Control Design Techniques in Power Electronics Devices

by Sira-Ramirez, Herbertt; Silva-Ortigoza, Ramon

• ISBN13: 9781846284588
• ISBN10: 1846284589
• Format: Hardcover
• Copyright: 2006-07-01
• Publisher: Springer Verlag

Summary

Power electronics systems are physical devices that can be modelled mathematically as controlled dynamical systems. This makes them suitable for the application of existing control theory, particularly in the design of their regulatory subsystems. For years there has been a perceived need to bring the disciplines of power electronics and theoretical control into closer co-operation, demonstrating the potentially great advantages of, at first sight, rather obscure control theory to power specialists while making control technicians better aware of the fundamental needs and limitations of power electronics design.Control Design Techniques in Power Electronics Devices deals specifically with control theories relevant to the design of control units for switched power electronics devices, for the most part represented by DC'DC converters and supplies, by rectifiers of different kinds and by inverters with varying topologies. The theoretical methods for designing controllers in linear and nonlinear systems are accompanied by multiple case studies and examples showing their application in the emerging field of power electronics. The book is introduced through the very important topic of modeling switched power electronics as controlled dynamical systems. Detailed circuit layouts, schematics and actual closed-loop control responses from a representative group of the plants under discussion and generated by applying the theory are included.The control theories which feature in the book are: sliding mode control and feedback control by means of approximate linearization (linear state feedback, static and dynamic proportional-integral-differential (PID control), output feedback trough observer design, Lyapunov-based control and passivity-based control). Nonlinear control design methods represented include: exact feedback linearization, input-output linearization, differential flatness, generalized PID control and, again, passivity-based control.This monograph will be of interest to researchers in power systems and their related control problems. It will also assist tutors and students in these fields with its dydactic style and its rich source of worked-out application examples from a broad spectrum of control theories.

Author Biography

Hebertt Sira-Ramirez has published his work in 4 books, 20 book chapters, many of them in Springer-Verlag volumes, 114 journal publications in credited, refereed, journals and over 192 specialized international conferences. He obtained his MSEE and his PhD, both from the Massachusetts Institute of Technology (Cambridge, USA) in 1972 and 1977, respectively. He worked as a professor, and researcher, for 28 years at the Universidad de Los Andes in Merida, Venezuela, and has worked for the last 7 years in a Scientific Research Institute in Mexico City (Cinvestav-IPN). He is a member of the IFAC Technical Committee on Non-Linear Control Systems.

Table of Contents

1 Introduction	1	(10)
Part I Modelling
2 Modelling of DC-to-DC Power Converters	11	(50)
2.1 Introduction	11	(2)
2.2 The Buck Converter	13	(7)
2.2.1 Model of the Converter	14	(1)
2.2.2 Normalization	15	(1)
2.2.3 Equilibrium Point and Static Transfer Function	16	(2)
2.2.4 A Buck Converter Prototype	18	(2)
2.3 The Boost Converter	20	(7)
2.3.1 Model of the Converter	22	(1)
2.3.2 Normalization	23	(1)
2.3.3 Equilibrium Point and Static Transfer Function	23	(1)
2.3.4 Alternative Model of the Boost Converter	24	(1)
2.3.5 A Boost Converter Prototype	25	(2)
2.4 The Buck-Boost Converter	27	(4)
2.4.1 Model of the Converter	27	(1)
2.4.2 Normalization	28	(1)
2.4.3 Equilibrium Point and Static Transfer Function	29	(1)
2.4.4 A Buck-Boost Converter Prototype	30	(1)
2.5 The Non-inverting Buck-Boost Converter	31	(3)
2.5.1 Model of the Converter	31	(1)
2.5.2 Normalization	32	(1)
2.5.3 Equilibrium Point and Static Transfer Function	33	(1)
2.6 The Cúk Converter	34	(4)
2.6.1 Model of the Converter	35	(1)
2.6.2 Normalization	36	(1)
2.6.3 Equilibrium Point and Static Transfer Function	37	(1)
2.7 The Sepic Converter	38	(3)
2.7.1 Model of the Converter	39	(1)
2.7.2 Normalization	39	(1)
2.7.3 Equilibrium Point and Static Transfer Function	40	(1)
2.8 The Zeta Converter	41	(3)
2.8.1 Model of the Converter	41	(2)
2.8.2 Normalization	43	(1)
2.8.3 Equilibrium Point and Static Transfer Function	43	(1)
2.9 The Quadratic Buck Converter	44	(2)
2.9.1 Model of the Converter	44	(1)
2.9.2 Normalized Model	45	(1)
2.9.3 Equilibrium Point	45	(1)
2.9.4 Static Transfer Function	46	(1)
2.10 The Boost-Boost Converter	46	(4)
2.10.1 Model of the Boost-Boost Converter	47	(1)
2.10.2 Average Normalized Model	47	(1)
2.10.3 Equilibrium Point and Static Transfer Function	47	(2)
2.10.4 Alternative Model of the Boost-Boost Converter	49	(1)
2.10.5 A Boost-Boost Converter Experimental Prototype	50	(1)
2.11 The Double Buck-Boost Converter	50	(2)
2.11.1 Model of the Double Buck-Boost Converter	51	(1)
2.11.2 Average Normalized Model	51	(1)
2.11.3 Equilibrium Point and Static Transfer Function	51	(1)
2.12 Power Converter Models with Non-ideal Components	52	(2)
2.13 A General Mathematical Model for Power Electronics Devices	54	(7)
2.13.1 Some Illustrative Examples of the General Model	56	(5)
Part II Controller Design Methods
3 Sliding Mode Control	61	(62)
3.1 Introduction	61	(1)
3.2 Variable Structure Systems	62	(9)
3.2.1 Control of Single Switch Regulated Systems	62	(2)
3.2.2 Sliding Surfaces	64	(1)
3.2.3 Notation	65	(1)
3.2.4 Equivalent Control and the Ideal Sliding Dynamics	65	(2)
3.2.5 Accessibility of the Sliding Surface	67	(2)
3.2.6 Invariance Conditions for Matched Perturbations	69	(2)
3.3 Control of the Boost Converter	71	(7)
3.3.1 Direct Control	71	(1)
3.3.2 Indirect Control	72	(2)
3.3.3 Simulations	74	(1)
3.3.4 Experimental Implementation	75	(3)
3.4 Control of the Buck-Boost Converter	78	(4)
3.4.1 Direct Control	79	(1)
3.4.2 Indirect Control	80	(1)
3.4.3 Simulations	81	(1)
3.5 Control of the Cúk Converter	82	(5)
3.5.1 Direct Control	83	(1)
3.5.2 Indirect Control	84	(2)
3.5.3 Simulations	86	(1)
3.6 Control of the Zeta Converter	87	(4)
3.6.1 Direct Control	88	(1)
3.6.2 Indirect Control	88	(2)
3.6.3 Simulations	90	(1)
3.7 Control of the Quadratic Buck Converter	91	(4)
3.7.1 Direct Control	92	(1)
3.7.2 Indirect Control	93	(2)
3.7.3 Simulations	95	(1)
3.8 Multi-variable Case	95	(7)
3.8.1 Sliding Surfaces	97	(2)
3.8.2 Equivalent Control and Ideal Sliding Dynamics	99	(1)
3.8.3 Invariance with Respect to Matched Perturbations	100	(1)
3.8.4 Accessibility of the Sliding Surface	101	(1)
3.9 Control of the Boost-Boost Converter	102	(6)
3.9.1 Direct Control	103	(1)
3.9.2 Indirect Control	104	(1)
3.9.3 Simulations	105	(1)
3.9.4 Experimental Sliding Mode Control Implementation	105	(3)
3.10 Control of the Double Buck-Boost Converter	108	(4)
3.10.1 Direct Control	109	(1)
3.10.2 Indirect Control	110	(1)
3.10.3 Simulations	111	(1)
3.11 Σ – Δ Modulation	112	(11)
3.11.1 Σ – Δ-Modulators	113	(2)
3.11.2 Average Feedbacks and Σ – Δ-Modulation	115	(3)
3.11.3 A Hardware Realization of a Σ – Δ-Modulator	118	(5)
4 Approximate Linearization in the Control of Power Electronics Devices	123	(112)
4.1 Introduction	123	(1)
4.2 Linear Feedback Control	124	(18)
4.2.1 Pole Placement by Full State Feedback	124	(2)
4.2.2 Pole Placement Based on Observer Design	126	(2)
4.2.3 Reduced Order Observers	128	(2)
4.2.4 Flatness	130	(3)
4.2.5 Generalized Proportional Integral Controllers	133	(3)
4.2.6 Passivity Based Control	136	(3)
4.2.7 A Hamiltonian Systems Viewpoint	139	(3)
4.3 The Buck Converter	142	(26)
4.3.1 Generalities about the Average Normalized Model	142	(2)
4.3.2 Controller Design by Pole Placement	144	(1)
4.3.3 Proportional-Derivative Control via State Feedback	145	(1)
4.3.4 Trajectory Tracking	146	(4)
4.3.5 Fliess' Generalized Canonical Forms	150	(2)
4.3.6 State Feedback Control via Observer Design	152	(2)
4.3.7 GPI Controller Design	154	(2)
4.3.8 Passivity Based Control	156	(3)
4.3.9 The Hamiltonian Systems Viewpoint	159	(3)
4.3.10 Implementation of the Linear Passivity Based Control for the Buck Converter	162	(6)
4.4 The Boost Converter	168	(21)
4.4.1 Generalities about the Average Normalized Model	168	(4)
4.4.2 Control via State Feedback	172	(2)
4.4.3 Proportional-Derivative State Feedback Control	174	(2)
4.4.4 Trajectory Tracking	176	(5)
4.4.5 Fliess' Generalized Canonical Form	181	(1)
4.4.6 State Feedback Control via Observer Design	182	(1)
4.4.7 GPI Controller Design	183	(2)
4.4.8 Passivity Based Control	185	(2)
4.4.9 The Hamiltonian Systems Viewpoint	187	(2)
4.5 The Buck-Boost Converter	189	(21)
4.5.1 Generalities about the Model	189	(4)
4.5.2 State Feedback Controller Design	193	(2)
4.5.3 Dynamic Proportional-Derivative State Feedback Control	195	(3)
4.5.4 Trajectory Tracking	198	(1)
4.5.5 Fliess' Generalized Canonical Forms	199	(1)
4.5.6 Control via Observer Design	200	(2)
4.5.7 GPI Controller Design	202	(2)
4.5.8 Passivity Based Control	204	(1)
4.5.9 The Hamiltonian Systems Viewpoint	205	(2)
4.5.10 Experimental Passivity based Control of the Buck-Boost Converter	207	(3)
4.6 The Cúk Converter	210	(4)
4.6.1 Generalities about the Model	210	(3)
4.6.2 The Hamiltonian System Approach	213	(1)
4.7 The Zeta Converter	214	(5)
4.7.1 Generalities about the Model	214	(4)
4.7.2 The Hamiltonian System Approach	218	(1)
4.8 The Quadratic Buck Converter	219	(10)
4.8.1 Generalities about the Model	219	(4)
4.8.2 State Feedback Controller Design	223	(4)
4.8.3 The Hamiltonian System Approach	227	(2)
4.9 The Boost-Boost Converter	229	(6)
4.9.1 Generalities about the Model	229	(4)
4.9.2 The Hamiltonian System Approach	233	(2)
5 Nonlinear Methods in the Control of Power Electronics Devices	235	(126)
5.1 Introduction	235	(1)
5.2 Feedback Linearization	236	(25)
5.2.1 Isidori's Canonical Form	236	(2)
5.2.2 Input-Output Feedback Linearization	238	(2)
5.2.3 State Feedback Linearization	240	(3)
5.2.4 The Boost Converter	243	(3)
5.2.5 The Buck-Boost Converter	246	(3)
5.2.6 The Cúk Converter	249	(5)
5.2.7 The Sepic Converter	254	(4)
5.2.8 The Zeta Converter	258	(3)
5.2.9 The Quadratic Buck Converter	261	(1)
5.3 Passivity Based Control	261	(21)
5.3.1 The Boost Converter	263	(3)
5.3.2 The Buck-Boost Converter	266	(3)
5.3.3 The Cúk Converter	269	(3)
5.3.4 The Sepic Converter	272	(2)
5.3.5 The Zeta Converter	274	(5)
5.3.6 The Quadratic Buck Converter	279	(3)
5.4 Exact Error Dynamics Passive Output Feedback Control	282	(27)
5.4.1 A General Result	282	(4)
5.4.2 The Boost Converter	286	(2)
5.4.3 Experimental Implementation	288	(3)
5.4.4 The Buck-Boost Converter	291	(2)
5.4.5 The Cúk Converter	293	(1)
5.4.6 The Sepic Converter	294	(4)
5.4.7 The Zeta Converter	298	(3)
5.4.8 The Quadratic Buck Converter	301	(3)
5.4.9 The Boost-Boost Converter	304	(2)
5.4.10 The Double Buck-Boost Converter	306	(3)
5.5 Error Dynamics Passive Output Feedback	309	(7)
5.5.1 The Boost Converter	312	(3)
5.5.2 Experimental Results	315	(1)
5.6 Control via Fliess' Generalized Canonical Form	316	(15)
5.6.1 The Boost Converter	317	(5)
5.6.2 The Buck-Boost Converter	322	(4)
5.6.3 The Quadratic Buck Converter	326	(5)
5.7 Nonlinear Observers for Power Converters	331	(6)
5.7.1 Full Order Observers	331	(2)
5.7.2 The Boost Converter	333	(2)
5.7.3 The Buck-Boost Converter	335	(2)
5.8 Reduced Order Observers	337	(6)
5.8.1 The Boost Converter	337	(4)
5.8.2 The Buck-Boost Converter	341	(2)
5.9 GPI Sliding Mode Control	343	(18)
5.9.1 The Buck Converter	344	(6)
5.9.2 The Boost Converter	350	(5)
5.9.3 The Buck-Boost Converter	355	(6)
Part III Applications
6 DC-to-AC Power Conversion	361	(24)
6.1 Introduction	361	(2)
6.2 Nominal Trajectories in DC-to-AC Power Conversion	363	(8)
6.2.1 The Buck Converter	363	(2)
6.2.2 Two-Sided Σ – Δ Modulation	365	(1)
6.2.3 The Boost Converter	366	(4)
6.2.4 The Buck-Boost Converter	370	(1)
6.3 An Approximate Linearization Approach	371	(3)
6.3.1 The Boost Converter	371	(2)
6.3.2 The Buck-Boost Converter	373	(1)
6.4 A Flatness Based Approach	374	(4)
6.4.1 The Double Bridge Buck Converter	374	(1)
6.4.2 The Boost Converter	375	(1)
6.4.3 The Buck-Boost Converter	376	(2)
6.5 A Sliding Mode Control Approach	378	(2)
6.5.1 The Boost Converter	378	(1)
6.5.2 A Feasible Indirect Input Current Tracking Approach	378	(2)
6.6 Exact Tracking. Error Dynamics Passive Output Feedback Control	380	(5)
6.6.1 The Double Bridge Buck Converter	380	(1)
6.6.2 The Boost Converter	381	(2)
6.6.3 The Buck-Boost Converter	383	(2)
7 AC Rectifiers	385	(30)
7.1 Introduction	385	(1)
7.2 Boost Unit Power Factor Rectifier	386	(6)
7.2.1 Model of the Monophasic Boost Rectifier	386	(1)
7.2.2 The Control Objectives	387	(1)
7.2.3 Steady State Considerations	387	(1)
7.2.4 Exact Open Loop Tracking Error Dynamics and Controller Design	388	(1)
7.2.5 Simulations	389	(1)
7.2.6 The Use of the Differential Flatness Property in the Passive Controller Design	389	(3)
7.2.7 Simulations	392	(1)
7.3 Three Phase Boost Rectifier	392	(8)
7.3.1 The Three Phase Boost Rectifier Average Model	393	(2)
7.3.2 A Static Passivity Based Controller	395	(1)
7.3.3 Trajectory Planning	395	(3)
7.3.4 Switched Implementation of the Average Design	398	(1)
7.3.5 Simulations	399	(1)
7.4 A Unit Power Factor Rectifier-DC Motor System	400	(8)
7.4.1 The Combined Rectifier-DC Motor Model	400	(3)
7.4.2 The Exact Tracking Error Dynamics Passive Output Feedback Controller	403	(1)
7.4.3 Trajectory Generation	403	(2)
7.4.4 Simulations	405	(3)
7.5 A Three Phase Rectifier-DC Motor System	408	(7)
7.5.1 The Combined Three Phase Rectifier DC Motor Model	408	(1)
7.5.2 The Exact Tracking Error Dynamics Passive Output Feedback Controller	409	(1)
7.5.3 Trajectory Generation	410	(2)
7.5.4 Simulations	412	(3)
References	415	(6)
Index	421