Homework Answers
![from part 6 feedback gains [ 6.6006 -10.1830 controller-ur-feedback gains ** * = AX + Ble * =(A-BK) * * :]-[:][c.com o = -5.6](http://img.homeworklib.com/questions/20d4e9e0-6e2d-11eb-aee3-714d8244b732.png?x-oss-process=image/resize,w_560)
![s-plane, so poles are lying on left side of Systems is stable part ② = maTLAB Ka [ 6.6006 -10.1831] alue = - 3.1421, -1.4584](http://img.homeworklib.com/questions/21818d60-6e2d-11eb-b732-8580a3ac2d95.png?x-oss-process=image/resize,w_560)
part b::
>> A=[1 0;-1 1];
>> B=[1; 0];
>> Q=1; R=0.1;
>> [feedback_gains,S,eigen_values] = lqr(a,b,Q*eye(2),R)
feedback_gains =
6.6006 -10.1831
S =
0.6601 -1.0183
-1.0183 4.6848
eigen_values =
-3.1421
-1.4584
>>
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t)...
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3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t) [0.1 0 0.1x2(t) X3(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) Kx(t) + Gr(t) (a) Find the desired regon of the S-plane for two...
Consider the LTI system. Design a state-feedback control law of
the form u(t)= -kx(t) such that x(t) goes to zero faster than
e^-t;
Problem 1: (15 points) Consider the LTI system 3 -1 (t)1 3 0 (t)2ut 0 0-1 Desig lim sate-feedback control law of the form u(t)ka(t) such that (t goes to zero faster than e i.e. Hint: fhink of where you want to place the eigenvalues of the closed-loop system.
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is...
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%...
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Problem 2. Eigenvalue and Eigenvector Consider the mass-spring system in Fig. P13.5. The frequencies for the mass vibrations can be determined by solving for the eigenvalues and by applying Mi + kx = 0, which yields m 0 07/31 (2k -k -k X1 (0 0 m2 0 {2}+{-k 2k -kX{X2} = {0} LO 0 m3] 1 iz) 1-k -k 2kJ (x3) lo Applying the guess x = xoeiat as a solution, we get the fol- lowing matrix: 52k - m102...
Problem 1 An inverted pendulum driven by a d-c motor is governed by the following differential and algcbraic equa tions: (a) Determine the transfer function of the process. (b) It is proposed to control the process using "proportional control": where yr is a constant reference value. Determine the value Kmir for which the gain K must exceed in order that the closed-loop system be stable. (c) Determine the value of K for which the magnitude of the error is less...
4. Consider the position control of a rigid body, Figure, where u(t) is the control force. An analog PID control law is described as de u)kpe)k kije0)dt; e({)= x4C)x) dt 0 kp. ky only a position sensor is available. are controller gains. Also, xq (t) is the desired position of the mass. It is assumed that kJ where and Derive a difference equation for the implementation of this PID control law on a digital computer. Use backward difference and trapezoidal...
Problem 4 A full-state feedback control law is to be designed which . Forces the state r to zero from a nonzero starting state, and . Makes toe poles of the the closed loop system lie at Problem 5 The Full state feedback control law of Problem 4 is to be moditied to where ru is a desired (nonzero) value of the output. Determine Gu
Problem 3. Consider the system -2 01 Design feedback control u =-Kx such that the closed-loop poles are at s=-2+)2 and s=-2-j2. Assume K= [k1
Problem 3. Consider the system -2 01 Design feedback control u =-Kx such that the closed-loop poles are at s=-2+)2 and s=-2-j2. Assume K= [k1
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