Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives

Transcription

1 Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives Ralph M. Kennel, Technische Universitaet Muenchen,Germany Marian Kazmierkowski, Technical University of Warsaw, Poland José Rodríguez, Universidad Técnica Federico Santa María, Chile

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3 Outline Introduction Predictive Control Methods Predictive Control versus Cascaded Control Conclusions/Discussion

4 Outline Introduction Predictive Control Methods Predictive Control versus Cascaded Control Conclusions/Discussion

5 State of the Art : Field Oriented Control r field coordinates stator coordinates mains flux controller speed controller i s current controllers e j e -j u s PWM 6 i s u s r model M 3~ encoder

6 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

7 Problems of Linear Algorithms Feedforward Control high dynamic behaviour no impact by sensor characteristics Feedback Control Advantages high accuracy high reliability Disadvantages models are not absolutely accurate high accuracy requires knowledge of all quantuities temperature and drift behaviour often cannot be described/modeled high longterm stability simple optimization/adjustment procedure controlled quantities can be monitored (re)action only, when there is a control difference already sensors cause measuring errors

8 Problems of Linear Algorithms any controller optimization is a compromise making the inverter unnecessarily slow in many operation points controllers with parameter adaptation and/or structure adaptation are very complex they often have bad effects during the adaptation process itself converters cause harmonics leading to offset effects in combination with fast control loops the elimination of harmonics by filtering causes a time delay in the feedback and therefore leads to a less dynamic control

9 Problems of Linear Algorithms any controller optimization is a compromise making the inverter unnecessarily slow in many operation points controllers with parameter adaptation and/or structure adaptation are very complex they often have bad effects during the adaptation process itself converters cause harmonics leading to offset effects in combination with fast control loops the elimination of harmonics by filtering causes a time delay in the feedback and therefore leads to a less dynamic control

10 Typical Cascaded Structure of Drive Control position controller speed controller current controller power electronics motor windings I inertia gear etc.

11 Typical Cascaded Structure of Drive Control position controller speed controller current controller power electronics motor windings I inertia gear etc.

12 Problems of Linear Algorithms using cascaded PI(D) control most problems (= differences between theory and practical results) occur with the (inner) current control a linear controller tries to control an extremely non-linear inverter whose behaviour is depending on the modultaion method most developments of converter control deal with current control or flux control because these elements are closest to the inverter itself the behaviour of any improved current control is expected to be more linear than the inverter itself speed and position controllers can be designed as PI(D) controllers as before

13 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

14 Outline Introduction Predictive Control Methods Predictive Control versus Cascaded Control Conclusions/Discussion

15 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!!!

16 Usual Structure of Drive Control DC link PI controller

17 Usual Structure of Drive Control why PWM? linearization of the inverter consequences? very high switching frequency DC link PI controller

18 Structure of a Direct Control DC link direct controller

19 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

20 Family tree of predictive control algorithms hysteresisbasedstrategies trajectorybasedstrategies adaptive switching pattern (ASP) (Nagy) predictive current control (Holtz/Stadtfeld) PROMC current control (Kohlmeier et.al.) hysteresis control (bang bang) PROMC voltage control (Hintze) space vector control (Kazmierkowski, et.al.) adaptive and optimized regulator (Ackva, et.al.) direct current control (Pfaff/Wick) current control method (Salama et.al) space vector control (Wuest/Jenni) direct torque control (DTC) (Takahashi/Nogushi) (Tiitinen/Lalu) direct torque control (DTC) (Chapuis, et.al.) multilevel hysteresis DTC (Purcell/Acarnley) direct mean torque control (DMTC) (Flach, et.al.) torque pulsation reduced DTC (Vas, et.al.) DTC + dithering (Noguchi, et.al.) DTDTC (Maes/Melkebeek) DTC with ORS (Moucary et.al.) DTC-PPWC (Nillesen et.al.) new direct torque control (Kang/Sul) DTC-SVM (Lascu et.al.) DTC with reduction of torque ripple (La/Shin/Hyun) DTC-DSVM (Casadei et.al) vectorial torque control (Attaianese, et.al.) sliding mode control (Emeljanov) direct self control (DSC) (Depenbrock) optimal on-line-tuning current regulator (du Toit Mouton/Enslin) predictive current control for resonant link inverter (Oh/Jung/Youn) integral space-vector PWM (Trzynadlowski, et.al.) direct speed control (DSPC) (Mutschler) direct self control (DSC) (Bonanno, et.al.) digital current controller (Betz/Cook/Henriksen) 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)

21 Family tree of predictive control algorithms Part 2 MPC Continuous-Set-Model based strategies Finite-Set-Model based strategies DMC (Cutler/Ramaker) GPC (Clarke) Fast online optimization Explicit MPC (Bemporad) Dead beat control (Lee) CRHPC (Clarke/Scattolini) GPC--PID (Nakano) GPC for motor control (Linder/Kennel) Fast gradient method for converter control (Richter/Morari) LP solution for quadratic cost (Stumper/Kennel) MPC with MPT (Kvasnica) MPC for PMSM (Kuehl/Bolognani/Kennel) MPTC (Rodriguez) Predictive current control (Rodriguez) Predictive speed control (Fuentes/Rodriguez/Kennel) Heuristic direct MPC (Stolze/Kennel) Sensorless MPC (Wojciechowski/Strzelecki) Saliency based encoderless PTC (Landsmann/Kennel) Observer-based sensorless PTC (Davari/Wang/Kennel) Weighting factors design (Cortes/Rodriguez) Weighting factor optimization (Davari/Kennel) 2-steps MPC of 3 phase UPS inverter (Cortes/Rodriguez) FPGA-based PCC (Naouar/Monmasson) Modular multilevel converter (Perez/Rodriguez) Direct matrix converter (Vargas/Rodriguez) Indirect matrix converter (Correa/Rodriguez/Espinoza) 2L-VSI (Cortes/Rodriguez) 3L-NPC (Geyer/Rodriguez) CHB (Perez/Rodriguez/Cortes) Flying capacitor converter (Lezana/Aguilera/Quevedo) Current source rectifier (Correa/Rodriguez) ac-ac converter dc-ac converter ac-dc converter dc-dc converter (Geyer/Morari)

22 Outline Introduction Predictive Control Methods (Kennel) Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection

23 Outline Introduction Predictive Control Methods (Kennel) Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection

24 Example : Trajectory Based Predictive Control Predictive Current Control acc. to Kennel DC drive supplied by a line commutated thyristor inverter U 0 grid = - - -

25 Example : Trajectory Based Predictive Control Predictive Current Control acc. to Kennel

26 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

27 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

28 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

29 Example : Trajectory Based Predictive Control Direct Self Control (DSC) acc. to Depenbrock

30 Example : Hysteresis Based Predictive Control Direct Self Control acc. to Takahashi

31 Outline Introduction Predictive Control Methods (Kennel) Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection

32 Hysteresis Based Predictive Control Strategies switching of inverter takes place at the (multi-dimensional) border(s) of a hysteresis area

33 Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz

34 Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz

35 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

36 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

37 Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz

38 Comparison of different predictive control schemes

39 Flux Trajectories 10 Hz fundamental frequency 500 Hz switching frequency standard PWM DSC (Depenbrock) bang-bang control DSC (Takahashi) 7 % hysteresis predictive control (Holtz) DSC (Takahashi) 2 % hysteresis source Andreas Haun, Vergleich von Steuerverfahren, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:

40 Flux Trajectories 40 Hz fundamental frequency 500 Hz switching frequency standard PWM DSC (Depenbrock) bang-bang control DSC (Takahashi) 7 % hysteresis predictive control (Holtz) DSC (Takahashi) 2 % hysteresis source Andreas Haun, Vergleich von Steuerverfahren, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:

41 Stator Current Trajectories 40 Hz fundamental frequency 500 Hz switching frequency standard PWM DSC (Depenbrock) bang-bang control DSC (Takahashi) 7 % hysteresis predictive control (Holtz) DSC (Takahashi) 2 % hysteresis source Andreas Haun, Vergleich von Steuerverfahren, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:

42 Frequency Spectrum of Torque a) 40 Hz fundamental frequency 250 Hz switching frequency b) 45 Hz fundamental frequency 500 Hz switching frequency 1. standard PWM 2. bang-bang control 3. predictive control (Holtz) 4. DSC (Depenbrock) 5. DSC (Takahashi) with 7 % hysteresis source Andreas Haun, Vergleich von Steuerverfahren, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:

43 Additional Losses under Inverter Supply a) variable fundamental frequency 500 Hz switching frequency b) 40 Hz fundamental frequency variable switching frequency 1. standard PWM 2. bang-bang control 3. predictive control (Holtz) 4. DSC (Depenbrock) 5. DSC (Takahashi) with 7 % hysteresis 6. DSC (Takahashi) with 7 % hysteresis source Andreas Haun, Vergleich von Steuerverfahren, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:

44 Outline Introduction Predictive Control Methods (Kennel) Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection

45 predictive control categories another way of distinction switching control SVM (space vector modulation) directly steps of prediction (prediction horizon) 1 direct control of IM currents DFC DTC DSC DSPC DMC DMPC >1 GPC

46 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

47 Model Predictive Control History Future Page 47

48 Model Predictive Control Overview Page 48

49 Direct Model Predictive Control System Model / Cost Function

50 Direct Model Predictive Control System Model / Cost Function

51 Characteristics of Model Based Predictive Control basic ideas are derived from state-space control the past is explicitely considered (mostly by the system state) future control values are pre-calculated and optimized the first of the precalculated control values only model parameters can be estimated on-line until a (pre-)defined horizon is transmitted to the controlled system extension to MIMO-control is possible with little additional effort use of non-linear model is possible for non-linear control systems a lot of calculation power is required

52 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

53 Model Based Predictive Current Control complete enumeration extensive processing power needed there are 7 (or 8) possiblities for the following switching state the respective system behaviour (current) can be calculated in advance a chess player, however, does not really consider each possibility

54 Model Based Predictive Current Control complete enumeration extensive processing power needed there are 7 (or 8) possiblities for the following switching state the respective system behaviour (current) can be calculated in advance so why should we do that in predictive control???

55 Model Based Predictive Current Control further prediction, however, is only considered for the candidate sequences staying within the permitted limits so why should we do that in predictive control???

56 Model Based Predictive Current Control determine those switching possibilities only that are either feasible or point in the proper direction these are candidate sequences feasible pointing in the proper direction

57 Model Based Predictive Current Control determine those switching possibilities only that are either feasible or point in the proper direction these are candidate sequences not feasible not pointing in the proper direction

58 Model Based Predictive Current Control for the candidate sequences, further prediction (e. g. by a reduced system model) is performed example : the number of steps after which the first of the two variables the i sa and i isb leaves the feasible region is the number h

59 Model Based Predictive Current Control for the candidate sequences, further prediction (e. g. by a reduced system model) is performed example : the number of steps after which the first of the two variables the i sa and i isb leaves the feasible region is the number h h1 = 4 h 1 = 4

60 Model Based Predictive Current Control for the candidate sequences, further prediction (e. g. by a reduced system model) is performed example : the number of steps after which the first of the two variables the i sa and i isb h1 = 4 is the number h h2 leaves the feasible region = 10

61 Different Way of Thinking in Model Based Predictive Control 1. model of the controlled system this is no difference to conventional control the better the model, the better the prediction 2. cost function the engineer has to learn to describe what he wants the controlled system really to do!!! 3. stability that s a really good question next question? Page 61

62 Experimental Results (DMPC) current control comparison : PI control model predictive control

63 Experimental Results (DMPC) current control Low switching frequency high switching frequency dynamic of step response is identical!

64 Experimental Results (DMPC) current control a change of the cost function (nothing else!!!) results in different behaviour!

65 Features of (Longe Range) Predictive Control Advantages possibility to use foreknowledge about drive system (system model) 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 high processing capability required for industrial use change in teaching engineers necessary stationary accuracy and dynamic behaviour depend on accurracy of model parameters

66 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 more investigations should be done Page 66

67 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 more investigations should be done

68 Outline Introduction Predictive Control Methods (Kennel) Trajectory Based Predictive Control Hysteresis Based Predictive Control Long-Range Predictive Control Predictive Control with Heuristic Preselection

69 Control task Current control of a three-phase resistive-inductive-active load

70 Heuristic method 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 : Peter Stolze 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

71 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

72 Simulation Results Sinusoidal references Back EMF voltages R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs

73 Finite-Set Model Predictive Control of a Flying Capacitor Converter with Heuristic Voltage Vector Preselection Peter Stolze

74 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

75 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

76 Simulation Results Sinusoidal references Flying capacitor voltages R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF

77 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

78 Outline Introduction Predictive Control Methods Predictive Control versus Cascaded Control Conclusions/Discussion

79 State of the Art : Field Oriented Control r field coordinates stator coordinates mains flux controller speed controller i s current controllers e j e -j u s PWM 6 i s u s r model M 3~ encoder

80 Typical Cascaded Structure of Drive Control position controller speed controller current controller power electronics motor windings I inertia gear etc.

81 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

82 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.

83 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

84 Outline Introduction Predictive Control Methods Predictive Control versus Cascaded Control Conclusions/Discussion

85 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

86 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

87 Thank you!