Predictive Control in Power Electronics and Electrical Drives. Ralph M. Kennel, Technische Universitaet Muenchen, Germany
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1 Predictive Control in Power Electronics and Electrical Drives Ralph M. Kennel, Technische Universitaet Muenchen, Germany
2 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
3 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
4 State of the Art : Field Oriented Control r mains field coordinates stator coordinates flux controller i s e j u s PWM 6 speed controller current controllers e -j i s u s r model M 3~ encoder
5 Problems of Linear Algorithms Linear control characteristics Control unit and controlled unit are assumed to be linear Control unit are assumed to be time constant Linear circuits show identical reactions in each operation range under the same reference commands Drive systems characteristics Drive systems are non-linear Drive systems are time-variant The behavior of a drive system is depending on the operation range
6 Typical Cascaded Structure of Drive Control position controller speed controller current controller power electronics motor windings I inertia gear etc.
7 Problems of Linear Algorithms in cascaded control structures speed control must be much faster than position control and current control must be much faster than speed control current control must be very fast to achieve position control with reasonable cycle times in the controlled system (drive, converter, ) however, there is no time constant justifying cycle times of 100 µs or less
8 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
9 General Structure of a Predictive Controller prediction and calculation switching state actual machine state power electronics machine and power electronics model motor windings I inertia gear etc. reminds slightly to state control state control, however, is basically a linear control predictive control is not!!!
10 Usual Structure of Drive Control why PWM? linearization of the inverter consequences? very high switching frequency DC link PI controller
11 Structure of a Direct Control DC link direct controller
12 Principle of Predictive Control reference commands precalculation of the behaviour for each of the switching states comparison between precalculation and reference commands next switching state or switching time can be fixed definite number of equivalent circuits without switching elements definite number of switching states definite number of switching elements inverter
13 Family tree of predictive control algorithms hysteresisbasedstrategies strategies trajectorybasedstrategies strategies adaptive switching pattern (ASP) (Nagy) predictive current control (Holtz/Stadtfeld) hysteresis control (bang bang) GPC GPC (Clarke) Off-line MPC (Bemporad et.al) other MBPC schemes direct torque control (DTC) (Takahashi/Nogushi) (Tiitinen/Lalu) direct self control (DSC) (Depenbrock) direct direct torque mean torque integral control (DTC) space-vector PWM (Chapuis, et.al.) (Trzynadlowski, et.al.) direct control fast-response current control torque adaptive (DMTC) self-tuning control switching (DTC) multilevel direct speed PROMC hysteresis DTC control (DSPC) current control (Purcell/Acarnley) (Takahashi/Nogushi) (Flach, direct predictive pattern et.al.) self (Choi/Sul) on-off current control control (ASP) control (Mutschler) (Kohlmeier et.al.) space (Hoffmann) (Holtz, (DSC) vector et.al) direct mean torque direct self PROMC control (DMTC) (Depenbrock) current torque (Tiitinen/Lalu) sliding control (Nagy) pulsation mode control control (DSC) voltage control (Flach, et.al.) control (Bonanno, et.al.) (Hintze) torque (Holtz/Stadtfeld) reduced pulsation (Kazmierkowski, DTDTC (Emeljanov) DTC reduced DTC direct torque et.al.) (Maes/Melkebeek) predictive (Vas, et.al.) (Vas, et.al.) integral control new control (Kennel/Schröder) direct space-vector PROMC space vector torque control adaptive (DTC) and PWM control (Kang/Sul) (Chapuis, (Kazmierkowski, et.al.) (Trzynadlowski, current optimal DTC-SVM new optimized et.al.) control on-line-tuning direct regulator DTC with reduction adaptive and of torque (Kohlmeier (Lascu direct torque et.al.) current ripple et.al.) control direct et.al.) control optimized regulator (La/Shin/Hyun) improved multilevel current (Ackva, regulator direct control et.al.) (Ackva, et.al.) (Kang/Sul) speed of IM currents DTC + dithering space vector (Noguchi, et.al.) hysteresis (du Toit PROMC control space (Pfaff/Wick) DTC-DSVM Mouton/Enslin) vectorial torque control predictive control control GPC (DSPC) vector (Mayer/Pfaff) DTDTC (Wuest/Jenni) (Maes/Melkebeek) (Purcell/Acarnley) voltage (Casadei DTC with control control et.al) reduction (Attaianese, et.al.) (Warmer (Mutschler) et.al.) (Clarke) direct current DTC-SVM predictive current of control (Lascu et.al.) (Hintze) torque current controlripple (Pfaff/Wick) digital new DTC with (Wuest/Jenni) DTC-DSVM for predictive direct Off-line method ORS (La/Shin/Hyun) self MPC resonant direct link digital inverter predictive current control (Casadei et.al) method current controller sliding mode control DTC with hysteresis current (Moucary (Bemporad ORS (Salama control control et.al.) (DSC) et.al) current et.al) controller (Salama et.al) (Emeljanov) (Moucary DTC et.al.) + dithering (Oh/Jung/Youn) self-tuning (Betz/Cook/Henriksen) DTC-PPWC (bang DTC-PPWC (Hecht) (Bonanno, bang) (Holmes/Martin) et.al.) trajectory on-off control (Nillesen (Noguchi, et.al.) et.al.) optimal on-line-tuning digital (Hoffmann) other current regulator current controller (Nillesen MBPC schemes et.al.) tracking control (du Toit Mouton/Enslin) (Betz/Cook/Henriksen) vectorial torque control (Holtz/Beyer) model basedstrategies (Attaianese, et.al.) (longrangepredictivecontrol) model based strategies predictive current control for resonant link inverter (Oh/Jung/Youn) fast-response current control (Holtz, et.al) predictive control (Kennel/Schröder) improved predictive control (Warmer et.al.) new predictive current control (Hecht) current control (Choi/Sul) direct control of IM currents (Mayer/Pfaff) direct digital predictive current controller (Holmes/Martin) trajectory tracking control (Holtz/Beyer)
14 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
15 Trajectory Based Predictive Control Strategies system states are forced to follow (pre-)defined natural reference trajectories difference to sliding mode control there the trajectories are not natural
16 Example : Trajectory Based Predictive Control Direct Speed Control acc. to Mutschler * e model and prediction u k i s = ~ u d u s e / a k+1 k+1 S k+1 S k Hy e / a k+3 k+3 a = +Hy M 3~ e / a k k S k+2 e / a k+2 k+2 e = ref
17 Characteristics of Trajectory Based Predictive Control system states are forced to follow (pre-)defined reference trajectories switching takes place at intersections between different system-trajectories or at (pre-)defined instants switching frequency of the inverter can be fixed to a constant value control behaviour comparable to feedforward control exact knowledge of system parameters is required appropriate for realisation by digital circuits or controllers
18 Example : Trajectory Based Predictive Control Direct Self Control (DSC) acc. to Depenbrock
19 Example : Hysteresis Based Predictive Control Direct Self Control acc. to Takahashi
20 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
21 Hysteresis Based Predictive Control Strategies switching of inverter takes place at the (multi-dimensional) border(s) of a hysteresis area
22 Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz
23 Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz i s * i s i s u sk predict model u k di sk dt = u d ~ u s jim s i s * di n dt i s M 3~ 0 i s Re
24 Characteristics of Hysteresis Based Predictive Control switching takes place at borders of a hysteresis area a maximum error can be (pre-)defined switching frequency of the inverter is not constant control behaviour comparable to feedback control exact knowledge of system parameters is not required appropriate for realisation by analog circuits
25 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
26 The Human Behaviour of DMPC DMPC is like playing chess the player calculates in advance all possible moves until a prediction horizon the player chooses the move with the best expectations of success after each opponent s move pre-calculation and optimization is repeated
27 Characteristics of Model Based Predictive Control future control values are pre-calculated and optimized until a (pre-)defined horizon the first of the precalculated control values is transmitted to the controlled system only use of non-linear model is possible for non-linear control systems a lot of calculation power is required
28 Calculation Times DMPC - control, implicite solution strategy N p cases max. calculation time complete enumeration µs complete enumeration > 500 µs branch and bound µs branch and bound µs online-optimization is not applicable for drive control processor: 900 MHz AMD Duron, 128 MB RAM Linux with RTAI 1.3
29 Experimental Results (DMPC) current control
30 Experimental Results (DMPC) current control
31 Features of (Longe Range) Predictive Control Advantages possibility to use foreknowledge about drive system inverter limitations and dynamic behaviours are taken into account improved representation of non-linear systems no need for time challenging cascade structure improved dynamic behaviour Disadvantages step-by-step commissioning impossible for industrial use self-commissioning feature is required stationary accuracy and dynamic behaviour depend on accurracy of model parameters
32 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
33 Control task Current control of a three-phase resistive-inductive-active load
34 Heuristic method Peter Stolze Calculation effort rises exponentially with the prediction horizon Three or four prediction steps impossible in real-time (online as well as offline) Cost function to describe the performance to be obtained Basic idea of Heuristic Method : Optimum integer solution of a linear program is close to the continuous-valued solution of the integer problem => Important: Optimum integer solution is not necessarily the integer solution which is closest to the continuous-valued optimum => Not all integer points have to be examined, only the ones closest to the continuous-valued optimum
35 Heuristic method Continuous-valued switching states in the range [0; 1] Determination of the sector in which the continuous-valued optimum lies (I to VI) For the first two prediction steps the three closest integer solutions are used for an exhaustive search (corners of the triangle) For the 3rd and 4th prediction step only the 2 closest integer solutions are used 3 prediction steps: 18 possible combinations 4 prediction steps: 36 possible combinations In more than 95% of the cases the real optimum is still found
36 Simulation Results Sinusoidal references Back EMF voltages R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs
37 Finite-Set Model Predictive Control of a Flying Capacitor Converter with Heuristic Voltage Vector Preselection Peter Stolze
38 Control task Current control of a three-phase resistive-inductive-active load Hysteresis controller for voltage balancing S 11 S 21 S V dc S 12 C 1 i 1 S 22 C 2 i 2 S 32 C 3 i 3 S 13 S 23 S V dc S 14 S 24 S 34 E 1 E 2 E 3 R L R L R L
39 General remarks Im Heuristic voltage vector selection algorithm basically the same as for two-level inverters but now the continuous-valued switching states can be in the range [-1; 1] Re possible sectors
40 Simulation Results Sinusoidal references Flying capacitor voltages R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF
41 Predictive Control Strategies hysteresis based switching of inverter takes place at the (multi-dimensional) border(s) of a hysteresis area trajectory based system states are forced to follow (pre-)defined reference trajectories model based future control values are pre-calculated and optimized until a (pre-)defined horizon examples hysteresis control (bang-bang control) Direct Torque Control (DTC) examples Direct Self Control Direct Speed Control examples Dynamic Matrix Control Generalized Predictive Control Predictive Control with Heuristic Pre-Selection
42 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
43 Basic Idea: Saliency based Encoderless Predictive Torque Control without Signal Injection P. Landsmann, D. Paulus, P. Stolze and R. Kennel A Predictive Torque Controller neglecting the saliency in the model causes a prediction error containing the angle information. Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
44 Outline 1) Predictive torque control - Topology and Function - Neglection of saliency 2) Saliency tracking approach - Prediction error - Prediction error reconstruction - Phase locked loop scheme 3) Results - Simulations with PMSM - Measurements with RM Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
45 Predictive Torque Control Outer topology: Overview Predictive Torque Control Saliency Tracking Controller input: reference torque Actuating variable: stator voltage Simulation Results Measurements Conclusion Measurement of current and rotor angle required Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
46 Predictive Torque Control Current and PM flux linkage from measurements Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
47 Predictive Torque Control Current and PM flux linkage from measurements 7 voltages vectors from inverter Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
48 Predictive Torque Control Current and PM flux linkage from measurements 7 voltages vectors from inverter prediction of current and respective torque Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
49 Predictive Torque Control Current and PM flux linkage from measurements 7 voltages vectors from inverter prediction of current and respective torque Overview Predictive Torque Control Saliency Tracking Selecting optimum of cost function Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
50 Predictive Torque Control Overview Predictive Torque Control Saliency Tracking Simulation Results Discrete model of the machine Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
51 Predictive Torque Control Overview Predictive Torque Control Saliency Tracking Simulation Results Discrete model of the machine Measurements Current prediction based on mean inverse inductance Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
52 Saliency Tracking Approach Predicted current progression Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
53 Saliency Tracking Approach Predicted current progression Overview Predictive Torque Control Real current progression Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
54 Saliency Tracking Approach Predicted current progression Overview Predictive Torque Control Real current progression Saliency Tracking Prediction error Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
55 Saliency Tracking Approach Measured prediction error Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
56 Saliency Tracking Approach Measured prediction error Overview Reconstructed prediction error Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
57 Saliency Tracking Approach Measured prediction error Overview Reconstructed prediction error Predictive Torque Control Saliency Tracking PLL controller input Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
58 Saliency Tracking Approach Measured prediction error Overview Reconstructed prediction error Predictive Torque Control Saliency Tracking PLL controller input Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
59 Saliency Tracking Approach Measured prediction error Overview Reconstructed prediction error Predictive Torque Control Saliency Tracking PLL controller input Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
60 Saliency Tracking Approach Measured prediction error Overview Reconstructed prediction error Predictive Torque Control Saliency Tracking PLL controller input Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
61 Saliency Tracking Approach Measured prediction error Overview Reconstructed prediction error Predictive Torque Control Saliency Tracking PLL controller input Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
62 Saliency Tracking Approach Measured prediction error Overview Reconstructed prediction error Predictive Torque Control Saliency Tracking PLL controller input Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
63 Saliency Tracking Approach Saliency tracking scheme (STS) Overview Predictive Torque Control Saliency Tracking Measured prediction error Reconstructed prediction error Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
64 Simulation Results for PMSM Simulation parameter of PMSM Overview Predictive Torque Control Saliency Tracking Speed controlled encoderless predictive torque control Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
65 Simulation Results for PMSM Speed controlled step response to rated speed very good dynamics in simulation Overview Predictive Torque Control dependency on torque gradients Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
66 Measurements with Reluctance Machine Data of transverse laminated RM Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
67 Measurements with Reluctance Machine Speed controlled step response to 160% rated speed Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
68 Measurements with Reluctance Machine Response to 66% rated torque load step at speed controlled standstill Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
69 Summary Proposed Scheme: Neglect the saliency in PTC equations Prediction error contains angle information Reconstruct Prediction Error using PLL angle Vectorproduct of both is PLL input Benefits: Saliency based: permanent operation at standstill No signal injection: operation at high speed Overview Predictive Torque Control Saliency Tracking Simulation Results Measurements Conclusion Institute for Electrical Drive Systems & Power Electronics Technische Universität München Arcisstr. 21, D Munich - peter.landsmann@tum.de
70 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
71 State of the Art : Field Oriented Control r mains field coordinates stator coordinates flux controller i s e j u s PWM 6 speed controller current controllers e -j i s u s r model M 3~ encoder
72 Typical Cascaded Structure of Drive Control position controller speed controller current controller power electronics motor windings I inertia gear etc.
73 Problems of Linear Algorithms in cascaded control structures speed control must be much faster than position control and current control must be much faster than speed control current control must be very fast to achieve position control with reasonable cycle times in the controlled system (drive, converter, ) however, there is no time constant justifying cycle times of 100 µs or less
74 General Structure of a Predictive Controller prediction and calculation switching state actual machine state power electronics machine and power electronics model motor windings I inertia gear etc.
75 Predictive Control Strategies hysteresis based control behaviour comparable to feedback control exact knowledge of system parameters is not required a maximum error can be (pre-)defined trajectory based control behaviour comparable to feedforward control exact knowledge of system parameters is required appropriate for realisation by digital circuits or controllers model based the past is explicitely considered future control values are pre-calculated and optimized until a (pre-)defined horizon model parameters can be estimated on-line use of non-linear model is possible for non-linear control systems
76 Actual Situation in cascaded control structures speed control must be much faster than position control and current control must be much faster than speed control current control must be extremely fast to achieve position control with reasonable cycle times at the time most requirements in industrial applications are satisfied sufficiently there is no strong need for improvement in industry however at a certain time there will be a demand for improvement with respect to a future increase of requirements investigations should be done
77 Outline Introduction Predictive Control Methods Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection Encoderless Predictive Torque Control (without Signal Injection) Predictive Control versus Cascaded Control Conclusions/Discussion
78 Conclusions/Discussion predictive control strategies offer the possibility to use foreknowledge about the drive system physical limitations and dynamic behaviour of power electronics non-linear systems are represented better (by non-linear models) no need for time challenging cascaded structures the way of thinking is different are taken into account model of the controlled system cost function with respect to a future increase of requirements investigations should be done
79
80 Thank you!
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