x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z). x(t)-A()x(t)...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
x() — А() x() + B()u(t) Consider the following time-varying system У() %3D С()x() + D()u(t) Assume that the impulse response function is given by g(t,e-)-2e2-) Derive the least dimensional quadruplet {A(t), B(t),C(t),D(t)} x() — А() x() + B()u(t) Consider the following time-varying system У() %3D С()x() + D()u(t) Assume that the impulse response function is given by g(t,e-)-2e2-) Derive the least dimensional quadruplet {A(t), B(t),C(t),D(t)}
find the following: a)state transition matrix? b)output as function of time? c)design a state feedback controller to place closed loop at (-3) and (-5) Question (: (10 hO Considering the following system, 01x + 0 t<0 tt t20 Where x(0)-L1] , u(t)-(% ,u(t) a) Find the state transition matrix. (3 marks) b) Find the output as a function of time. (3 marks) c) Design a state feedback controller to place the closed loop poles at (-3) and (-5). (4 marks)...
Problem 5 5. Find the state transition matrix, the zero-input response, the zero-state response, and the complete response for the following continuous-time system -2 0 3 -5 1]x(t) x(t) = dt x(t)u() x(0) = 2/3 y(t) =[0 u(t) = et for t20
Consider and impulse response h(t)= p(t ,T ), where p(t,T) is the pulse function u(t) - u(t - T) Find the output for the following inputs to the system via convolution: a) p(t,T) b) u(t) c) r(t) = 0, t < 0 a t, 0 < t < T 0, t > T
Prelab Answer the following questions 1. What is the unit-step response of a system with trans fer function G(s)- ST +1 where and τ are constants > 0? 2. Make a hand-sketch of the response of the unit-step response of the system in Part 1 3. What is the value of the step response of the system in Part 1 when t? 4. Find or derive the expression for the transfer function from voltage to angular speed of an unloaded...
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,...
1 Find the impulse response of H(z), where H(z) is the system 1-2+2 function of the difference equation of the 2nd-order IIR filter given by the block diagram Y(z) X(z) + X + +
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%...
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-...