SCIENCE CHINA Information Sciences, Volume 61, Issue 7: 070203(2018) https://doi.org/10.1007/s11432-017-9337-1

## Constrained control of free piston engine generator based on implicit reference governor

• ReceivedOct 30, 2017
• AcceptedDec 29, 2017
• PublishedMay 31, 2018
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### Abstract

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 two-cylinder 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. Thereference governor utilizes Newton's method applied to an implicitnonlinear model for response predictionand a bisection search algorithm to enforce the constraints for all the future time instants byadjusting the reference command. Additionally, the error in applying one iteration of Newton's method in predictingthe 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.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61703177, 61520106008), and Jilin Provincial Science Foundation of China (Grant No. 20180101037JC).

### References

[1] Mikalsen R, Roskilly A P. A review of free-piston engine history and applications. Appl Therm Eng, 2007, 27: 2339-2352 CrossRef Google Scholar

[2] Mikalsen R, Roskilly A P. The control of a free-piston engine generator. Part 1: Fundamental analyses. Appl Energ, 2010, 87: 1273-1280 CrossRef Google Scholar

[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 CrossRef Google Scholar

[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. Google Scholar

[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. Google Scholar

[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 CrossRef Google Scholar

[7] Lin J M, Xu Z P, Chang S Q. Thermodynamic simulation and prototype testing of a four-stroke free-piston engine. J Eng Gas Turb Power, 2014, 136: 051505 CrossRef Google Scholar

[8] Jia B, Zuo Z, Feng H. Effect of closed-loop controlled resonance based mechanism to start free piston engine generator: simulation and test results. Appl Energ, 2016, 164: 532-539 CrossRef Google Scholar

[9] Gong X, Zaseck K, Kolmanovsky I. Dual-loop Control of Free Piston Engine Generator. IFAC-PapersOnLine, 2015, 48: 174-180 CrossRef Google Scholar

[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. Google Scholar

[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 CrossRef Google Scholar

[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, doi: 10.7641/CTA.2017.60575. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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 CrossRef Google Scholar

[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. Google Scholar

[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. Google Scholar

[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 CrossRef Google Scholar

[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 CrossRef Google Scholar

[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 CrossRef Google Scholar

[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 CrossRef Google Scholar

[22] Bemporad A. Reference governor for constrained nonlinear systems. IEEE Trans Autom Control, 1998, 43: 415-419 CrossRef Google Scholar

[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. Google Scholar

[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. Google Scholar

[25] Miller R H, Kolmanovsky I, Gilbert E G. Control of constrained nonlinear systems: a case study. IEEE Control Syst Mag, 2000, 20: 23-32 CrossRef Google Scholar

[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 CrossRef Google Scholar

[27] Kailath T. Nonlinear Systems. Englewood Cliffs: Prentice-Hall, 2002. Google Scholar

[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 CrossRef Google Scholar

[29] Hubbard J H, Hubbard B H. Vector Analysis, Linear Algebra, and Differential Forms: A Unified Approach. Ithaca: Matrix Editions, 2001. Google Scholar

• Figure 1

(Color online) Schematics of the proposed FPEG.

• Figure 2

(Color online) Piston position during different phases of the motion including at turn around time instants $k-1$, $k$, and $k+1$.

• Figure 3

(Color online) Control architecture of FPEG motion control system.

• Figure 4

A schematic of reference governor as applied within a closed-loop [15].

• Figure 5

Computing flow diagram of the iterative reference governor.

• Figure 6

Computing flow diagram for the one-step iterative reference governor.

• Figure 7

(Color online) Comparison between full iterative RG and one-step iterative RG. (a) The time history of clearance height, set-point and the constraints; (b) the time history of reference load and actual load.

• Figure 8

(Color online) Comparison of one-step iterative RG with different initial values. (a) The time history of clearance height, set-point and the constraints; (b) the time history of reference load and actual load.

• Figure 9

(Color online) Comparison between full iterative RG and one-step iterative RG in AMESim model. (a) The time history of clearance height, set-point and the constraints; (b) the time history of load regulation; (c) the time history of fuel regulation.

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