Constrained control of free piston engine generator based on implicit reference governor
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摘要
The free piston engine generator(FPEG) is a novel power plant concept for series hybrid electric vehicles(HEV) that requires reliable control to regulate piston motion and guarantee safe operation during load transitions. This paper focuses on the control and constraint enforcement in a FPEG using a reference governor. A discrete, implicit, control oriented model describing the piston motion in a two-stroke twocylinder FPEG at the turnaround point is derived based on energy balance and a feedback controller is designed to track the desired turnaround position by regulating fuel. An implicit reference governor is developed to guarantee safe piston motion by managing the load transitions. The reference governor utilizes Newton's method applied to an implicit nonlinear model for response prediction and a bisection search algorithm to enforce the constraints for all the future time instants by adjusting the reference command.Additionally, the error in applying one iteration of Newton's method in predicting the response of the implicit nonlinear system is estimated and accounted for in constraint tightening to guarantee that constraints are robustly enforced. The simulation results show that the feedback control scheme incorporating the developed implicit reference governor can effectively enforce the prescribed constraints during load transition.
The free piston engine generator(FPEG) is a novel power plant concept for series hybrid electric vehicles(HEV) that requires reliable control to regulate piston motion and guarantee safe operation during load transitions. This paper focuses on the control and constraint enforcement in a FPEG using a reference governor. A discrete, implicit, control oriented model describing the piston motion in a two-stroke twocylinder FPEG at the turnaround point is derived based on energy balance and a feedback controller is designed to track the desired turnaround position by regulating fuel. An implicit reference governor is developed to guarantee safe piston motion by managing the load transitions. The reference governor utilizes Newton's method applied to an implicit nonlinear model for response prediction and a bisection search algorithm to enforce the constraints for all the future time instants by adjusting the reference command.Additionally, the error in applying one iteration of Newton's method in predicting the response of the implicit nonlinear system is estimated and accounted for in constraint tightening to guarantee that constraints are robustly enforced. The simulation results show that the feedback control scheme incorporating the developed implicit reference governor can effectively enforce the prescribed constraints during load transition.
The free piston engine generator(FPEG) is a novel power plant concept for series hybrid electric vehicles(HEV) that requires reliable control to regulate piston motion and guarantee safe operation during load transitions. This paper focuses on the control and constraint enforcement in a FPEG using a reference governor. A discrete, implicit, control oriented model describing the piston motion in a two-stroke twocylinder FPEG at the turnaround point is derived based on energy balance and a feedback controller is designed to track the desired turnaround position by regulating fuel. An implicit reference governor is developed to guarantee safe piston motion by managing the load transitions. The reference governor utilizes Newton's method applied to an implicit nonlinear model for response prediction and a bisection search algorithm to enforce the constraints for all the future time instants by adjusting the reference command.Additionally, the error in applying one iteration of Newton's method in predicting the response of the implicit nonlinear system is estimated and accounted for in constraint tightening to guarantee that constraints are robustly enforced. The simulation results show that the feedback control scheme incorporating the developed implicit reference governor can effectively enforce the prescribed constraints during load transition.
引文
[1] Mikalsen R,Roskilly A P.A review of free-piston engine history and applications.Appl Therm Eng,2007,27:2339–2352
2 Mikalsen R,Roskilly A P.The control of a free-piston engine generator.Part 1:fundamental analyses.Appl Energ,2010,87:1273–1280
3 Mikalsen R,Roskilly A P.The control of a free-piston engine generator.Part 2:engine dynamics and piston motion control.Appl Energ,2010,87:1281–1287
4 Kosaka H,Akita T,Moriya K,et al.Development of Free Piston Engine Linear Generator System.Part 1:Investigation of Fundamental Characteristics.SAE Technical Paper 2014-01-1203,2014
5 Goto S,Moriya K,Kosaka H,et al.Development of Free Piston Engine Linear Generator System.Part 2:Investigation of Control System for Generator.SAE Technical Paper 2014-01-1193,2014
6 Li K,Sadighi A,Sun Z X.Active motion control of a hydraulic free piston engine.IEEE/ASME Trans Mech,2014,19 :1148–1159
7 Lin J M,Xu Z P,Chang S Q,et al.Thermodynamic simulation and prototype testing of a four-stroke free-piston engine.J Eng Gas Turb Power,2014,136:051505
8 Jia B,Zuo Z,Feng H,et al.Effect of closed-loop controlled resonance based mechanism to start free piston engine generator:simulation and test results.Appl Energ,2016,164:532–539
9 Gong X,Zaseck K,Kolmanovsky I,et al.Dual-loop control of free piston engine generator.IFAC-Papers On Line,2015,48 :174–180
10 Gong X,Zaseck K,Kolmanovsky I,et al.Modeling and predictive control of free piston engine generator.In:Proceedings of American Control Conference,Chicago,2015.4735–4740
11 Zaseck K,Brusstar M,Kolmanovsky I.Stability,control,and constraint enforcement of piston motion in a hydraulic free-piston engine.IEEE Trans Control Syst Technol,2017,25:1284–1296
12 Gong X,Hu Y F,Yang R B,et al.Piston motion control of free piston engine based on iterative reference governor.Control Theory Appl,2017,3:188–196
13 Zaseck K,Kolmanovsky I,Brusstar M.Constraint enforcement of piston motion in a free-piston engine.In:Proceedings of American Control Conference,Portland,2014.1487–1492
14 Yang R B,Gong X,Hu Y F,et al.Motion control of free piston engine generator based on LQR.In:Proceedings of Chinese Control Conference,Hangzhou,2015.8091–8096
15 Garone E,Di Cairano S,Kolmanovsky I.Reference and command governors for systems with constraints:a survey on theory and applications.Automatica,2017,75:306–328
16 Kapasouris P,Athans M,Stein G.Design of feedback control systems for stable plants with saturating actuators.In:Proceedings of the 27th IEEE Conference on Decision and Control,Austin,1988.469–479
17 Gilbert E,Kolmanovsky I,Tan K T.Nonliner control of discrete-time linear systems with state and control constraints:a reference governor with global convergence properties.In:Proceedings of the 33rd IEEE Conference on Decision and Control,Lake Buena Vista,1994.144–149
18 Gilbert E G,Tan K T.Linear systems with state and control constraints:the theory and application of maximal output admissible sets.IEEE Trans Autom Control,1991,36:1008–1020
19 Gilbert E G,Ong C J.Constrained linear systems with hard constraints and disturbances:an extended command governor with large domain of attraction.Automatica,2011,47:334–340
20 Kolmanovsky I,Gilbert E G.Theory and computation of disturbance invariant sets for discrete-time linear systems.Math Probl Eng,1998,4:317–367
21 Gilbert E G,Kolmanovsky I,Tan K T.Discrete-time reference governors and the nonlinear control of systems with state and control constraints.Int J Robust Nonlinear Control,1995,5:487–504
22 Bemporad A.Reference governor for constrained nonlinear systems.IEEE Trans Autom Control,1998,43:415–419
23 Kalabic U,Kolmanovsky I.Reference and extended command governors for control of turbocharged gasoline engines based on linear models.In:Proceedings of IEEE International Conference on Control Applications,Denver,2011.319 –325
24 Gilbert E,Kolmanovsky I.Set-point control of nonlinear systems with state and control constraints:a Lyapunov function reference governor approach.In:Proceedings of the 38th IEEE Conference on Decision and Control,Phoenix,1999.2507–2512
25 Miller R H,Kolmanovsky I,Gilbert E G,et al.Control of constrained nonlinear systems:a case study.IEEE Control Syst Mag,2000,20:23–32
26 Sun J,Kolmanovsky I V.Load governor for fuel cell oxygen starvation protection:a robust nonlinear reference governor approach.IEEE Trans Control Syst Technol,2005,13:911–920
27 Kailath T.Nonlinear Systems.Englewood Cliffs:Prentice-Hall,2002
28 Gilbert E,Kolmanovsky I.Nonlinear tracking control in the presence of state and control constraints:a generalized reference governor.Automatica,2002,38:2063–2073
29 Hubbard J H,Hubbard B H.Vector Analysis,Linear Algebra,and Differential Forms:A Unified Approach.Ithaca:Matrix Editions,2001
2 Mikalsen R,Roskilly A P.The control of a free-piston engine generator.Part 1:fundamental analyses.Appl Energ,2010,87:1273–1280
3 Mikalsen R,Roskilly A P.The control of a free-piston engine generator.Part 2:engine dynamics and piston motion control.Appl Energ,2010,87:1281–1287
4 Kosaka H,Akita T,Moriya K,et al.Development of Free Piston Engine Linear Generator System.Part 1:Investigation of Fundamental Characteristics.SAE Technical Paper 2014-01-1203,2014
5 Goto S,Moriya K,Kosaka H,et al.Development of Free Piston Engine Linear Generator System.Part 2:Investigation of Control System for Generator.SAE Technical Paper 2014-01-1193,2014
6 Li K,Sadighi A,Sun Z X.Active motion control of a hydraulic free piston engine.IEEE/ASME Trans Mech,2014,19 :1148–1159
7 Lin J M,Xu Z P,Chang S Q,et al.Thermodynamic simulation and prototype testing of a four-stroke free-piston engine.J Eng Gas Turb Power,2014,136:051505
8 Jia B,Zuo Z,Feng H,et al.Effect of closed-loop controlled resonance based mechanism to start free piston engine generator:simulation and test results.Appl Energ,2016,164:532–539
9 Gong X,Zaseck K,Kolmanovsky I,et al.Dual-loop control of free piston engine generator.IFAC-Papers On Line,2015,48 :174–180
10 Gong X,Zaseck K,Kolmanovsky I,et al.Modeling and predictive control of free piston engine generator.In:Proceedings of American Control Conference,Chicago,2015.4735–4740
11 Zaseck K,Brusstar M,Kolmanovsky I.Stability,control,and constraint enforcement of piston motion in a hydraulic free-piston engine.IEEE Trans Control Syst Technol,2017,25:1284–1296
12 Gong X,Hu Y F,Yang R B,et al.Piston motion control of free piston engine based on iterative reference governor.Control Theory Appl,2017,3:188–196
13 Zaseck K,Kolmanovsky I,Brusstar M.Constraint enforcement of piston motion in a free-piston engine.In:Proceedings of American Control Conference,Portland,2014.1487–1492
14 Yang R B,Gong X,Hu Y F,et al.Motion control of free piston engine generator based on LQR.In:Proceedings of Chinese Control Conference,Hangzhou,2015.8091–8096
15 Garone E,Di Cairano S,Kolmanovsky I.Reference and command governors for systems with constraints:a survey on theory and applications.Automatica,2017,75:306–328
16 Kapasouris P,Athans M,Stein G.Design of feedback control systems for stable plants with saturating actuators.In:Proceedings of the 27th IEEE Conference on Decision and Control,Austin,1988.469–479
17 Gilbert E,Kolmanovsky I,Tan K T.Nonliner control of discrete-time linear systems with state and control constraints:a reference governor with global convergence properties.In:Proceedings of the 33rd IEEE Conference on Decision and Control,Lake Buena Vista,1994.144–149
18 Gilbert E G,Tan K T.Linear systems with state and control constraints:the theory and application of maximal output admissible sets.IEEE Trans Autom Control,1991,36:1008–1020
19 Gilbert E G,Ong C J.Constrained linear systems with hard constraints and disturbances:an extended command governor with large domain of attraction.Automatica,2011,47:334–340
20 Kolmanovsky I,Gilbert E G.Theory and computation of disturbance invariant sets for discrete-time linear systems.Math Probl Eng,1998,4:317–367
21 Gilbert E G,Kolmanovsky I,Tan K T.Discrete-time reference governors and the nonlinear control of systems with state and control constraints.Int J Robust Nonlinear Control,1995,5:487–504
22 Bemporad A.Reference governor for constrained nonlinear systems.IEEE Trans Autom Control,1998,43:415–419
23 Kalabic U,Kolmanovsky I.Reference and extended command governors for control of turbocharged gasoline engines based on linear models.In:Proceedings of IEEE International Conference on Control Applications,Denver,2011.319 –325
24 Gilbert E,Kolmanovsky I.Set-point control of nonlinear systems with state and control constraints:a Lyapunov function reference governor approach.In:Proceedings of the 38th IEEE Conference on Decision and Control,Phoenix,1999.2507–2512
25 Miller R H,Kolmanovsky I,Gilbert E G,et al.Control of constrained nonlinear systems:a case study.IEEE Control Syst Mag,2000,20:23–32
26 Sun J,Kolmanovsky I V.Load governor for fuel cell oxygen starvation protection:a robust nonlinear reference governor approach.IEEE Trans Control Syst Technol,2005,13:911–920
27 Kailath T.Nonlinear Systems.Englewood Cliffs:Prentice-Hall,2002
28 Gilbert E,Kolmanovsky I.Nonlinear tracking control in the presence of state and control constraints:a generalized reference governor.Automatica,2002,38:2063–2073
29 Hubbard J H,Hubbard B H.Vector Analysis,Linear Algebra,and Differential Forms:A Unified Approach.Ithaca:Matrix Editions,2001