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observers - Observer Design and Output Feedback 1 2 3 4 5 6...

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Observer Design and Output Feedback 1. Review of state feedback control 2. State estimation 3. Illustrative example 4. Chemical reactor example 5. Separation principle 6. Simulink example
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State Feedback Control Linear state-space model State feedback control law » K is the controller gain matrix » Requires measurement of all state variables mxn mn m n R k k k k = - = 1 1 11 K Kx u m m n n R u u u R x x x dt d = = = + = 2 1 2 1 0 ) 0 ( u x x x Bu Ax x
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State Estimation Motivation » State variables are often unmeasured » Implement control law with estimated state variables State estimator » State-space model and available measurements used to estimate unmeasured state variables » Often called a state observer State Feedback Controller Observer Process u (t) x (t) y (t) ) ( ˆ t x Estimated state variables Unmeasured state variables Measured output variables
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Luenberger Observer State-space model » Linear observation equation Observer form » L is the observer gain matrix to be determined nxp np n p R l l l l dt d = - + + =       1 1 11 correction Output model loop - Open ) ˆ ( ˆ ˆ L x C y L Bu x A x pxn pn p n
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