Loop Transfer Recovery: Analysis and Design

1 Introduction.- 1.1 Introduction.- 1.2 Problem formulation.- 1.3 Preliminaries.- 2 Preliminary Analysis of Continuous LTR.- 2.1 Introduction.- 2.2 Preliminary analysis.- 2.2.1 Luenberger observer based controller.- 2.2.2 Full order observer based controller.- 2.2.3 Reduced order observer based controller.- 2.2.4 Relationship between the recovery matrices Mf(s) and Mr(s).- 2.A Proof of Lemma 2.2.1.- 2.B Proof of Proposition 2.2.2.- 3 Continuous LTR - Detailed Analysis.- 3.1 Introduction.- 3.2 Recovery analysis while not using the knowledge of F.- 3.3 Analysis for recoverable target loop transfer functions.- 3.4 Recovery analysis in a given subspace.- 3.5 Duality of LTRI and LTRO.- 3.A Proof of Lemma 3.2.1.- 3.B Proof of Lemma 3.2.2.- 3.C Proof of Proposition 3.2.2.- 3.D Proof of Lemma 3.2.3.- 3.E Proof of Corollary 3.3.2.- 3.F Proof of Lemma 3.4.2.- 3.G Proof of Lemma 3.4.3.- 4 Continuous LTR - Design.- 4.1 Introduction.- 4.2 Design constraints and the available freedom.- 4.3 ATEA design method.- 4.3.1 General ATEA design.- 4.3.2 Design for exactly recoverable target loop transfer functions.- 4.4 Optimization based design methods.- 4.4.1 H2-optimization based design algorithms.- 4.4.2 H?-optimization based design algorithms.- 4.5 Design for recovery over a specified subspace.- 4.6 LTR design for output break point.- 4.7 Comparison of ATEA and optimization based design algorithms.- 4.A Proof of Theorem 4.3.1.- 4.B Proof of Theorem 4.3.2.- 4.C Proof of Theorem 4.4.2.- 5 Introduction to Discrete LTR.- 5.1 Introduction.- 5.2 Problem formulation.- 5.3 Preliminaries.- 6 Preliminary Analysis of Discrete LTR.- 6.1 Introduction.- 6.2 Controller structures for discrete LTR.- 6.2.1 Luenberger estimator based controller.- 6.2.2 Prediction estimator based controller.- 6.2.3 Current estimator based controller.- 6.2.4 Reduced order estimator based controller.- 6.3 Preliminary analysis.- 6.A Proof of Proposition 6.3.1.- 7 Discrete LTR - Detailed Analysis.- 7.1 Introduction.- 7.2 Recovery analysis while not using the knowledge of F.- 7.3 Analysis for recoverable target loop transfer functions.- 7.4 Recovery analysis in a given subspace.- 7.5 Duality of LTRI and LTRO.- 7.A Proof of Lemma 7.2.2.- 7.B Proof of Corollary 7.3.1.- 7.C Proof of Theorem 7.4.4.- 8 Discrete LTR - Design.- 8.1 Introduction.- 8.2 Design constraints and the available freedom.- 8.3 Design by eigenstructure assignment.- 8.4 Optimization based design methods.- 8.4.1 H?-optimization based algorithm.- 8.4.2 H2-optimization based algorithm.- 8.5 Design for recovery over a specified subspace.- 8.6 LTR design for output break point.- 8.A Proof of Theorem 8.4.1.- 9 Closed-Loop Transfer Recovery.- 9.1 Introduction.- 9.2 Continuous CLTR.- 9.2.1 Problem formulation.- 9.2.2 General analysis.- 9.2.3 Design methods and examples.- 9.3 Discrete CLTR.- 9.3.1 Problem formulation.- 9.3.2 General analysis.- 9.3.3 Design methods and examples.- 9.A Proof of Lemma 9.2.1.- 10 Some Issues of Controller Architecture.- 10.1 Introduction.- 10.2 Recoverability with an arbitrarily structured controller.- 10.3 CSS architecture based controllers for LTR.- 10.3.1 Full order CSS architecture based controller.- 10.3.2 Reduced order CSS architecture based controller.- 10.3.3 Properties of the CSS architecture based controllers.- 10.4 Design examples.- 10.5 Open research problems.- 10.A Proof of Theorem 10 2 1.- 10.B Proof of Lemma 10.3.1.- 10.C Proof of Theorem 10 3 1.