4. The state space model of a nonlinear system is x1(t) = 2x22(t)-50, x2(t) = -x1(t)...
4. The state space model of a nonlinear system is x1(t) = 2x22(t)-50, x2(t) = -x1(t) - 3x2(t) +u(t). where x1(t) and x2(t) are the states, and u(t) is the input. The output of the system is x2(t). PLEASE WRITE/EXPLAIN EVERYTHING.
a. Find the state space model of this system linearized at the equilibrium point (-15, 5).
b. Find the transfer function of this linearized system.
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4. The state space model of a nonlinear system is
x1(t) = 2x22(t)-50,
x2(t) = -x1(t)...
6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) =...
6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x) = x/2-44 a. Find the equilibrium points. (5 pts.) b. Find the linearized system around each equilibrium point. (5 pts.) C. Which of these equilibrium points is (are) and what the pole values for the stable equilibrium points? (5 pts.) 6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x)...
Model the nonlinear system using state space, where x and i are outputs of the system....
Model the nonlinear system using state space, where x and i are outputs of the system. 4. * = 2vi? + x2 + x2 - 16, where u and v are inputs to the system ...
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of...
Write neatly please =)
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of Pontryagin to find the input u that minimizes u2 a. Determine the state function of Pontryagin H b. Find the optimal input and Ho c. Find the matrix A that will yield the governing equations Xy x2 12 If X1 (0) = 1,x2(0)=0 and x1(1)-x-(1)=0 determine the govern equations for λ! (0) and d. (0) in terms of...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...
Problem 5. Consider the dynamics of two mass mechanical system captured by d2xi(t) Middt?t2+k(x1(t)-x2(t)) = f(t)...
Problem 5. Consider the dynamics of two mass mechanical system captured by d2xi(t) Middt?t2+k(x1(t)-x2(t)) = f(t) d'x2(t) dt2 + k(x2(t)-x where M, , M2, and k are constants. Suppose the input is () and the output is X2 (t), find the transfer function G(s) of the system. Note: Consider all zero initial conditions.
3. a) Find a state space representation for a linear system represented by the following differen...
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...
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt c...
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The...
Problem 8: A simplified model of a glider is where y is the flight path angle in radians, v is the airspeed in m/sec, n -L/mg is the load factor, L is the lift in Newtons, m is the mass in kg, and...
Problem 8: A simplified model of a glider is where y is the flight path angle in radians, v is the airspeed in m/sec, n -L/mg is the load factor, L is the lift in Newtons, m is the mass in kg, and k 61.6594 and k 4.8747x103 are constants for the glider. (a) Given that y -0.15 rad, and the airspeed is 50.8691 m/sec, find the necessary load factor to maintain equilibriunm (b) Let the state vector be [7...
Consider a system described by the following equations: · 1 = I1 – 2x122 + u,...
Consider a system described by the following equations: · 1 = I1 – 2x122 + u, º2 = X122 – 22, where x = (x1, x2) is the state and u is an input. (a) Find all equilibrium points for u = 0. (b) For each equilibrium point x = (ū1, 72), find the linearization of the system about the equilibrium. Express your results in state- space form, ż= Az + Bu, where z=x-. Also give the output equation y=...
For this problem we consider a radiant heat transfer system commonly found in space/room heaters. The input to the plan...
For this problem we consider a radiant heat transfer system commonly found in space/room heaters. The input to the plant is (heat) energy q(Watts) and the output of the system is its temperature (K). The ODE that describes the system is given below Where, 8a is the ambient temperature (27°C), b-91.6 is an input constant, m 0.1 kg is the mass, C 420 J/Kg.K is the specific heat of the heater and a-AEo. A0.25 m2 is the surface area of...
6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x) = x/2-44 a. Find the equilibrium points. (5 pts.) b. Find the linearized system around each equilibrium point. (5 pts.) C. Which of these equilibrium points is (are) and what the pole values for the stable equilibrium points? (5 pts.) 6) For the nonlinear autonomous system dx/dt = f(x), where X = (X1,x2)" and f.(X) = 4x2 - X2?; f(x)...
Model the nonlinear system using state space, where x and i are outputs of the system. 4. * = 2vi? + x2 + x2 - 16, where u and v are inputs to the system ...
Write neatly please =)
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of Pontryagin to find the input u that minimizes u2 a. Determine the state function of Pontryagin H b. Find the optimal input and Ho c. Find the matrix A that will yield the governing equations Xy x2 12 If X1 (0) = 1,x2(0)=0 and x1(1)-x-(1)=0 determine the govern equations for λ! (0) and d. (0) in terms of...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...
Problem 5. Consider the dynamics of two mass mechanical system captured by d2xi(t) Middt?t2+k(x1(t)-x2(t)) = f(t) d'x2(t) dt2 + k(x2(t)-x where M, , M2, and k are constants. Suppose the input is () and the output is X2 (t), find the transfer function G(s) of the system. Note: Consider all zero initial conditions.
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...
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The...
Problem 8: A simplified model of a glider is where y is the flight path angle in radians, v is the airspeed in m/sec, n -L/mg is the load factor, L is the lift in Newtons, m is the mass in kg, and k 61.6594 and k 4.8747x103 are constants for the glider. (a) Given that y -0.15 rad, and the airspeed is 50.8691 m/sec, find the necessary load factor to maintain equilibriunm (b) Let the state vector be [7...
Consider a system described by the following equations: · 1 = I1 – 2x122 + u, º2 = X122 – 22, where x = (x1, x2) is the state and u is an input. (a) Find all equilibrium points for u = 0. (b) For each equilibrium point x = (ū1, 72), find the linearization of the system about the equilibrium. Express your results in state- space form, ż= Az + Bu, where z=x-. Also give the output equation y=...
For this problem we consider a radiant heat transfer system commonly found in space/room heaters. The input to the plant is (heat) energy q(Watts) and the output of the system is its temperature (K). The ODE that describes the system is given below Where, 8a is the ambient temperature (27°C), b-91.6 is an input constant, m 0.1 kg is the mass, C 420 J/Kg.K is the specific heat of the heater and a-AEo. A0.25 m2 is the surface area of...
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