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E-grāmata: First Course in Predictive Control

(University of Sheffield, UK)
  • Formāts: 426 pages
  • Izdošanas datums: 17-Apr-2018
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781351597166
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First Course in Predictive ControlPalielināt
  • Formāts: 426 pages
  • Izdošanas datums: 17-Apr-2018
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781351597166
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The book presents a significant expansion in depth and breadth of the previous edition. It includes substantially more numerical illustrations and copious supporting MATLAB code that the reader can use to replicate illustrations or build his or her own. The code is deliberately written to be as simple as possible and easy to edit. The book is an excellent starting point for any researcher to gain a solid grounding in MPC concepts and algorithms before moving into application or more advanced research topics. Sample problems for readers are embedded throughout the chapters, and in-text questions are designed for readers to demonstrate an understanding of concepts through numerical simulation.

Recenzijas

"The book seems to be one of the first in presenting teaching level concepts of predictive control. Indeed, it is a view from industrial point of view since it discusses the PFC which was one of the first ideas of predictive control in the 70s. Since then, of course, things evolved drastically with the computational power, allowing a fiddlers paradise of predictive control algorithms and designs, and some of the most popular are mentioned in the book (GPC, DMC). I find it commendable of the author, a well-established scholar in our community, to pursue such a project, and I am very happy to promote it. I myself am teaching predictive control and I already have found that the content of this book (as it is at this moment in time) is very useful and approachable for engineering students.

The comparison with PID controller is of course necessary and justified, since 95% of the loops in industry are indeed performed by PID controllers. The remaining ones need optimization and thus predictive control has gained a broad access in manufacturing and process industry. I believe the section "why is predictive control logical" will stir and stimulate a lot of brainstorming sessions in both academia and research community, which is very nice indeed. The examples and overall structure of the book is excellently constructed to allow step-by-step systematic teaching structure and thus enhancing the potential impact on the students learning curve. The supplementing with Matlab code is very useful indeed. The pedagogical skills exercised by the author are indeed expected since he is an active member in control education community. Overall, this book bears a significant added value to the academic and why not, the research community." Clara Mihaela Ionescu, Ghent University, Belgium "The book seems to be one of the first in presenting teaching level concepts of predictive control. Indeed, it is a view from industrial point of view since it discusses the PFC which was one of the first ideas of predictive control in the 70s. Since then, of course, things evolved drastically with the computational power, allowing a fiddlers paradise of predictive control algorithms and designs, and some of the most popular are mentioned in the book (GPC, DMC). I find it commendable of the author, a well-established scholar in our community, to pursue such a project, and I am very happy to promote it. I myself am teaching predictive control and I already have found that the content of this book (as it is at this moment in time) is very useful and approachable for engineering students.

The comparison with PID controller is of course necessary and justified, since 95% of the loops in industry are indeed performed by PID controllers. The remaining ones need optimization and thus predictive control has gained a broad access in manufacturing and process industry. I believe the section "why is predictive control logical" will stir and stimulate a lot of brainstorming sessions in both academia and research community, which is very nice indeed. The examples and overall structure of the book is excellently constructed to allow step-by-step systematic teaching structure and thus enhancing the potential impact on the students learning curve. The supplementing with Matlab code is very useful indeed. The pedagogical skills exercised by the author are indeed expected since he is an active member in control education community. Overall, this book bears a significant added value to the academic and why not, the research community." Clara Mihaela Ionescu, Ghent University, Belgium

Overview and guidance for use xix
Book organisation xxi
Acknowledgements xxiii
1 Introduction and the industrial need for predictive control 1(34)
1.1 Guidance for the lecturer/reader
2(1)
1.2 Motivation and introduction
2(1)
1.3 Classical control assumptions
3(2)
1.3.1 PID compensation
3(1)
1.3.2 Lead and Lag compensation
4(1)
1.3.3 Using PID and lead/lag for SISO control
4(1)
1.3.4 Classical control analysis
4(1)
1.4 Examples of systems hard to control effectively with classical methods
5(12)
1.4.1 Controlling systems with non-minimum phase zeros
5(2)
1.4.2 Controlling systems with significant delays
7(1)
1.4.3 Illustration: Impact of delay on margins and closed-loop behaviour
8(2)
1.4.4 Controlling systems with constraints
10(2)
1.4.5 Controlling multivariable systems
12(4)
1.4.6 Controlling open-loop unstable systems
16(1)
1.5 The potential value of prediction
17(2)
1.5.1 Why is predictive control logical?
18(1)
1.5.2 Potential advantages of prediction
19(1)
1.6 The main components of MPC
19(12)
1.6.1 Prediction and prediction horizon
20(1)
1.6.2 Why is prediction important?
20(2)
1.6.3 Receding horizon
22(1)
1.6.4 Predictions are based on a model
23(2)
1.6.5 Performance indices
25(2)
1.6.6 Degrees of freedom in the predictions or prediction class
27(1)
1.6.7 Tuning
28(1)
1.6.8 Constraint handling
28(2)
1.6.9 Multivariable and interactive systems
30(1)
1.6.10 Systematic use of future demands
31(1)
1.7 MPC philosophy in summary
31(2)
1.8 MATLAB files from this chapter
33(1)
1.9 Reminder of book organisation
33(2)
2 Prediction in model predictive control 35(48)
2.1 Introduction
36(1)
2.2 Guidance for the lecturer/reader
36(1)
2.2.1 Typical learning outcomes for an examination assessment
37(1)
2.2.2 Typical learning outcomes for an assignment/coursework
37(1)
2.3 General format of prediction modelling
37(2)
2.3.1 Notation for vectors of past and future values
38(1)
2.3.2 Format of general prediction equation
38(1)
2.3.3 Double subscript notation for predictions
38(1)
2.4 Prediction with state space models
39(10)
2.4.1 Prediction by iterating the system model
39(1)
2.4.2 Predictions in matrix notation
40(3)
2.4.3 Unbiased prediction with state space models
43(2)
2.4.4 The importance of unbiased prediction and deviation variables
45(1)
2.4.5 State space predictions with deviation variables
46(2)
2.4.6 Predictions with state space models and input increments
48(1)
2.5 Prediction with transfer function models - matrix methods
49(11)
2.5.1 Ensuring unbiased prediction with transfer function models
50(2)
2.5.2 Prediction for a CARIMA model with T(z) = 1: the SISO case
52(3)
2.5.3 Prediction with a CARIMA model and T not = to 1: the MIMO case
55(2)
2.5.4 Prediction equations with T(z) 1: the SISO case
57(6)
2.5.4.1 Summary of the key steps in computing prediction equations with a T-filter
57(1)
2.5.4.2 Forming the prediction equations with a T-filter beginning from predictions (2.59)
58(2)
2.6 Using recursion to find prediction matrices for CARIMA models
60(3)
2.7 Prediction with independent models
63(5)
2.7.1 Structure of an independent model and predictions
64(1)
2.7.2 Removing prediction bias with an independent model
65(1)
2.7.3 Independent model prediction via partial fractions for SISO systems
66(2)
2.7.3.1 Prediction for SISO systems with one pole
66(1)
2.7.3.2 PFC for higher-order models having real roots
67(1)
2.8 Prediction with FIR models
68(5)
2.8.1 Impulse response models and predictions
69(2)
2.8.2 Prediction with step response models
71(2)
2.9 Closed-loop prediction
73(8)
2.9.1 The need for numerically robust prediction with open-loop unstable plant
73(1)
2.9.2 Pseudo-closed-loop prediction
74(2)
2.9.3 Illustration of prediction structures with the OLP and CLP
76(1)
2.9.4 Basic CLP predictions for state space models
77(1)
2.9.5 Unbiased closed-loop prediction with autonomous models
78(1)
2.9.6 CLP predictions with transfer function models
79(2)
2.10
Chapter Summary
81(1)
2.11 Summary of MATLAB code supporting prediction
82(1)
3 Predictive functional control 83(34)
3.1 Introduction
84(1)
3.2 Guidance for the lecturer/reader
85(1)
3.3 Basic concepts in PFC
86(9)
3.3.1 PFC philosophy
86(1)
3.3.2 Desired responses
87(1)
3.3.3 Combining predicted behaviour with desired behaviour: the coincidence point
88(1)
3.3.4 Basic mathematical definition of a simple PFC law
89(1)
3.3.5 Alternative PFC formulation using independent models
89(2)
3.3.6 Integral action within PFC
91(1)
3.3.7 Coping with large dead-times in PFC
91(2)
3.3.8 Coping with constraints in PFC
93(1)
3.3.9 Open-loop unstable systems
94(1)
3.4 PFC with first-order models
95(5)
3.4.1 Analysis of PFC for a first-order system
95(2)
3.4.2 Numerical examples of PFC on first-order systems
97(3)
3.4.2.1 Dependence on choice of desired closed-loop pole λ with ny = 1
97(1)
3.4.2.2 Dependence on choice of coincidence horizon ny with fixed λ
97(1)
3.4.2.3 Effectiveness at handling plants with delays
98(1)
3.4.2.4 Effectiveness at handling plants with uncertainty and delays
98(1)
3.4.2.5 Effectiveness at handling plants with uncertainty, constraints and delays
99(1)
3.5 PFC with higher-order models
100(11)
3.5.1 Is a coincidence horizon of 1 a good choice in general?
101(2)
3.5.1.1 Nominal performance analysis with ny = 1
102(1)
3.5.1.2 Stability analysis with ny = 1
102(1)
3.5.2 The efficacy of λ as a tuning parameter
103(3)
3.5.2.1 Closed-loop poles/behaviour for G1 with various choices of ny
104(1)
3.5.2.2 Closed-loop poles/behaviour for G3 with various choices of ny
104(1)
3.5.2.3 Closed-loop poles/behaviour for G2 with various choices of ny
105(1)
3.5.2.4 Closed-loop poles/behaviour for G4 with various choices of ny
105(1)
3.5.3 Practical tuning guidance
106(13)
3.5.3.1 Closed-loop poles/behaviour for G5 with various choices of ny
106(1)
3.5.3.2 Mean-level approach to tuning
106(1)
3.5.3.3 Intuitive choices of coincidence horizon to ensure good behaviour
107(1)
3.5.3.4 Coincidence horizon of ny = 1 will not work in general
108(1)
3.5.3.5 Small coincidence horizons often imply over-actuation
109(1)
3.5.3.6 Example 1 of intuitive choice of coincidence horizon
109(1)
3.5.3.7 Example 6 of intuitive choice of coincidence horizon
110(1)
3.6 Stability results for PFC
111(1)
3.7 PFC with ramp targets
112(3)
3.8
Chapter summary
115(1)
3.9 MATLAB code available for readers
115(2)
4 Predictive control - the basic algorithm 117(50)
4.1 Introduction
118(1)
4.2 Guidance for the lecturer/reader
119(1)
4.3 Summary of main results
119(1)
4.3.1 GPC control structure
120(1)
4.3.2 Main components of an MPC law
120(1)
4.4 The GPC performance index
120(10)
4.4.1 Concepts of good and bad performance
121(1)
4.4.2 Properties of a convenient performance index
121(1)
4.4.3 Possible components to include in a performance index
122(3)
4.4.4 Concepts of biased and unbiased performance indices
125(2)
4.4.5 The dangers of making the performance index too simple
127(1)
4.4.6 Integral action in predictive control
128(1)
4.4.7 Compact representation of the performance index and choice of weights
129(1)
4.5 GPC algorithm formulation for transfer function models
130(16)
4.5.1 Selecting the degrees of freedom for GPC
130(1)
4.5.2 Performance index for a GPC control law
131(1)
4.5.3 Optimising the GPC performance index
132(1)
4.5.4 Transfer function representation of the control law
133(1)
4.5.5 Numerical examples for GPC with transfer function models and MATLAB code
134(2)
4.5.6 Closed-loop transfer functions
136(1)
4.5.7 GPC based on MFD models with a T-filter (GPCT)
137(4)
4.5.7.1 Why use a T-filter and conceptual thinking?
137(1)
4.5.7.2 Algebraic procedures with a T-filter
138(3)
4.5.8 Sensitivity of GPC
141(4)
4.5.8.1 Complementary sensitivity
142(1)
4.5.8.2 Sensitivity to multiplicative uncertainty
142(1)
4.5.8.3 Disturbance and noise rejection
143(1)
4.5.8.4 Impact of a T-filter on sensitivity
144(1)
4.5.9 Analogies between PFC and GPC
145(1)
4.6 GPC formulation for finite impulse response models and Dynamic Matrix Control
146(2)
4.7 Formulation of GPC with an independent prediction model
148(5)
4.7.1 GPC algorithm with independent transfer function model
148(3)
4.7.2 Closed-loop poles in the IM case with an MFD model
151(2)
4.8 GPC with a state space model
153(8)
4.8.1 Simple state augmentation
153(3)
4.8.1.1 Computing the predictive control law with an augmented state space model
154(2)
4.8.1.2 Closed-loop equations and integral action
156(1)
4.8.2 GPC using state space models with deviation variables
156(5)
4.8.2.1 GPC algorithm based on deviation variables
157(3)
4.8.2.2 Using an observer to estimate steady-state values for the state and input
160(1)
4.8.3 Independent model GPC using a state space model
161(1)
4.9
Chapter summary and general comments on stability and tuning of GPC
161(2)
4.10 Summary of MATLAB code supporting GPC simulation
163(4)
4.10.1 MATLAB code to support GPC with a state space model and a performance index based on deviation variables
163(1)
4.10.2 MATLAB code to support GPC with an MFD or CARIMA model
164(1)
4.10.3 MATLAB code to support GPC using an independent model in MFD format
165(1)
4.10.4 MATLAB code to support GPC with an augmented state space model
165(2)
5 Tuning GPC: good and bad choices of the horizons 167(40)
5.1 Introduction
168(1)
5.2 Guidance for the lecturer/reader
168(1)
5.3 Poor choices lead to poor behaviour
169(2)
5.4 Concepts of well-posed and ill-posed optimisations
171(8)
5.4.1 Examples
172(2)
5.4.2 What is an ill-posed objective/optimisation?
174(5)
5.4.2.1 Parameterisation of degrees of freedom
174(1)
5.4.2.2 Choices of performance index
175(1)
5.4.2.3 Consistency between predictions and eventual behaviour
176(2)
5.4.2.4 Summary of how to avoid ill-posed optimisations
178(1)
5.5 Illustrative simulations to show impact of different parameter choices on GPC behaviour
179(16)
5.5.1 Numerical examples for studies on GPC tuning
179(1)
5.5.2 The impact of low output horizons on GPC performance
179(3)
5.5.3 The impact of high output horizons on GPC performance
182(5)
5.5.3.1 GPC illustrations with ny large and nu = 1
182(3)
5.5.3.2 When would a designer use large ny and nu = 1?
185(2)
5.5.3.3 Remarks on the efficacy of DMC
187(1)
5.5.4 Effect on GPC performance of changing nu and prediction consistency
187(4)
5.5.5 The impact of the input weight λ on the ideal horizons and prediction consistency
191(2)
5.5.6 Summary insights on choices of horizons and weights for GPC
193(2)
5.6 Systematic guidance for "tuning" GPC
195(4)
5.6.1 Proposed offline tuning method
196(1)
5.6.2 Illustrations of efficacy of tuning guidance
196(3)
5.7 MIMO examples
199(2)
5.8 Dealing with open-loop unstable systems
201(4)
5.8.1 Illustration of the effects of increasing the output horizon with open-loop unstable systems
202(1)
5.8.2 Further comments on open-loop unstable systems
203(1)
5.8.3 Recommendations for open-loop unstable processes
204(1)
5.9
Chapter summary: guidelines for tuning GPC
205(1)
5.10 Useful MATLAB code
206(1)
6 Dual-mode MPC (OMPC and SOMPC) and stability guarantees 207(46)
6.1 Introduction
208(1)
6.2 Guidance for the lecturer
209(1)
6.3 Foundation of a well-posed MPC algorithm
209(7)
6.3.1 Definition of the tail and recursive consistency
210(2)
6.3.2 Infinite horizons and the tail imply closed-loop stability
212(1)
6.3.3 Only the output horizon needs to be infinite
213(1)
6.3.4 Stability proofs with constraints
214(1)
6.3.5 Are infinite horizons impractical?
215(1)
6.4 Dual-mode MPC - an overview
216(6)
6.4.1 What is dual-mode control in the context of MPC?
216(1)
6.4.2 The structure/parameterisation of dual-mode predictions
217(1)
6.4.3 Overview of MPC dual-mode algorithms: Suboptimal MPC (SOMPC)
218(1)
6.4.4 Is SOMPC guaranteed stabilising
219(1)
6.4.5 Why is SOMPC suboptimal?
220(1)
6.4.6 Improving optimality of SOMPC, the OMPC algorithm
221(1)
6.5 Algebraic derivations for dual-mode MPC
222(6)
6.5.1 The cost function for linear predictions over infinite horizons
223(1)
6.5.2 Forming the cost function for dual-mode predictions
224(1)
6.5.3 Computing the SOMPC control law
225(1)
6.5.4 Definition of terminal mode control law via optimal control
225(1)
6.5.5 SOMPC reduces to optimal control in the unconstrained case
226(1)
6.5.6 Remarks on stability and performance of SOMPC/OMPC
227(1)
6.6 Closed-loop paradigm implementations of OMPC
228(10)
6.6.1 Overview of the CLP concept
229(2)
6.6.2 The SOMPC/OMPC law with the closed-loop paradigm
231(2)
6.6.3 Properties of OMPC/SOMPC solved using the CLP
233(1)
6.6.3.1 Open-loop unstable systems
233(1)
6.6.3.2 Conditioning and structure of performance index J
233(1)
6.6.4 Using autonomous models in OMPC
234(3)
6.6.4.1 Forming the predicted cost with an autonomous model
235(1)
6.6.4.2 Using autonomous models to support the definition of constraint matrices
236(1)
6.6.4.3 Forming the predicted cost with an expanded autonomous model
236(1)
6.6.5 Advantages and disadvantages of the CLP over the open-loop predictions
237(1)
6.7 Numerical illustrations of OMPC and SOMPC
238(8)
6.7.1 Illustrations of the impact of Q,R on OMPC
238(1)
6.7.2 Structure of cost function matrices for OMPC
239(1)
6.7.3 Structure of cost function matrices for SOMPC
240(1)
6.7.4 Demonstration that the parameters of KSOMPC vary with nc
241(1)
6.7.5 Demonstration that JK is a Lyapunov function with OMPC and SOMPC
241(2)
6.7.6 Demonstration that with SOMPC the optimum decision changes each sample
243(1)
6.7.7 List of available illustrations
244(2)
6.8 Motivation for SOMPC: Different choices for mode 2 of dual-mode control
246(5)
6.8.1 Dead-beat terminal conditions
247(1)
6.8.2 A zero terminal control law
248(1)
6.8.3 Input parameterisations to eliminate unstable modes in the prediction
249(1)
6.8.4 Reflections and comparison of GPC and OMPC
249(2)
6.8.4.1 DMC/GPC is practically effective
250(1)
6.8.4.2 The potential role of dual-mode algorithms
250(1)
6.9
Chapter summary
251(1)
6.10 MATLAB files in support of this chapter
251(2)
6.10.1 Files in support of OMPC/SOMPC simulations
251(1)
6.10.2 MATLAB files producing numerical illustrations from Section 6.7
252(1)
7 Constraint handling in GPC/finite horizon predictive control 253(30)
7.1 Introduction
254(1)
7.2 Guidance for the lecturer
254(1)
7.3 Introduction
255(4)
7.3.1 Definition of a saturation policy and limitations
255(1)
7.3.2 Limitations of a saturation policy
255(3)
7.3.3 Summary of constraint handling needs
258(1)
7.4 Description of typical constraints and linking to GPC
259(8)
7.4.1 Input rate constraints with a finite horizon (GPC predictions)
260(1)
7.4.2 Input constraints with a finite horizon (GPC predictions)
261(1)
7.4.3 Output constraints with a finite horizon (GPC predictions)
262(1)
7.4.4 Summary
263(1)
7.4.5 Using MATLAB to build constraint inequalities
264(3)
7.5 Constrained GPC
267(6)
7.5.1 Quadratic programming in GPC
267(1)
7.5.2 Implementing constrained GPC in practice
268(1)
7.5.3 Stability of constrained GPC
268(1)
7.5.4 Illustrations of constrained GPC with MATLAB
269(4)
7.5.4.1 Illustration: Constrained GPC with only input constraints
269(1)
7.5.4.2 Illustration: Constrained GPC with output constraints
270(2)
7.5.4.3 Illustration: Constrained GPC with a T-filter
272(1)
7.5.4.4 Illustration: Constrained GPC with an independent model
272(1)
7.6 Understanding a quadratic programming optimisation
273(6)
7.6.1 Generic quadratic function optimisation
273(1)
7.6.2 Impact of linear constraints on minimum of a quadratic function
274(3)
7.6.2.1 Illustration: Contour curves, constraints and minima for a quadratic function (7.32)
274(2)
7.6.2.2 Illustration: Impact of change of linear term in quadratic function (7.34) on constrained minimum
276(1)
7.6.3 Illustrations of MATLAB for solving QP optimisations
277(1)
7.6.4 Constrained optimals may be counter-intuitive: saturation control can be poor
278(1)
7.7
Chapter summary
279(1)
7.8 MATLAB code supporting constrained MPC simulation
280(3)
7.8.1 Miscellaneous MATLAB files used in illustrations
280(1)
7.8.2 MATLAB code for supporting GPC based on an MFD model
281(1)
7.8.3 MATLAB code for supporting GPC based on an independent model
282(1)
8 Constraint handling in dual-mode predictive control 283(46)
8.1 Introduction
285(1)
8.2 Guidance for the lecturer/reader and introduction
285(1)
8.3 Background and assumptions
285(2)
8.4 Description of simple or finite horizon constraint handling approach for dual-mode algorithms
287(6)
8.4.1 Simple illustration of using finite horizon inequalities or constraint handling with dual-mode predictions
287(1)
8.4.2 Using finite horizon inequalities or constraint handling with unbiased dual-mode predictions
288(2)
8.4.3 MATLAB code for constraint inequalities with dual-mode predictions and SOMPC/OMPC simulation examples
290(2)
8.4.3.1 Illustration: Constraint handling in SISO OMPC
290(1)
8.4.3.2 Illustration: Constraint handling in MIMO OMPC
291(1)
8.4.4 Remarks on using finite horizon inequalities in dual-mode MPC
292(1)
8.4.5 Block diagram representation of constraint handling in dual-mode predictive control
292(1)
8.5 Concepts of redundancy, recursive feasibility, admissible sets and autonomous models
293(18)
8.5.1 Identifying redundant constraints in a set of inequalities
294(1)
8.5.2 The need for recursive feasibility
294(2)
8.5.3 Links between recursive feasibility and closed-loop stability
296(1)
8.5.4 Terminal regions and impacts
297(1)
8.5.5 Autonomous model formulations for dual-mode predictions
297(3)
8.5.5.1 Unbiased prediction and constraints with autonomous models
298(1)
8.5.5.2 Constraint inequalities and autonomous models with deviation variables
299(1)
8.5.5.3 Core insights with dual-mode predictions and constraint handling
300(1)
8.5.6 Constraint handling with maximal admissible sets and invariance
300(11)
8.5.6.1 Maximal admissible set
301(5)
8.5.6.2 Concepts of invariance and links to the MAS
306(1)
8.5.6.3 Efficient definition of terminal sets using a MAS
307(1)
8.5.6.4 Maximal controlled admissible set
308(2)
8.5.6.5 Properties of invariant sets
310(1)
8.6 The OMPC/SOMPC algorithm using an MCAS to represent constraint handling
311(3)
8.6.1 Constraint inequalities for OMPC using an MCAS
311(2)
8.6.2 The proposed OMPC/SOMPC algorithm
313(1)
8.6.3 Illustrations of the dual-mode prediction structure in OMPC/SOMPC
313(1)
8.7 Numerical examples of the SOMPC/OMPMC approach with constraint handling
314(8)
8.7.1 Constructing invariant constraint sets/MCAS using MATLAB
314(1)
8.7.2 Closed-loop simulations of constrained OMPC/SOMPC using ompc_simulate_constraints.m: the regulation case
315(3)
8.7.2.1 Illustration: ompc_constraints_examplel.m
315(1)
8.7.2.2 Illustration: ompc_constraints_example2.m
316(1)
8.7.2.3 Illustration: ompc_constraints_example3.m
316(1)
8.7.2.4 Illustration: For OMPC, the optimal choice of input perturbation ck does not change
317(1)
8.7.3 Closed-loop simulations of constrained OMPC/SOMPC using ompc_simulate_constraintsb.m: the tracking case
318(1)
8.7.3.1 Illustration: ompc_constraints_example4.m
318(1)
8.7.3.2 Illustration: ompc_constraints_example5.m
319(1)
8.7.4 More efficient code for the tracking case and disturbance uncertainty
319(3)
8.8 Discussion on the impact of cost function and algorithm selection on feasibility
322(1)
8.9
Chapter summary
323(1)
8.10 Summary of MATLAB code supporting constrained OMPC simulation
324(5)
8.10.1 Code for supporting SOMPC/OMPC with constraint handling over a pre-specified finite horizon
325(1)
8.10.2 Code for supporting SOMPC/OMPC with constraint handling using maximal admissible sets
326(3)
9 Conclusions 329(6)
9.1 Introduction
329(1)
9.2 Design choices
330(4)
9.2.1 Scenario and funding
330(1)
9.2.2 Effective tuning
330(1)
9.2.3 Constraint handling and feasibility
331(1)
9.2.4 Coding complexity
332(1)
9.2.5 Sensitivity to uncertainty
333(1)
9.3 Summary
334(1)
A Tutorial and exam questions and case studies 335(14)
A.1 Typical exam and tutorial questions with minimal computation
336(6)
A.2 Generic questions
342(1)
A.3 Case study based questions for use with assignments
343(6)
A.3.1 SISO example case studies
344(2)
A.3.2 MIMO example case studies
346(3)
B Further reading 349(22)
B.1 Introduction
349(1)
B.2 Guidance for the lecturer/reader
350(1)
B.3 Simple variations on the basic algorithm
350(2)
B.3.1 Alternatives to the 2-norm in the performance index
350(1)
B.3.2 Alternative parameterisations of the degrees of freedom
351(1)
B.4 Parametric approaches to solving quadratic programming
352(3)
B.4.1 Strengths and weaknesses of parametric solutions in brief
352(1)
B.4.2 Outline of a typical parametric solution
353(2)
B.5 Prediction mismatch and the link to feedforward design in MPC
355(3)
B.5.1 Feedforward definition in MPC
356(1)
B.5.2 Mismatch between predictions and actual behaviour
356(2)
B.6 Robust MPC: ensuring feasibility in the presence of uncertainty
358(5)
B.6.1 Constraint softening: hard and soft constraints
360(1)
B.6.2 Back off and borders
361(2)
B.7 Invariant sets and predictive control
363(7)
B.7.1 Link between invariance and stability
363(1)
B.7.2 Ellipsoidal invariant sets
364(1)
B.7.3 Maximal volume ellipsoidal sets for constraint satisfaction
365(1)
B.7.4 Invariance in the presence of uncertainty
366(6)
B.7.4.1 Disturbance uncertainty and tube MPC
367(1)
B.7.4.2 Parameter uncertainty and ellipsoidal methods
368(2)
B.8 Conclusion
370(1)
C Notation, models and useful background 371(12)
C.1 Guidance for the lecturer/reader
371(1)
C.2 Notation for linear models
372(6)
C.2.1 State space models
372(1)
C.2.2 Transfer function models single-input-single-output and multi-input-multi-output
373(1)
C.2.3 Author's MATLAB notation for SISO transfer function and MFD models
374(2)
C.2.4 Equivalence between difference equation format and vector format
376(1)
C.2.5 Step response models
376(1)
C.2.6 Sample rates
376(1)
C.2.7 Summary
377(1)
C.3 Minimisation of functions of many variables
378(2)
C.3.1 Gradient operation and quadratic functions
378(1)
C.3.2 Finding the minimum of quadratic functions of many variables
379(1)
C.4 Common notation
380(3)
References 383(14)
Index 397
Dr. Rossiter has been researching predictive control since the late 1980s, and he has published over 300 articles in journals and conferences on the topic. His particular contributions have focused on stability, feasibility and computational simplicity. He also has a parallel interest in developing good practice in university education. He has a Bachelors degree and a doctorate from the University of Oxford. He spent 9 years as a Lecturer at Loughborough University, and he is currently a Reader at the University of Sheffield.
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