43 - optexmp43 filled

# 43 - optexmp43 filled - ME 575 Handouts LQE Symmetric Root...

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ME 575 Handouts 1 ME575 Session 43: Optimal Control Example School of Mechanical Engineering Purdue University Slide 1 LQE Symmetric Root Locus LQE Symmetric Root Locus LQR Algebraic Riccati Riccati Equation: LQE Algebraic LQE Algebraic Riccati Riccati Equation: Equation: By analogy: TT T 1 A PP ACq CP B rBP0 ++ = T 1 ee e e A A G W GP C V C P 0 = T e A A, P P, C G, B C ⇔⇔⇔⇔ ME575 Session 43: Optimal Control Example School of Mechanical Engineering Purdue University Slide 2 LQE Symmetric Root Locus LQE Symmetric Root Locus By analogy: By analogy: where EE E E W D(s )D( s )1 G( s )G(s ) 0 V ⎡⎤ +− = ⎢⎥ ( ) ( ) () T E 1 1 T E D (s) det s A det s A G(s ) G s A C Cs A G =− = II

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ME 575 Handouts 2 ME575 Session 43: Optimal Control Example School of Mechanical Engineering Purdue University Slide 3 [] 01 0 0 xx u w 1 1 y1 0 x v ⎤⎡ =+ + ⎥⎢ ⎦⎣ ± T 1 ee KP C V = e ˆˆ ˆ xA x B u Ky C x + ± T ˆ PI min e e , where e x x ⎡⎤ == ⎣⎦ LQE Design Example ME575 Session 43: Optimal Control Example School of Mechanical Engineering Purdue University Slide 4 LQE Design Example LQE Design Example ( ) 1 E G(s ) Cs A G =− I
ME 575 Handouts 3 ME575 Session 43: Optimal Control Example School of Mechanical Engineering Purdue University Slide 5 LQE Symmetric Root Locus LQE Symmetric Root Locus -2 -1 0 1 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Real Axis Imag Axis Symmetric Root Locus ME575 Session 43: Optimal Control Example School of Mechanical Engineering Purdue University Slide 6 Plant is given by Plant is given by

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43 - optexmp43 filled - ME 575 Handouts LQE Symmetric Root...

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