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Unformatted text preview: Integral control Integral control Recall the idea behind integral control. If we consider the integral of the error at time, t , integraldisplay t ( r ( τ ) − y ( τ )) dτ, we want to make this quantity go zero. In other words, lim t −→∞ integraldisplay t ( r ( τ ) − y ( τ )) dτ = 0 . This means that as t −→ ∞ , the error must go to zero, y ( t ) −→ r ( t ) . If this wasn’t the case (i.e. in steady state y negationslash = r ), then the integral would end up going to ∞ . Approach Make the integral of the error ( r ( k ) − y ( k )) go to zero for state feedback. Roy Smith: ECE 147b 15 : 2 Integral control Steady state tracking Recall that integral control gives zero steady state error to a step even in the presence of plant modelling mismatch. This does not happen in our state feedback reference tracking scheme. u ( k ) = K ( x ref − x ( k )) , so if x ( k ) −→ x ref then u ( k ) −→ 0. However with u ( k ) −→ 0, and no plant poles at z = 1, we have, y ( k ) −→ 0. Clearly then, y ( k ) negationslash = r ( k ), the reference. Feedforward compensation Recall that the matrix N u can provide some steady-state feedforward compensation: u ( k ) = K ( x ref...
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- Spring '07
- Integral Control, Roy Smith, Reference error format, Integral control Integral