《自动化仪表与过程控制》课程学习资料：Into the Next Millennium with Bode：From Linear to Nonlinear

大 Into the next millennium with bode From Linear to nonlinear 1999 Hendrik bode lecture Graham c. goodwin Department of Electrical and Computer Engineering The University of newcastle australia ★ 平x

Into the Next Millennium with Bode: From Linear to Nonlinear 1999 Hendrik Bode Lecture Graham C. Goodwin Department of Electrical and Computer Engineering, The University of Newcastle Australia

大 Purpose of This Talk We show that performance limitations in control are not only inherently interesting, but also have a major impact on real world problems ★ G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 Purpose of This Talk We show that performance limitations in control are not only inherently interesting, but also have a major impact on real world problems

大 In particular, by examining real world problems 1. We will see a progression from Linear to( nonlinear 2. We will also see strong evidence of the impact of performance limitations ★ G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 In particular, by examining real world problems: 1. We will see a progression: From 2. We will also see strong evidence of the impact of performance limitations. Linear to Nonlinear

大 Performance limitations Understanding what is not possible is as important as understanding what is possible! Recall examples from other areas: Shannon Channel Capacity, Cramer Rao Lower Bound, Second Law of Thermodynamics. etc .o Performance limitations in Control? ★ G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 Performance Limitations Understanding what is not possible is as important as understanding what is possible ! Recall examples from other areas: Shannon Channel Capacity, Cramer Rao Lower Bound, Second Law of Thermodynamics, etc. v Performance Limitations in Control ?

大 Brief review of fundamental limits for feedback Systems Core idea:( Sensitivity 7=GC(GC+)1 S=C+11 ★ G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 Brief Review of Fundamental Limits for Feedback Systems + - C G   1 1  S  GC    1 1  T  GC GC  Core idea: Sensitivity

大 Linear case Ⅴ ery well developed Bode. Horowitz, Kwakernaak Middleton Freudenberg, Chen, Francis, Zames, 今S+T=I ∫logS(o)o=z2n ∫gr(o)o=∑ 14i 令 RHP Zero→lS≥1 ★ 令 RHP Pole→>|l≥1 G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999      2 1 log ( ) 1      q n i i q v T j d Very well developed - Bode, Horowitz, Kwakernaak, Middleton, Freudenberg, Chen, Francis, Zames, … . v S + T = I     cn i i S j d p 1 v log ( )   v RHP Zero  S  1 v RHP Pole  T  1 Linear Case

大 Nonlinear case First Results(zames(1966), Shamma(1991), Seron(1995)) One approach uses Nonlinear operators on a Banach space G Nonlinear sensitivity operator S=hvd I Caution: Superposition Nonlinear complementary sensitivity operator does not apply ★ vrI d=o G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 v First Results (Zames (1966), Shamma (1991), Seron (1995)). One approach uses: Nonlinear operators on a Banach Space + - C G r + d Nonlinear sensitivity operator S = Hyd r=0 Nonlinear complementary sensitivity operator T = Hyrd=0 Caution: Superposition does not apply ! Nonlinear Case y

Results By considering the operators s and T as nonlinear operators on a Banach space, then (1)S+T=1 (i GC non-minimum phase (range of operator is strict subset of space) LIpschitz gain) (ii) GC unstable( domain of operator is strict subset of space)=T21 (iv) Nonlinear Water Bed Effect Nonminimum phase, then arbitrary small value for frequency weighted sensitivity results in arbitrarily large response to some admissible disturbance ★ G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 Results By considering the operators S and T as nonlinear operators on a Banach space, then (i) S + T = I (ii) GC non-minimum phase (range of operator is strict subset of space) (Lipschitz gain) (iii) GC unstable (domain of operator is strict subset of space) (iv) Nonlinear Water Bed Effect  1 L S  1 L T Nonminimum phase; then arbitrary small value for frequency weighted sensitivity results in arbitrarily large response to some admissible disturbance

大 Design examples 1. pH Control in Liquid Flows 2. Continuous Metal Casting 3. Shape control 4. Thickness Control in Strip rolling mills Food Manufacturing ★ G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 Design Examples 1. pH Control in Liquid Flows 3. Shape Control 4. Thickness Control in Strip Rolling Mills 5. Food Manufacturing 2. Continuous Metal Casting

大 1. pH Control Arguably the simplest non-trivial control problem Often encountered in industry(increasing emphasis due to environmental concerns) Here -simplified to make some points about nonlinear control ★ G C. Goodwin-Bode Lecture 1999

G.C. Goodwin - Bode Lecture 1999 1. pH Control Arguably the simplest non-trivial control problem. Often encountered in industry (increasing emphasis due to environmental concerns). Here - simplified to make some points about Nonlinear control