parameters 7 and v.. (5%) dv(1) (1b) According to the...
For the given RC circuit shown below, ys the output, and ut) is the input. Values of the components are marked on schematic i) Derive the system differential equation and transfer function Y(s)/U(s) ii) Choose voltage across capacitors as states and derive the state equations and state matrices (A, B, C,and D). iii) Validate the states by deriving the transfer function from state matrices. iv) Choose a different set of states and derive a different state equation and state Matrix...
signal and system 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
DONGGUK UNIVERSITY Division of Electronics and Electrical Engineering ENE4067-01 Modern control system Homework #2 Student ID: 1st Semester, 2020 Name: Note that you have to represent all the derivation process in detail. Problem 1. A spring-mass-friction system is described by the following differential equation. d?y(t) dy(t) dt2 + y(t) = r(t) dt (a) Define the state variables as xi(t) = y(t), x2(t) = y(t) + dy(t)/dt. Write the state equations in vector-matrix form. Find the state transition matrix of A....