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HWCE_6 - s< 1 sec e Find 2 1 l l L for a full-order...

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HW/CE# 6 Due Thursday, Nov 19, 2009 Work the following problems from Franklin’s text: 7.2c 7.3c 7.14 Hint: What does the left side of the matrix equation become in the steady state? 1. The F matrix for a certain system has eigenvalues –2, -1, and –6. What is matrix A m if we convert the system to modal canonical form? (several correct answers possible) 2. The state space description of a certain system is as follows:   0 0 1 5 . 33 0 315 . 2 5 . 33 1 0 J H G F a) Find ) ( ) ( ) ( s U s Y s G b) What are ζ and ω n ? c) Find Mp, t s , and t r for a step input to the system above. d) Find K = [K 1 K 2 ] using full-state feedback so that we have: M p < 5% and t
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Unformatted text preview: s < 1 sec e) Find 2 1 l l L for a full-order estimator such that the estimator error poles are at –15 + j15. f) Verify your hand calculations above for both K and L on MATLAB by using MATLAB’s Ackermann’s formula, i.e., the “acker” function. g) Find N such that steady state error for a step input is zero. See figure 7.15b on page 482, or with the estimator, figure 7.49b on page 527. The selection of N can be done independently of the estimator design if we do it this way. So, equations 7.100, and 7.101a,b apply. (These equations are also given in the reference sheet set.)...
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