Application of Dimensional Analysis in Systems Modeling and Control Design

Application of
Dimensional
Analysis in Systems
Modeling and
Control Design......Page 4
Contents......Page 6
Preface......Page 10
1.1 What is dimensional analysis?......Page 12
1.2 What is dimensional similarity?......Page 13
1.3.1 Structure of physical relations......Page 14
1.3.3 Dimensional similarity......Page 16
1.4 Application of dimensional analysis to control problems......Page 17
1.4.3 Control engineering......Page 19
1.5 Book contents......Page 20
2.1.3 Dimensions: fundamental and derived......Page 22
2.1.4 Arithmetic of dimensions......Page 23
2.2.1 System of units......Page 24
2.3 Buckingham pi theorem......Page 25
2.4.1 The dimensional matrix......Page 27
2.4.2 The dimensional set......Page 28
2.5 Dimensional similarity......Page 29
2.5.1 Scale factors......Page 31
2.6 Exercises......Page 32
References......Page 33
3.2 Transfer function dimensionless representation......Page 34
3.2.2 Transfer function parameters with independent dimensions......Page 35
3.2.3 Transfer function dimensionless numbers......Page 36
3.2.4 Dimensionless transfer function......Page 37
3.3 State space dimensionless representation......Page 38
3.3.1 Interpretation of the state space dimensionless transformation......Page 41
3.4 Comparison between transfer function and state space
dimensionless representation......Page 43
3.5.1 Discrete time transfer function dimensionless representation......Page 46
3.5.2 Discrete time state space model dimensionless representation......Page 47
References......Page 49
4.2.1 Transfer function dimensional similarity......Page 52
4.2.2 State space dimensional similarity......Page 55
4.3.2 Sampled-data transfer function similarity......Page 57
4.3.3 Discrete state space similarity......Page 58
4.4 Exercises......Page 59
References......Page 60
5.2 General procedure......Page 62
5.3.1 Problem statement......Page 63
5.3.2 Dimensionless representation of second order inverse
response model......Page 64
5.3.3 Identification procedure......Page 65
5.3.4 Application examples......Page 72
5.4.1 Problem statement......Page 75
5.4.2 Dimensionless representation of the reduced effective transfer
function......Page 78
5.4.3 Inverse response analysis......Page 79
5.4.4 Reduced order model: general case......Page 83
5.4.5 Reduced order model: particular cases......Page 84
5.4.6 Application examples......Page 86
References......Page 88
6.1 Introduction......Page 90
6.2.2 Homogeneous tuning rules characterization......Page 91
6.3.1 Loop transfer function......Page 94
6.3.2 Dimensionless closed loop transfer functions......Page 96
6.4 Optimality of homogeneous tuning rules......Page 98
6.4.1 Weighting factors......Page 99
6.5 Homogeneous and nonhomogeneous tuning rules......Page 100
References......Page 105
7.1 Introduction......Page 108
7.2 Elements of the comparative framework......Page 109
7.3 Dimensionless comparative framework......Page 110
7.4.3 Dimensionless integral errors......Page 111
7.5 Application example......Page 113
7.5.2 Dimensionless sensitivity bandwidth comparison......Page 114
7.5.4 Dimensionless integral absolute error......Page 115
7.6 PID tuning rules selection......Page 117
References......Page 119
8.1 Introduction......Page 120
8.2 Control of dimensionally similar systems......Page 121
8.3.2 Discrete time control......Page 122
8.4 Partial similarity......Page 124
8.5 Experimental case study......Page 126
References......Page 130
9.1 Introduction......Page 132
9.2.1 Control effort......Page 133
9.2.2 Similar model reference adaptive control......Page 134
9.3 SMRAC for first order plants......Page 137
9.4.1 SMRAC control scheme......Page 140
9.4.2 SMRAC stability analysis......Page 142
9.4.3 SMRAC operation modes......Page 144
9.5 Application example......Page 145
References......Page 148
Index......Page 150