Secondary Control of Discrete Displacement Cylinder

Nielsen, Anders ; Langkjær, Jens-Kristian Egsgaard ; Richter, Carl Christian Lund

4. term

Energy Engineering, Master

2016

186

Denne afhandling undersøger, om det er muligt at udvikle en optimal styringsstrategi for en sekundærstyret diskret slagvolumencylinder, der afvejer sporingspræcision mod energitab forårsaget af skift mellem diskrete trykniveauer. Ud fra en state-of-the-art-analyse formuleres hypotesen og der udvikles et detaljeret ikke-lineært modelgrundlag, som valideres mod eksperimentelle data. Systemets diskrete natur påviser grænsecirkler og udfordringer ved lastholdning, og begrænsninger i den fysiske testopstilling fører til en syntetisk anvendelsescase til evaluering. En ikke-lineær Model Predictive Control (NMPC) baseret på en reduceret diskret tidsmodel (med negligerede trykdynamikker), en vægtet omkostningsfunktion for sporingsfejl og skifteenergitab samt fysiske begrænsninger viser tæt på global optimalitet, men er ikke realtidsimplementerbar pga. beregningskrav. En eksplicit MPC udledes som en stykkevist konstant tilstandsrumsløsning, der approksimerer NMPC og i simulering reducerer skifteenergitab samtidig med god positions- og hastighedssporing. Til sammenligning udvikles lineære regulatorer; anti-windup fjerner grænsecirkler for hastighedsstyring mod en lille stationær fejl. Samlet viser simuleringer, at NMPC og eksplicit MPC kan reducere skifteenergitab markant ift. lineær styring med lignende eller bedre sporingspræstation, hvilket indikerer, at positions- og hastighedsstyring af en sekundærstyret diskret slagvolumencylinder er mulig. Alle resultater for regulatorerne stammer fra simulering på den udviklede model.

This thesis investigates whether an optimal control strategy can be devised for a secondary-controlled discrete displacement cylinder that balances tracking performance against energy losses from switching between discrete pressure levels. Building on a state-of-the-art review, a detailed nonlinear model is developed and validated against experimental data. The system’s discrete nature leads to limit cycles and load-holding challenges; constraints of the available test rig motivate a synthetic application case for evaluation. A Nonlinear Model Predictive Control (NMPC) scheme is formulated on a reduced discrete-time model (neglecting pressure dynamics), with a cost function penalizing tracking error and switching losses under physically motivated constraints; it yields a near-globally optimal solution but is not real-time implementable due to computational demands. An explicit MPC is then derived as a piecewise-constant state-space policy that approximates NMPC and, in simulation, reduces switching losses while maintaining good position and velocity tracking. For comparison, linear controllers are designed; anti-windup removes limit cycles in velocity control at the cost of a small steady-state error. Overall, simulations show that NMPC and explicit MPC significantly reduce switching losses relative to linear control with similar or improved tracking, indicating that position and velocity control of a secondary-controlled discrete displacement cylinder is feasible. All controller results are obtained in simulation on the developed model.

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Mode Predictive Control

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