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lecture14_small

# lecture14_small - Reference tracking Reference Tracking The...

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Reference inputs Reference inputs The reference state, x r , is determined by, x r ( k ) = N x r ( k ). For type 0 systems (no poles at z = 1), this will give a steady state error. In such systems u negationslash = 0 at a non-zero equilibrium, and so x negationslash = x r . Feedforward correction: u ss ( k ) provides a steady-state input. C z 1 A B K N x N u P ( z ) a27 a27 a14a13 a15a12 + a27 a27 a27 a27 a14a13 a15a12 + a27 a27 a27 a118 a118 a45 a54 a54 r ( k ) x r ( k ) x ( k ) x ( k ) y ( k ) a118 a27 a63 a14a13 a15a12 + u ss ( k ) The control input is: u ( k ) = K ( x r ( k ) x ( k )) + u ss ( k ). Roy Smith: ECE 147b 14 : 2 Reference tracking Reference Tracking The idea is to set the problem up as driving the state to a desired reference value. Approach: (assume state feedback for the moment) C z 1 A B K N x P ( z ) a27 a27 a14a13 a15a12 + a27 a27 a27 a14a13 a15a12 + a27 a27 a27 a118 a118 a45 a54 a54 r ( k ) x r ( k ) x ( k ) x ( k ) y ( k ) u ( k ) Design the state feedback gain, K , for good closed-loop pole positions. Implement it as: u ( k ) = K ( x r ( k ) x ( k )).

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