Model the nonlinear system using state space, where x and i are outputs of the system....
Problem 2- System Classification: Linearity (20pts) Circle all nonlinear terms (if any) in the following differential equations: (assume variables on left are outputs, at right are inputs) y'(t) *,4x, +4x, cos(x2) e. Problem 2- System Classification: Linearity (20pts) Circle all nonlinear terms (if any) in the following differential equations: (assume variables on left are outputs, at right are inputs) y'(t) *,4x, +4x, cos(x2) e.
For a Mechanical Engineering System Dynamics class 2. i) Obtain the state model for the reduced-form model 28 +62 + 12x = 10y(t). Use x, and xz as the state variables. Put the equations in standard form and find [A] and [B] matrices. Given the state variable model x = x; – 5x, + f (1) * = -30x, +10f2(1) where f(t) and f (t) are the inputs, and the output equations y = x, - x2 + f,0 Y2...
20e 82 amd M(M) is a three-state Problem I: Given the nonlinear system, in which G(s)amd N(M) is a three-state relay. Analyze the self-excited oscillation at the output of the system, if existing. 24 v(r) u(r) 0.5 0.5 -24 20e 82 amd M(M) is a three-state Problem I: Given the nonlinear system, in which G(s)amd N(M) is a three-state relay. Analyze the self-excited oscillation at the output of the system, if existing. 24 v(r) u(r) 0.5 0.5 -24
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)...
2. i) Obtain the state model for the reduced-form model 28 + 61 + 12x = 10y(t). Use x, and xz as the state variables. Put the equations in standard form and find [A] and [B] matrices. ii) where f (t) and f (t) are the inputs, Given the state-variable model i; = x; – 5x, +f,(t) * = -30x, +10f20) and the output equations Y; = x; – x2 + f (0) Y2 = x2 Yz = -x +...
- US+ U S The Values for L and C Inputs V, and I outputs to and i Giveni R, =12, R₂=202, R3=352, L=H, C = 15 Find: a) state-space representation b) Stability c) controllability d) observability رم
i) Obtain the state model for the reduced-form model 2x + 68 + 12x = 10y(t). Use x, and xz as the state variables. Put the equations in standard form and find [A] and [B] matrices. Given the state-variable model = x; – 5x, + f(t) , where fi(t) and f (t) are the inputs, *, = -30x, +10/20 and the output equations y = x; – x2 + f,0 y2 = x2 Y; = -x + f20 obtain the...
8. Consider the system where the performance of the system is given by V -d a. Find the state function of Pontryagin H. b. Using the state function determine the optimal input c. Determine the equations governing λ and x. d. Determine u°()given x(0)-0 and x(1) I 8. Consider the system where the performance of the system is given by V -d a. Find the state function of Pontryagin H. b. Using the state function determine the optimal input c....
8. Write down the state space equation for the system shown below US) + 2 y(s) $+3 2 s(s+1) 9. Derive the state space equation for the system shown where the coefficients of the system matrix are in diagonal form and the elements of the control matrix are unity. U(S) 1 X2 $+2 X 3+1 X = y $+3 $+4 S
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...