Model Predictive Control for Distributed Systems: Coordination Strategies & Structure

Transcription

1 The 26th Chinese Process Control Conference, 2015 Model Predictive Control for Distributed Systems: Coordination Strategies & Structure Yi ZHENG, Shaoyuan LI School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Aug. 1 st, 2015

2 Dynamic Systems Optimization Group -----Institute of Automation, Shanghai Jiao Tong University Team Member Pro. Shaoyuan Li Pro. Ning Li Associate Pro. Yi Zheng Associate Pro. Jing Wu Associate Pro. Dang Huang PhD: 14, Master: 21 Researching Fields Predictive Control for Large-Scale Systems Plant-wide optimization Fuzzy system Application of advance control

3 CONTENTS Background Coordination strategies System structure Applications Conclusion

4 Background Technology Development large scale complicated Large-scale process industry systems Chemical process Power station Sewage disposal Characteristics: More units with inputs and outputs Wide spatial distribution Couplings (Energy, mass, information) Ethylene catalytic Complicated models with constraints and multi-objects

5 Background Centralized and decentralized control systems DCS,PLC, Sensors transmitter Industrial field Cable Cable Master control room Centralized control.form H. Kirrmann s PPT (ABB)

6 Background Field bus, Intelligent instrument, Network convert of control structure and mode Network Field bus WSN Smart device Information exchange Local control separately Centralized control Distributed control systems Distributed control

7 Background Algorithms PID Robust Optimal Decoupling Application SISO MIMO Dynamic optimization Steady optimization Device1: local optimization (steady or dynamic optimization) FC High/low logic PID Lead/Lag PID SUM Device1: Decentralized PID PC TC Global steady optimization SUM LC Device2: local optimization (steady or dynamic optimization) Hierarchical structure of the industry process control From Qin s PPT FC Model Predictive control Device2: Decentralized PID PC TC LC

8 Background Large-scale system theory(1970 s) Decentralized/ Hierarchical control: Decentralized control Hierarchical control

9 Background Hierarchical Decentralized vs Distributed Model Predictive Control Time scale Hierarchical structure Distributed structure Networked distributed control systems

10 Background Optimization Steady economic optimization Real time optimization Distributed Control Time scale sp y 1 sp y 2 sp y 3 Network sp ym 1 sp y m Flexible * u 1 * * * * y1 u 2 y2 u 3 y3 u m-1 ym-1 u m ym Distributed system

11 Background Control problem of distributed large-scale system 90 Large-scale system theory European FP7 STREP project Hierarchical and Distributed Model Predictive Control of Large-Scale Systems IEEE TAC, Automatica, JPC W. B. Dunbar, IEEE TAC, 2007, 52, ; J.B. Rawlings, et. al. JPC,2008,18, ; H. Scheu, et.al. JPC, M. Farina, et.al. Automatica, 2012, 48, E. Camponogara, IEEE TAC, , R. Scattolini, JPC, 2009, 19, , Comp.&ChEng, 2013, 51, Applications in different process industry Morosana, Energy &Building, 2011 Focus on D Reactor/separator system By Al-Gherwi, JPC, 2011 hydro-power valley J. Zárate Flórez, Mathem. & Comp., 2012

12 Background hot

13 COORDINATION STRATEGIES FOR DISTRIBUTED MODEL PREDICTIVE CONTROL

14 Problems Distributed System Physically composed by many interacting small-scaled plants (Spatially distributed) Distributed control structure (communication with network) Distributed Good dynamic performance Constraints Practical Cont Cont Cont S 1 S 2 S3 Cont S * S * Cont Cont S Na-1 Cont S Na The performance of entire system under the control of D framework is not as good as that under the control of centralized yizheng@sjtu.edu.cn

15 Problems Existing Strategies of D Cataloged by Cost Function Local cost optimization min J ( k) U ik, i N 1 = min ˆ ˆ x + u + x Uik, i l= 0 ik, + lk ik, + lk Q ik, + Nk D. Jia, B.H. Krogh IEEE, TCST, 2001 X. Du, S. Li, Y. Xi, ACC, 2000 P i Iterative Nash optimality S. Li, Y. Zhang, Q. Zhu, Info. Sci Stabilized LCO-D M. Farina, R. Scattolini, Automatica, 2012 W.B. Dunbar, IEEE TAC, 2007 S 1 S 2 S3 S * S * S Na Global cost optimization Impact-region cost optimization S Na-1 yizheng@sjtu.edu.cn

16 Problems Existing Strategies of D Cataloged by Cost Function Local cost optimization Global cost optimization min J ( k) ( k ) j P U i min J ( k) U ik, i j N 1 = min xˆ u xˆ + + Uik, i l= 0 ik, + lk ik, + lk Q ik, + Nk P i Iterative Pareto optimality Venket. A. IEEE TCST, 2008 Y. Zheng, S. Li, et. Al IEEE TCST 2012 S 1 S 2 S3 S * S * S Na-1 S Na Impact-region cost optimization yizheng@sjtu.edu.cn

17 Problems Existing Strategies of D Cataloged by Cost Function ACC Process, BaoSteel Co. Ltd. by: Y. Zheng, S. Li, X. Wang JPC, 2009 Y. Zheng, S. Li, N. Li, CEP, 2011 Local cost optimization Global cost optimization Impact-region cost optimization min J ( k) U ( k ) j Pi i min J ( k) U ik, i j N 1 = min xˆ u xˆ + + Uik, i l= 0 ik, + lk ik, + lk Q ik, + Nk P i Stabilizing ICO-D (A general framework for linear systems) S. Li, Y. Zheng, Z. Lin, IEEE ASE, 2015 S 1 S 2 S3 S * S Na S * S Na-1 yizheng@sjtu.edu.cn

18 Problems With the increasing of coordination degree In most cases: Global Performance Existing Methods: Network connectivity not expected See. Al-Gherwi, et.al. JPC, (3): p Design a D which could increase coordination degree without any increasing of network connectivity?

19 Impact-Region Cost Optimization D Strategies: J i (k) Impaction to S p d i X J j (k) ¹ J i (k) Presumed states trajectory of S p d i i2 P d i S p d i downstream neighbors Optimizing the performance of impacted-region, increasing coordination degree Neighbor to neighbor communication Y. Zheng, S. Li. IFAC 2014

20 ICO-D Formulation Local Sub-system Model Assumption: There is a static feedback u i =k i x, such that the closedloop linear system is asymptotically stable. (u i =k i x i dunbar 2007 IEEE TAC, Farina2012 Automatica) Predictive Model (*) Impaction of input to its downstream neighbor

21 ICO-D Formulation Performance of each subsystem-based Assumption: A T o P A o + A T o P A d + A T d P A o < b Q=2:

22 ICO-D Formulation Optimization problem s.t. Feasibility constraint Terminal constraint m 1 = max i2 P n l = max max i2 V j 2 P i f number of elements in P i u g A ¹ l i A ij ) T P j ¹A o l i A ij 1 2 m ax l = 0; 1; ; N 1

23 ICO-D Dual-mode algorithm Controller i x ˆ ik,, uikk,: + N 1 Y 2 Check if x ε N x k x xˆ uˆ k 1 ik, + 1: k+ Nk jkk, : + N 1 k j P, j i x uˆ j1, k, j1, k: k+ N 1 k uˆ ikk, : + N 1 k x ik, CJ State Solve Calculate feedback Predictions 0 x ˆ j2, k, uj2, k: k+ N 1 k CJ2 x i ( k) No local feed-back control is also ok!

24 Analysis Assumptions There exists an initial feasible control for each subsystem Feasibility X l s = 1 l s jjx i ;k + s jk x i ;k + s jk 1 jj 2» " 2 p mm 1 u u, l = 1,, N 1 f ik, + l 1 k 1 ik, + l 1 k = f i ik, + N 1 k Kx, l= N Theorem 1: suppose that above assumption hold, xk ( 0) Xand all k > 1 f f constraint are satisfied. Then the control and state pair ( u, x ) is a feasible solution to ICO-D at every update ikk, : + N 1 k k+ 1: k+ Nki,

25 Analysis Stability Theorem 2: suppose that above assumption hold, xk ( 0) X and all constraints are satisfied, and the following parametric condition hold (N 1) ¹ 1 2 < 0 Then, by application of ICO-D algorithm, the closed loop system is asymptotically stabilized to the origin. Proof: details Please see the paper : Impacted-Region Optimization for Distributed Model Predictive Control Systems with Constraints

26 Simulation Multi-zone Building Temperature Regulation System Subsystem models:

27 Simulation Comparison with LCO-D, CD The evolution of the states under the centralized, LCO-D and ICO-D

28 Simulation Comparison with LCO-D, CD State square errors under each controller e x e e CD CD ICO-D: 3.04 (28.83%) LCO-D: (679.89%) Required network connectivity of each controller

29 SYSTEM STRUCTURE OF STABILIZED DISTRIBUTED MODEL PREDICTIVE CONTROL

30 Problem Large-scale complicated distributed systems Internet plus, cyber physics system, Industrial 4.0 Requires: Non global Information based asymptotically stabilized D with constraints! Global cost optimization Global information Stabilizing Non-global information (LCO, ICO) Non-global information based Assumption strictly present difficult Our Solution: Control structure design

31 System Structure Design Mass and energy coupling Steam flow Burning coal System Main pressure Load Improve performance through reasonable structure design Different structures for different control purposes

32 System Structure Design Structural characteristics of the information layer X X X X X X X X X X X Adjacency matrix Structure Knowledge Casual logic min ε Interaction (Strong, weak); Controllability; Observability. Ref: Theory of large-scale systems, Yugeng Xi Control for complex system, A. Zeˇcevi c & D.D. Šiljak.

33 System Structure Design Process network model for large-scale system Computers and Chemical Engineering 32 (2008) Bond-graph of mass and energy balance Easy performance analysis: closed-loop dissipativity condition Precondition: system structure design by the coupling relationship between mass and energy

34 Structure of Stabilized D Global Information is not necessary! GCO-D GCO-D GCO-D Information network GCO-D Iterative ICO-D Communication once Physical network

35 System decomposition Structure model x( k + 1) = Ax( k) A ij 1, = 0, if i is affected by j if i is not affected by j Advantages: Qualitative research Simple expression and easy to get Logic calculation Uniform model for nonlinear systems (Taylor series approximate) A = Adjacency matrix

36 System decomposition Dynamic system structural model A x( k + 1) = Ax( k) + Bu( k) y( k) = Cx( k) Adjacency matrix for dynamic system a x u y T T x A 0 C = T u B 0 0 y N-step Adjacency Matrix xak, + 1 A B 0 xak, uak, + 1 = uak, y C 0 0 y ak, ak, 1 State state State output Input state Input output T N 1 T N 2 T ( A + I) 0 ( A + I) C R=( I Aa ) = B ( A + I) I B ( A + I) C 0 0 I N 1 T T N 2 T T N 3 T

37 Controllability of subsystems G c Structure Controllability Condition 1 Condition 2 System is controllable, if and only if 2 gr( G ) = n B I A B I A = B I A B c System is controllable, if and only if 1. Input reachable 2. gr([ A B]) = n gr( A) = max( rank( A)) Is the maxim rank of numerical matrices related to the structural matrix

38 APPLICATIONS OF DISTRIBUTED MODEL PREDICTIVE CONTROL

39 Laminar Cooling Process Heavy Plate Mill, Baoshan Irion & Steel Co. Ltd. Control objective Cooling curve of strip Final temperature Average temperature Manipulated variables Strip speed Water fluxes of jet State of cooling water jet

40 Laminar Cooling Process Control structure Applied result FT qualification rate: 60% 85% Hit rate of finished strip: 80% 95% Production: ton/hour (Zheng & Li, JPC, 2009)

41 Micro-Grid Energy Management System Renewable energy Grid Distributed generation Renewable energies (wind turbine, photovoltaic) Adjustable energy (diesel engine, gas turbine) Storage Storage battery Loads Shift-able loads Un-adjustable loads Distributed Generation Wind turbine Photovoltaic Adjustable energy Gas turbine Diesel engine Storage battery Shift able loads Un-adjustable loads Energy storage Loads Micro-grid Structure of Wuning Technical Park, Shanghai, China

42 Micro-Grid Energy Management System Control strategy Multi-objective D Economic, pollution, peak value Initialization

43 Micro-Grid Energy Management System Numeric results

44 Reference E. Camponogara, D. Jia, B.H. Krogh, and S. Talukdar, Distributed Model Predictive Control, IEEE Control Systems Magazine, vol. 22, no. 1, pp , Li, S., Y. Zhang, and Q. Zhu, Nash-optimization enhanced distributed model predictive control applied to the Shell benchmark problem. Information Sciences, (2 4): p Venkat, A.N., et al., Distributed Strategies With Application to Power System Automatic Generation Control. IEEE Transactions on Control Systems Technology, (6): p W.B. Dunbar, Distributed Receding Horizon Control of Dynamically Coupled Nonlinear Systems, IEEE Trans. on Automatic Control, vol. 52, no. 7, pp , M. Farina and R. Scattolini, Distributed predictive control: A non-cooperative algorithm with neighbor-to-neighbor communication for linear systems, Automatica, vol. 48, no. 6, pp , 2012.

45 Conclusion & Future Work Conclusion D algorithm which could increase coordination degree without any increasing of network connectivity Structure decomposition which provide an implementation framework for large scale coupling systems Future work Non global communication based constraint D with guaranteeing of stabilization?

46 Thanks for your attention!