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 eq...
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...
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin to find the input u that minimizes dt a. Determine the state function of Pontryagin H. b. Find the optimal input and H c. Find the matrix A that will yield the governing equations x1 ai If xi (0) : 0.x2(0) = O and xi (1) = İ. x 2(1) =0 determine the govem equations for λǐ(0) and λ2(0) in terms of the elements...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
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,...
Part D Part D marhal A Lif ysi (a) Determine the system function H(z). (b) Find the impulse response of this system. (c) Determine the response of this system to the input x[n] 4(0.1)hu[n]. Hint: use the system function. (d) Determine the steady state response to the input xIn] 3 cos(0.1 Ttn). Hint: use the requency response.
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0.9)-10:491 -ones (1,50) s- conv(u,h) 2. Plot h and u using stem function for 50 samples only stem(10:491, s(1:50) 1. Given a system described by the following difference equation: yIn] 1143yn 1 0.4128y[n -2 0.0675x[n0.1349xn 0.675x[n-2] Determine the output y in response to zero input and the initial conditionsy-11 and yl-2] 2 for 50 samples using the following commands: a -,-1.143,...
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%...
at a zero.) 4.11 Consider the network in figure 4.14 to be a 2-input, 2-output filter with input vector x(n) and output vector s(n) a. Write state equations for the network. b. Find the state matrices A, B, C, D (all 2 x 2) c. Find the matrix system function (z) relating the vector z transforms X(z) and S(z), which is given by the general- ization of (4.4.13), i.e., H(z) D + C(zI - A) B. +oking s(n) (n) Z...
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...
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input