Model Predictive Control of Low-Speed Partial Stroke Operated Digital Displacement Pump Unit

Abstract

To enhance the use of the Digital Displacement Machine (DDM) technology as the future solution for low speed fluid power pump and motor units, a Model Predictive Control (MPC) strategy is presented. For a low speed DDM, the conventional full stroke operation strategy is unsuitable, since the control update rate is proportional to the machine speed. This creates an incentive to utilize sequential partial stroke operation where a fraction of the full stroke is used, which thereby increases the control update rate and control signal resolution. By doing this, the energy loss is increased and may become undesirable large if the control objective is purely set-point tracking, why a trade-off is considered advantageous. Discretizing the full stroke based on a chosen update rate results in a Discrete Linear Time Invariant (DLTI) model of the system with discrete input levels. In this paper, the Differential Evolution Algorithm (DEA) is used to determine the optimal control input based on the trade-off between set-point tracking and energy cost in the prediction horizon. The paper presents a flow and a pressure control strategy for a fixed speed digital displacement pump unit and shows the trade-off influence on the optimal solution through simulation. Results show the applicability of the control strategy and indicate that a much higher energy efficiency may be obtained with only a minor decrease in tracking performance for pressure control.

Dynamic Response of a Digital Displacement Motor Operating with Various Displacement Strategies

“…Fifty percent displacement corresponds to changing the cylinder state from active to inactive when θ cyl,i = π/2. From Equation (11), it can be seen that at this shaft position, the torque contribution is at its highest. The smoothest output torque occurred when operating with very high or very low displacement ratios, meaning that the valves were switched close to TDC or BDC where the torque contribution from each cylinder was low.…”

“…The high pressure line was used to supply the modified cylinder chamber, and the intermediate pressure line was used to supply the four remaining cylinder chambers and for flushing of the machine casing by using the flow control valve (9). During motor operation, the 4/2 directional control valve (2) was set opposite of drawn, the gate valve (11) was open, the pressure relief valve (5) was set to high pressure level, and the remaining cylinder chambers were short circuited by setting the 3/2 directional control valve (7) opposite of drawn. The accumulators were used to reduce the pressure oscillations introduced by the digital displacement operation.…”

“…Both continuous, discrete, and hybrid dynamical system approximations have been investigated. The continuous and discrete approximations are sufficient to describe the fundamental dynamics if the number of cylinders and displacement fraction is sufficiently high [5][6][7][8][9][10][11]. In the case of applying linear control theory on a variable speed unit, the shaft speed of the machine should not be lower than the speed used during linearization of the system.…”

Challenges with Respect to Control of Digital Displacement Hydraulic Units

“…Similarly to partial stroke operation, MPC has a high potential for sequential partial stroke operation, since energy efficiency and pressure ripples become increasingly important with an increased number of switchings. MPC for a sequential partial stroke operated DDM is very similar to conventional MPC control of continuous dynamical systems, since the input may be updated at every sample Pedersen et al (2018e). However, the input is limited to be a discrete set of displacements, which requires optimization algorithms capable of handling such problem.…”

Hardware-in-the-Loop Validation of Model Predictive Control of a Discrete Fluid Power Power Take-Off System for Wave Energy Converters

“…MPC strategies have been proposed in, for example, References [17,18] for digital fluid power systems but also in this research area the lack of experimental validation and tests are distinct. This lacking validation of MPC algorithms including physical based loss models exists both in the field of wave energy and digital fluid power system.…”