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A SYSTEM MODELED WITH THE SECOND ORDER DIFFERENTIAL EQUATION PRESENTS THE FOLLOWING RESPONSE TO ZERO STATE y(t) = u(t)...
Solving simple system differential equation to understand Zero-State response, Initial Condition response, Total response, and Steady...
Solving simple system differential equation to understand Zero-State response, Initial Condition response, Total response, and Steady State response: Unit Impulse response and Convolution Integral (Zero-State response): 9) Two LTI systems in parallel h1(t)- e "u(t) and h2(t)- h1(t-2) a. Find the expression of the combined unit impulse response h(t) b. Find the zero state response y2s(t) in the expression of piecewise function to the input signal x(t)-[u(t)-u(t-10)] Sketch y2s(t) Show that the combined system h(t) is causal as well as...
3. Consider the following second order differential equation: If we let u y andv-y then express the second order differ...
3. Consider the following second order differential equation: If we let u y andv-y then express the second order differential equation as an AUTONOMOUS first order system.
3. Consider the following second order differential equation: If we let u y andv-y then express the second order differential equation as an AUTONOMOUS first order system.
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
A linear, time-invariant system is modeled by the ordinary differential equation y(t) + 7y(t) = 14f(t)...
A linear, time-invariant system is modeled by the ordinary
differential equation
y(t) + 7y(t) = 14f(t)
Let f(t) = e^-t cos(2t)u(t) and y(0-) = -1.
(a) Find the transfer function of the system and place your
answer in the standard form
H(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 +
... + a1s + a0
(b) Determine the output of the system as
Y(s) = Yzs(s) + Yzi(s)
and place both the zero...
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
An LT-I system with the following differential equation y’(t) + 3 y(t) = x(t) has a...
An LT-I system with the following differential equation y’(t) + 3 y(t) = x(t) has a Zero State Response of yzsr(t) = -2 exp(-5t) u(t) + 2 exp(-3t) u(t) when an input signal: x(t) = 4 exp(-5t) u(t) is applied to the system. What is the Zero State Response of the following system beginning at time t = 0 seconds, y’(t) + 3 y(t) = x’(t) -2 x(t) if the same input signal is applied to the system, and it...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
15. A dynamical system is modeled by the following differential equation under zero initial conditions: d’y(t)...
15. A dynamical system is modeled by the following differential equation under zero initial conditions: d’y(t) d’y(t) dy(t) du(t) + 5 + dt4 + 15 dt3 + 2y(t) = 8 + 10u(t) dt2 dt dt d4y(t) Write the system's state equation and the system's output equation.
Problem 7.2 The differential equations for a second-order thermal system are y=x2 where u is the control input. (a) Show that the plant is type zero. As a consequence, the steady-state error using pr...
Problem 7.2 The differential equations for a second-order thermal system are y=x2 where u is the control input. (a) Show that the plant is type zero. As a consequence, the steady-state error using proportional control is non-zero. Find the steady-state error as a function of G (b) To achieve zero steady-state error, integral control will be used, by adding the state variable zo with which is appended to the original equations, making the system third-order. For the resulting third-order system,...
Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response y(t) subject to ut) 3cos(0.5t -0.5). (Hi...
Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response y(t) subject to ut) 3cos(0.5t -0.5). (Hint: use the frequency response formula.) (996) (Easy)
Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response y(t) subject to ut) 3cos(0.5t -0.5). (Hint: use the frequency response formula.) (996) (Easy)
Solving simple system differential equation to understand Zero-State response, Initial Condition response, Total response, and Steady State response: Unit Impulse response and Convolution Integral (Zero-State response): 9) Two LTI systems in parallel h1(t)- e "u(t) and h2(t)- h1(t-2) a. Find the expression of the combined unit impulse response h(t) b. Find the zero state response y2s(t) in the expression of piecewise function to the input signal x(t)-[u(t)-u(t-10)] Sketch y2s(t) Show that the combined system h(t) is causal as well as...
3. Consider the following second order differential equation: If we let u y andv-y then express the second order differential equation as an AUTONOMOUS first order system.
3. Consider the following second order differential equation: If we let u y andv-y then express the second order differential equation as an AUTONOMOUS first order system.
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
A linear, time-invariant system is modeled by the ordinary
differential equation
y(t) + 7y(t) = 14f(t)
Let f(t) = e^-t cos(2t)u(t) and y(0-) = -1.
(a) Find the transfer function of the system and place your
answer in the standard form
H(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 +
... + a1s + a0
(b) Determine the output of the system as
Y(s) = Yzs(s) + Yzi(s)
and place both the zero...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
15. A dynamical system is modeled by the following differential equation under zero initial conditions: d’y(t) d’y(t) dy(t) du(t) + 5 + dt4 + 15 dt3 + 2y(t) = 8 + 10u(t) dt2 dt dt d4y(t) Write the system's state equation and the system's output equation.
Problem 7.2 The differential equations for a second-order thermal system are y=x2 where u is the control input. (a) Show that the plant is type zero. As a consequence, the steady-state error using proportional control is non-zero. Find the steady-state error as a function of G (b) To achieve zero steady-state error, integral control will be used, by adding the state variable zo with which is appended to the original equations, making the system third-order. For the resulting third-order system,...
Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response y(t) subject to ut) 3cos(0.5t -0.5). (Hint: use the frequency response formula.) (996) (Easy)
Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response y(t) subject to ut) 3cos(0.5t -0.5). (Hint: use the frequency response formula.) (996) (Easy)
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