Internal Model Principle 1. Internal Model Principle 1. v G c ( z - PowerPoint PPT Presentation

Internal Model Principle 1.

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A −

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A − • α ( z ) = least common multiple of the unstable poles of R c ( z ) and of V ( z ) ,

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A − • α ( z ) = least common multiple of the unstable poles of R c ( z ) and of V ( z ) , all polynomials in z − 1

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A − • α ( z ) = least common multiple of the unstable poles of R c ( z ) and of V ( z ) , all polynomials in z − 1 • Let there be no common factors between α ( z ) and B ( z )

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A − • α ( z ) = least common multiple of the unstable poles of R c ( z ) and of V ( z ) , all polynomials in z − 1 • Let there be no common factors between α ( z ) and B ( z ) • Can find a controller G c ( z ) for servo/tracking (following R c )

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A − • α ( z ) = least common multiple of the unstable poles of R c ( z ) and of V ( z ) , all polynomials in z − 1 • Let there be no common factors between α ( z ) and B ( z ) • Can find a controller G c ( z ) for servo/tracking (following R c ) and regulation (rejection of disturbance V )

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A − • α ( z ) = least common multiple of the unstable poles of R c ( z ) and of V ( z ) , all polynomials in z − 1 • Let there be no common factors between α ( z ) and B ( z ) • Can find a controller G c ( z ) for servo/tracking (following R c ) and regulation (rejection of disturbance V ) if R c con- tains α ,

Internal Model Principle 1. v G c ( z ) = S c G ( z ) = B r e u y R c A − • α ( z ) = least common multiple of the unstable poles of R c ( z ) and of V ( z ) , all polynomials in z − 1 • Let there be no common factors between α ( z ) and B ( z ) • Can find a controller G c ( z ) for servo/tracking (following R c ) and regulation (rejection of disturbance V ) if R c con- tains α , say, R c = αR 1 :