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

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

Apr 21, 2023 553 likes •656 views

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 ( z ) = least common multiple of the

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SLIDE 1

1.

Internal Model Principle

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SLIDE 2

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

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SLIDE 3

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

  • α(z) = least common multiple of the unstable poles of

Rc(z) and of V (z),

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SLIDE 4

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

  • α(z) = least common multiple of the unstable poles of

Rc(z) and of V (z), all polynomials in z−1

slide-5
SLIDE 5

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

  • α(z) = least common multiple of the unstable poles of

Rc(z) and of V (z), all polynomials in z−1

  • Let there be no common factors between α(z) and B(z)
slide-6
SLIDE 6

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

  • α(z) = least common multiple of the unstable poles of

Rc(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 Gc(z) for servo/tracking (following

Rc)

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SLIDE 7

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

  • α(z) = least common multiple of the unstable poles of

Rc(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 Gc(z) for servo/tracking (following

Rc) and regulation (rejection of disturbance V )

slide-8
SLIDE 8

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

  • α(z) = least common multiple of the unstable poles of

Rc(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 Gc(z) for servo/tracking (following

Rc) and regulation (rejection of disturbance V ) if Rc con- tains α,

slide-9
SLIDE 9

1.

Internal Model Principle

r − G(z) = B A Gc(z) = Sc Rc u e y v

  • α(z) = least common multiple of the unstable poles of

Rc(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 Gc(z) for servo/tracking (following

Rc) and regulation (rejection of disturbance V ) if Rc con- tains α, say, Rc = αR1: