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.
Research within digital fluid power (DFP) transmissions is receiving an increased attention as an alternative to conventional transmission technologies. The use of DFP displacement machines entails a need for applicable control algorithms. However, the design and analysis of controllers for such digital systems are complicated by its non-smooth behavior. In this paper a control design approach for a digital displacement machine® is proposed and a performance analysis of a wind turbine using a DFP transmission is presented. The performance evaluation is based on a dynamic model of the transmission with a DFP motor, which has been combined with the NREL 5-MW reference wind turbine model. A classical variable speed control strategy for wind speeds below rated is proposed for the turbine, where the pump displacement is fixed and the digital motor displacement is varied for pressure control. The digital motor control strategy consists of a full stroke operation strategy, where a Delta-Sigma pulse density modulator is used to determine the chamber activation sequence. In the LQR-control design approach, the discrete behavior of the motor and Delta-Sigma modulator is described by a discrete linear time invariant model. Using full-field flow wind profiles as input, the design approach and control performance is verified by simulation in the dynamic model of the wind turbine featuring the DFP transmission. Additionally, the performance is compared to that of the conventional NREL reference turbine, transmission and controller.
The design and analysis of feedback controllers for digital displacement machines requires a control oriented model. The displacement throughput of a full stroke operated machine is altered on a stroke-by-stroke basis at fixed rotation angles. In the case of a fixed speed operation, it may be treated as a Discrete Linear Time Invariant control problem with synchronous sampling rate. To make synchronous linear control theory applicable for a variable speed digital displacement machine, a method based on event-driven control is presented. Using this method, the time domain differential equations are converted into the spatial (position) domain to obtain a constant sampling rate and thus allowing for use of classical control theory. The method is applied to a down scaled digital fluid power motor, where the motor speed is controlled at varying references under varying pressure and load torque conditions. The controller synthesis is carried out as a discrete optimal deterministic problem with full state feedback. Based on a linear analysis of the feedback control system, stability is proven in a pre-specified operation region. Simulation of a non-linear evaluation model with the controller implemented shows great performance, both with respect to tracking and disturbance rejection.
This paper investigates the many complications arising when controlling a digital displacement hydraulic machine with non-smooth dynamical behavior. The digital hydraulic machine has a modular construction with numerous independently controlled pressure chambers. For proper control of dynamical systems, a model representation of the systems fundamental dynamics is required for transient analysis and controller design. Since the input is binary (active or inactive) and it may only be updated discretely, the machine comprises both continuous and discrete dynamics and therefore belongs to the class of hybrid dynamical systems. The study shows that the dynamical system behavior and control complexity are greatly dependent on the configuration of the machine, the operation strategy, and in which application it is used. Although the system has non-smooth dynamics, the findings show that simple continuous and discrete approximations may be applicable for control development in certain situations, whereas more advanced hybrid control theory is necessary to cover a broader range of situations.
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