Question

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% and a 3. a) Use the augmented state vetor Xand find the state space equations. b) Next, make a change of coordinates, so that the new state vector is z- where e- X-X c) Find the closed loop transfer function Ga ()-where R(s) is the reference Y(s) R(s) signal, and determine the eigenvalues of the closed-loop system. 4. Build the Simulink model of the closed loop system a) b) Use the state-space block to simulate the observer. Simulate the step response of the closed loop system and check the design specifications. The initial conditions of the system are: xi (0)--0.2 , xa(0) = 0, x, (0) 0.2 Plot on the same graphs the actual state variables and the estimated variables as well as the estimation errors. c)

Answer 1

Given sygtem is -2-2 St 2 2 o St ST-グ ad CSI- A) 2 2.

6dj CJJ-A) - St S 2 Set o StI) S t SHリ C- じ) S+ I -2CH 1 ) SA cs+1) S-t (S4リれ. St 2 S+ ST-A) 3x 3x.3

sft 3x/ 邛3