Event-Driven Control of a Speed Varying Digital Displacement Machine

Abstract

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.

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

“…The displacement fraction is converted into a cylinder actuation sequence by a first-order delta-sigma modulator, which determines whether the current cylinder shall be active or inactive. This method was first proposed by Johansen et al [23] and later used in several control papers [5,[7][8][9]. A block diagram of the controller is shown in Figure 3.…”

“…There were in all three pressure transmitters mounted on the valve block. They measured the pressure in the low pressure source (5), high pressure source (6), and in the cylinder chamber (7). For safety reasons, a pressure relief valve with anti-cavitation function (8) was connected to the cylinder chamber to avoid very high cylinder chamber pressure and cavitation.…”

“…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.…”

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

“…To allow for model based closed loop control design, a Discrete Linear Time Invariant (DLTI) approximation to the digital machine dynamics is developed by Johansen et al (2017) for constant speed operation. To expand the use of this method to be applicable for variable speed operation, Pedersen et al (2017a) transform the DLTI model to the spatial domain, resulting in a fixed angle sampling rate allowing for classical control synthesis. A combination of the PDM technique and the DLTI model is further used for control of a digital fluid power transmission by Pedersen et al (2017bPedersen et al ( , 2018b.…”

“…The MPC control strategy is tested for both flow and pressure control by simulation in a non-linear model representing the physical system. A fixed speed pump unit is considered in this paper, but the strategy is also applicable to variable speed pump-motor units by the spatial domain transformation method presented by Pedersen et al (2017a).…”