A REVIEW OF SWITCHED INERTANCE HYDRAULIC CONVERTER TECHNOLOGY

Digital hydraulics is a new technology providing an alternative to conventional proportional or servovalve-controlled systems in the area of fluid power. Digital hydraulic applications, such as digital pumps, digital valves and actuators, switched inertance hydraulic converters (SIHCs) and digital hydraulic power management systems, promise high-energy efficiency and less contamination sensitivity. Research on digital hydraulics is driven by the need for highly energy efficient hydraulic machines but is relatively immature compared to other energy-saving technologies. This review introduces the development of SIHCs particularly focusing on the work being undertaken in the last 15 years and evaluates the device configurations, performance and control strategies that are found in current SIHC research. Various designs for high-speed switching valves are presented, and their advantages and limitations are compared and discussed. Current limitations of SIHCs are discussed and suggestions for the future development of SIHCs are made. This review is an extended version of a paper presented at the BATH/ASME 2018 Symposium on Fluid Power and Motion Control [1].


INTRODUCTION
Digital hydraulic systems, such as digital pumps, valves and actuators, switched inertance hydraulic converters (SIHCs) and digital hydraulic power management systems, promise high energy efficiency and control flexibility. Unlike conventional hydraulic servo systems, which are widely used for precise control in hydraulics, digital hydraulic systems have the potential to be more cost-efficient, robust and less sensitive to contamination.
The SIHC concept is a sub-domain of digital hydraulics. An SIHC normally consists of high-speed switching valves, inertance tubes or mechanical inertial elements (motors, flywheels, oscillating pistons [2,3] or load inertia), and accumulators. In an analogous approach to the electrical buck converter in Fig. 1 (a), a schematic of a three-port hydraulic SIHC is shown in Fig. 1 (b). It makes use of the inherent reactive behaviour of hydraulic components including a high-speed switching valve (switch function), a small diameter tube (inductive effect) and an accumulator (capacitive effect) in the SIHC acting as a switch, an inductor and a capacitor in the electrical circuit. When the high-speed switching valve connects to the supply pump, the high-velocity fluid passes from the pump to the load; when the valve switches from the pump to reservoir, the momentum of the fluid in the inertance tube draws the continuous flow from DS-19-1197, Pan 2 the reservoir to the delivery port despite the adverse pressure gradient. As long as the switching time of the valve is short, the reduction in delivery flow will be very small, and the average delivery flow could be significantly higher than the supply flow, so this SIHC configuration is also called a flow booster. SIHCs have the potential to operate close to 100% efficiency, if friction, valve switching losses and leakage can be kept small [4], compared with conventional valve-controlled hydraulic systems which can have substantial losses; for example an average efficiency of about 30% is quoted in [5]. The earliest design of using fluid inertia is Montgolfier's hydraulic ram for raising water in 1796 [6] and the pioneer work related to addressing the use of fluid inertia was done by Constantinesco et al in which the pistons was actuated by periodic liquid impulses to generate the rotation of the motor in 1916 [7]. The concept of harnessing fluid inertia for power transmission by using alternating flows has also been discussed in [8]. The concept of SIHCs was relaunched by Brown et al in 1987 and the team proposed and investigated a series of SIHC configurations including a step-down transformer (flow booster), step-up transformer (pressure booster), switching gyrator and four-port SIHC analogously to electrical switched inductance transformers [9]. They concluded that the hydraulic transformers have clear potential to improve hydraulic system bandwidth and energy efficiency based on comprehensive theoretical studies. They designed a high-speed rotary switching valve [9], which inspired the development of various rotary valves used in today's research [4], to carry out the experimental validation. The rotary valve was used in a four-port SIHC prototype for static and dynamic studies [10]. However, the experimental results were not as predicted because cavitation and large pressure pulsations occurred. Brown et al suggested that more fundamental research should be focused on the fluid dynamics of SIHCs, the reasons for cavitation and nonlinearity, and the design and optimization of high-speed valves [10]. The team later designed and modelled an electrohydraulic flapper-nozzle valve [11]. The valve can be driven by a Pulse Width Modulation (PWM) signal with a frequency up to 500 Hz. The experimental dynamic response of the valve at 100 Hz agrees well with the analytical results, but the static characteristics were not discussed. The success of Brown et al's work inspired subsequent research on the design of high-speed switching valves and the investigation of SIHC characteristics.
In this review, the first section reviews different configurations of SIHCs and presents state-of-the-art modelling techniques. The second section reviews the designs of various high-speed switching valves and evaluates the valves in terms of pressure-flow characteristics, response time and manufacturing cost. It concludes with some suggestions for the future developments of high-speed switching valves and SIHCs.  Figure 3 shows the research can be categorised into three main aspects: the system, the components and the current problems (noise and cavitation).   [14]. However, the main stage response speed is about 2 ms, which limits the switching frequency of SIHCs. The team also investigated the hydraulic buck converter (HBC) [15]. A typical HBC consists of a two-port high-speed on-off valve and a check valve is shown in Fig. 4, where the check valve is arranged in the return line to prevent back flow. In this configuration, the check valve characteristics affects HBC performance and may cause cavitation due to the high-pressure drop across the valve. To eliminate cavitation, a nonlinear oscillator was designed to boost the tank line pressure [16]. The oscillator was driven by an ideally assumed rectangular pressure wave. Simulated results showed that the oscillator can increase the tank pressure to 15 bar. However, it results in more complex system dynamics and the oscillator needs to be further investigated combined with the real HBC system. In 2008, Kogler and Scheidl reviewed two basic concepts of hydraulic switching converters and concluded that the performance of hydraulic converters is affected by the valve dynamics, parasitic effects, wave propagation along the pipe, system nonlinearities and pressure pulsations [17]. These effects should be well understood for the design and optimization of SIHCs. An extended HBC including two switching valves and two check valves was developed to provide bi-direction ability as shown in Fig. 5. The HBC was designed in a more compact way by arranging the pipes in a loop in 2010 so that the HBC could be easily integrated into a machine, vehicle or robot [18]. Load pressure and efficiency of the compact HBC were investigated for the 'forward mode' and the 'reverse mode'. The results

SIHC SYSTEM RESEARCH
show 34% energy was saved compared with conventional resistance control. The performance of HBC in the pressure control mode was also analysed by driving a cylinder at load. The result shows that energy consumption was reduced by at least 59% [19].  [4]. Detailed simulation models were developed for the flow booster and pressure booster, where the systems include a 3/2 way switching valve, an inertance tube and an accumulator, as shown in Fig. 6. In a flow booster, the common port of the inertance tube is alternately connected to the high-pressure port (HP) and the low-pressure port (LP) when it operates. In a pressure booster, the outlet of inertance tube is alternately connected to the delivery port and the reservoir. The proportion of the switching cycle during which the HP is connected (or delivery port in a pressure booster) is defined as the switching ratio.  The experimental work was performed using a rotary valve which had been designed as a flow pulse generator for fluid-borne noise research [21]. The valve can only be used for very short periods due to the extreme noise and vibration. The wave propagation effect was studied by Wang et al [22], and the optimal switching ratios and frequencies were deduced. Later, Pan et al developed ideal analytical distributed models of a three-port SIHC and further enhanced the models including valve switching transition dynamics, non-linearity and leakage in 2014 [23,24]. The models were studied in the time and frequency domains and validated through numerical simulations and experiments. A commercial proportional directional valve from Parker Hannifin (DFplus) was used as a high-speed valve in the early stages, and later a high-speed rotary valve and a linear valve were developed and used for the purpose [25,26].
A four-port SIHC is shown in Fig. 7, where two inertance tubes are used. The system can be considered as the combination of two threeport valve configurations with the same average delivery flow in opposite directions. The difference is that the four-port SIHC is able to reverse the direction of motion or force through the same control action, providing real four-quadrant operation and seamless changes in direction [27]. It also enables a combination of meter-in and meter-out control which can handle over-running load situations DS-19-1197, Pan 6 effectively [27]. However, the four-port SIHC is not as efficient as a three-port SIHC because of an increased tube resistance in the system. Simulation of a pressure booster showed an efficiency of 58% and a flow booster showed an efficiency of 63%, with a switching frequency of 5 Hz [28]. The flow booster was used to study hydraulic pulsation by Wang et al in 2010 [29]. The system was modelled at a low switching frequency (below 20 Hz) and it was concluded that increasing the switching frequency and inertia of the motor could reduce the hydraulic pulsation.
As an application of the HBC, researchers in Linz collaborated with the Italian Institute of Technology to apply the HBC to control the leg of a quadruped robot [30,31]. The experimental results showed that the HBC could track the position as well as the conventional proportional drive and achieve lower energy consumption. However, the energy-saving advantage in experiments was not as significant as simulated results because the HBC used was oversize for the application [30,31]. The HBC was also used to control caster mould resonant drives in 2009 [32]. The simulated results showed that good efficiency was achieved but inaccuracy of motion control resulted due to the wave propagation. Kolger et al then proposed a flatness-based control for the HBC which made its trajectory tracking as precise as a proportional drive in simulation and experiments [33,34]. They also designed a stepper converter and applied the similar switching concept on a knee joint exoskeleton [35][36][37]. The simulated results on squat motion showed good control performance and demonstrated the potential of the application but effects in real situations such as friction, leakage, weight and size were not considered in the simulation.
Pressure pulsation also occurred in an HBC configuration thus accumulators were used for noise attenuation, which adds extra compliance to the system. In 2012, Kogler and Scheidl proposed a new approach of utilizing the load capacitance to attenuate the pressure pulsations instead of an accumulator [38]. They explored a multi-HBC system and operated the HBCs in a phase shifted way to attenuate the pressure pulsations to avoid the use of accumulator at the load side. The system relied on the capacitance of the load cylinder without accumulators at the load. The simulated results showed that the velocity pulsation was significantly attenuated from a range of 0.04mm/s to 0.02mm/s in the shifted way but the results were not verified by experiment. In 2015, they further analysed the pressure response in a pipe line considering the wave propagation caused by the switching [39]. They found that optimisation of the valve size and the pipe impedance could reduce pressure oscillations in a certain range.

Inertance tube
Switching valve Recently, research has been carried out in the areas of switching loss, cavitation, fluid compressibility and parameter optimization. In 2015, Wiens et al modelled and quantified the switching loss for an HBC and suggested that a shaped inertance tube and a tank-flow valve positioned along the tube could reduce the switching loss. The methods were investigated in simulation, and showed increased volumetric and energy efficiencies [40,41]. In 2018, the team proposed an improved transmission line model (TLM) for a tapered tube by optimising the weighting functions of conventional TLM models [23]. The model could be used for accurate design and modelling of tapered inertance tubes in SIHCs. Van de Ven developed a computational model to investigate the energy loss due to the fluid compressibility [42,43]. He concluded that the switched volume between the inertia motor and the switching valve should be minimized to achieve the maximum efficiency. The model was validated in experiments and showed some discrepancies, which could be reduced by using more accurate bulk modulus measurement and fluid compressibility model [42,43]. The group also developed a time-domain cavitation pipeline model of a pressure booster to effectively predict the condition resulting in cavitation [44]. Pan optimised the diameter and length of the inertance tube using a genetic algorithm and found global optimal parameters for designing an SIHC for maximum efficiency [45]. The approach is based on a constant delivery flow rate and could be expanded to a varying loading condition. In 2017, Wiens and Das summarized the limitations of components such as flow and pressure limits, heat transfer based on the comparison of the hydraulic and electronic converter theoretically [46].

MODELLING OF SWITCHED INERTANCE HYDRAULIC CONVERTERS
Research work on the modelling of SIHCs characteristics is mainly conducted in the Centre for Power Transmission and Motion Control at the University of Bath and in the Institute of Machine Design and Hydraulic Drives at Johannes Kepler University in Linz. The former concentrates on the characteristics of the three-port and four-port SHICs and their design improvements, while the latter focuses on the design of high-speed switching valves and the investigations of HBCs and their applications.
In 2009, Johnston studied the characteristics of SIHCs and the system energy efficiency [4]. Experimental results showed the actual efficiency was considerably lower than simulated results due to valve leakage and switching transition. A better designed high-speed switching valve could be used to minimize the leakage and transition effects so that the system dynamics could be further improved.
Wang et al found that the wave propagation along the inertance tube affects system performance and the optimal operating parameters could be determined. The optimal switching frequency equates the wave period to the duration of the shorter pulse within one cycle [22]. Pressure pulsations caused by the wave effects and from the nature of switching are synchronized at the optimal frequency, thus the wave effects are almost eliminated, which leads to the highest efficiency. Their work laid the foundation for the further investigations experimental results especially on the frequency at which the minimum flow loss and power loss occurred. This can be effectively predicted by using the enhanced analytical model which includes valve switching transition dynamics, nonlinearity and leakage [24].
The analytical and experimental results achieved from the enhanced model show that the flow loss and power loss actually increase with high delivery flow rates, and the flow loss curve is asymmetric with the minimum loss at the switching ratio slightly greater than 0.5.
Using the optimal switching frequencies and ratios could significantly reduce the flow loss and power loss [23,24]. The experimental validation was performed with low flow rates and switching frequencies due to the limitations of the switching valve and pressure pulsations. A rotary valve with a high bandwidth of more than 300 Hz was designed to construct a new SIHC prototype [25]. A maximum switching frequency of 317 Hz and a delivery flow rate of 20 L/min were applied on the prototype. The dynamic test of delivery pressure operated at 317 Hz verified that the delivery pressure is independent of the switching frequency. And the experimental result accurately showed the trend predicted by the analytical model though with a slight shift. However, when the system was operated at 20 L/min the system flow loss result deviated from the predicted result at lower switching ratio (0.2-0.4), which will be discussed in Section 5.
The analytical model of a four-port SIHC was proposed by Johnston et al in 2015 [27] and then validated on the SIHC prototype in 2017 [48].  [49]. The model was further extended to an HBC in 2013 [50]. The team at Linz proved the feasibility of the HBC experimentally in 2008 [51]. The experiments were performed with a fixed switching frequency and ratio. The results show an increment of 16% in efficiency of the HBC shown in Fig. 4 compared with the resistance control provided by a conventional valve. The use of a check valve also effectively prevents the back flow loss to the reservoir. Later, the team further investigated the static and dynamic flow-pressure characteristics of an HBC using varying switching ratios and loading conditions [17]. The results indicate that the change of load has almost no effect on the efficiency of an HBC and shows a maximum increased efficiency of 30% over a proportional valve controlled system.

DESIGN OF HIGH-SPEED SWITCHING VALVES
The high-speed switching valve is a key component of SIHCs. It switches the flow source between the high-pressure supply line and the low-pressure supply line. The performance of the high-speed valve significantly affects the characteristics of SIHCs. Therefore, the development of a high performance valve with a low resistance, large flow rate and high bandwidth is essential to the development of 8 [10]. The main components of the valve arranged coaxially include the stator, the rotor and the control shaft as in Fig. 8 (a). The stator has six ports, three of which denoted Pa are connected together to be used as delivery port A, and the other three as delivery port B. In the control shaft, three ports are connected as the supply port and the other three as the tank port. When the rotor rotates, the supply port switches from the delivery port A to the delivery port B while and the tank port switches from the delivery port B to the delivery port A.
The view of the straight-line motion of the valve is shown in Fig. 8 (b). The switching frequency is determined by the rotating speed of the rotor and the switching ratio is determined by the angle between the stator and the control shaft.
DS-19-1197, Pan 10 This rotary valve can achieve a maximum switching frequency of 500 Hz, but it is not possible to perform precise rectangular wave control at the frequency. The valve was implemented on a four-port SIHC in experiments but did not achieve the expected results due to severe cavitation. Brown et al concluded that the design could be improved by introducing a small accumulator-like bladder or foam pockets of gas to eliminate cavitation. They also suggested that the fundamental fluid mechanics of the unsteady cavitation, compliance, resistance and inductance of SIHCs should be thoroughly studied and understood [10]. Another rotary valve was designed by Cui et al in 1991 [52]. The valve was constructed as a single-stage but acted in a two-stage way, as shown in Fig. 9. In the first stage, the motor rotates the spool to a position where the chamber B and A are connected through the slot on the spool. The pressurized fluid goes from the chamber A to chamber C via channel B, which results in a pressure imbalance between chamber C and the load volume. Therefore, the spool is moved to the right at which the load is connected to the source pressure. In the meantime, the chamber C is connected to the second stage (tank port). The spool is pushed back when the load pressure is higher than the pressure in the chamber C. The valve switches cyclically between the two stages to deliver the flow to the load.  found that there is a considerable deviation between the simulated and experimental results with a higher switching frequency of 75 Hz due to the fluid compressibility effect [54]. The valve creatively utilized the flow force during the switching to self-spin the spool indicating the potential to effectively raise the system efficiency, which also simplifies the valve configuration. However, the problem is that the rotating speed (related to the switching frequency) is limited by the flow rate and affected by the fluid viscosity, making it difficult to operate the valve at a higher frequency. They proposed a continuous phase-shift rotary valve, using a rotating valve plate between two tiers to channel the flow into different ports as shown in Fig. 11 [55,56]. When the valve plate rotates clockwise from the initial position as in Fig. 11 the port A is connected to the port T until it reaches to 90-degree respect to the initial position. At this point, the port T is closed but the port P begins to open and be connected to the port A via the other end of the valve plate. In a cycle, the valve switches twice between the supply port P and the tank port T which doubles the switching frequency. The relative phase angle between the two tiers determines the duty ratio which is 0.5 with the position in Fig. 11, whilst the rotary speed of the valve plate determines the switching frequency. The phase-shift mode of the valve was validated in experiments and the valve can deliver a flow rate of 10 L/min at 0.5 bar pressure drop with a switching frequency of 100 Hz. Further investigation with a higher flow rate is needed to study the valve performance.

Linear valves
In 1991, Yokota designed a high-speed poppet valve using two multi-layered piezoelectric actuators, which enable the valve to operate with a very high frequency rectangular wave (2 kHz), as shown in Fig. 12 [57]. The design utilizes two piezoelectric actuators to strike the spool to the left and right stroke, making the supply line connected to load A and load B respectively.  Fig. 13 [58]. This valve features the advantage of recuperating the kinetic energy of the spool by integrating the custom-built accumulators into the valve as Fig. 13 shows.
The bottom frontal fluid volume, the spool, the plate, and the top fluid volume forms a mass-spring system with an eigenfrequency of 400 Hz. The solenoid-driven plate generates a resonant excitation of the spool through the fluid at the eigenfrequency and the spool moves upwards and downwards to deliver supply pressure and tank pressure to port A. The valve has a maximum flow rate of 100 L/min with a pressure drop of 5 bar. The solenoid-driven design made it easy to control and the resonance enabled it to switch at a high frequency with a low power input. However, the oscillation amplitude of the spool at 400 Hz was limited due to the excessive eddy-  In 2008, a piezoelectric valve was proposed by Ouyang et al [59]. Similar to the valve in [57], the design utilizes two piezoelectric actuators to strike the spool to the left and right stroke and stops it with the dampers. This innovative design solved the conflicts between the small displacement of the piezo (in the order of micrometres) and the relatively large stroke (in the order of millimetres) needed in the switching valve. In this way, a displacement amplifier for the piezoelectric actuator could be avoided. However, the proposed design DS-19-1197, Pan 16 Winkler et al designed a multi-poppet switching valve to increase the flow rate by using multiple poppets to increase the flow capacity without increasing the response time in 2010 [60]. Figure 16a shows the solenoid-drive pilot valve they used to activate the main stage.
When port A and port P are connected, it delivers the supply pressure to the port X in the main stage, which turns off the poppet as Fig.   16b shows because there is no pressure difference across the poppet. When the Port A of the pilot valve is connected to the tank port, it keeps the tank pressure at the port X in the main stage, which turns on the poppet due to higher pressure at the bottom of the poppet.
The pilot valve could reach a switching time of below 2ms and a flow rate of 10 L/min under 5bar.
Poppets are arranged circularly as in Fig. 16c, which enables the valve to operate with 85 L/min with a pressure drop of 5 bar. A shim ring is used and its position is measured as the poppet position but the flexible deformation of the ring makes it difficult to determine the position of poppets since they are different. A more accurate measurement of the poppet position to calculate the switching time of the valve is needed. Despite this, using multiple small on/off valves is a novel solution, making it easy to achieve a high flow rate within a compact configuration. In 2012, Kudzma et al proposed the concept of a multi-edge spool to realize the same goal as the multi-poppet concept and designed a 2/3-way two-stage linear high-speed switching valve [26]. The spool with multiple grooves which is driven by an electrohydraulic servovalve moves inside the housing with paired grooves as shown in Fig. 17. The servovalve provides the pressure difference to move the spool to switch the input between the high-pressure supply line and the low-pressure supply line. The four pairs of metering edges in both high-pressure flow route and low-pressure flow route as Fig. 17 shows give the valve a large flow area with a small spool displacement which contributes to a shorter switching time.
The valve was anticipated to achieve 65 L/min with a pressure drop of 10 bar but actually 50 L/min was achieved at 10 bar due to the manufacturing tolerances, and the valve could switch in around 1ms and closely track a 200 Hz square wave [61]. Sell  Lantela et al applied a similar concept to [60] and developed a miniature valve system, as shown in Fig. 19a [62]. When the pilot spool is driven to the bottom the pilot supply line is connected to the pilot channel and keeps the main stage closed. In contrast, when the pilot spool is driven to the top the pilot supply line is blocked while the tank line is connected to the pilot channel. Therefore, the main stage valve opens due to the higher pressure of the supply channel. The valve is capable of delivering a flow rate of 9 L/min at a pressure drop of 35 bar with a response time of 0.9-1.3ms. The maximum operating pressure is at least 300 bar. This gives a possibility to form a valve system with a high flow rate (70 L/min) by arranging a number of miniature switching valves in a manifold. Later, in 2017, this was realized by integrating 32 valves into a valve system to construct a 3/2 way switching valve [63] as shown in Fig. 19b. The flow rate through the valve system at a pressure difference of 35 bar reached 78 L/min. This is lower than the sum of the individual valve flows due to the leakage of approximately 0.6 L/min per pilot valve. Precise manufacturing of the pilot spool could reduce the leakage to 0.05 L/min or using a seat pilot valve is a promising alternative to minimize the leakage. Another problem is that the internal channels of the manifold are extremely complex and need to rely on some special manufacturing techniques such as the lamination method. In 2017, Koktavy et al designed a new switching valve with two spools combined and driven by a crank-slider mechanism to alternately switch the flow from the supply line to port A or port B shown in Fig. 20 [64]. The valve showed very good performance with a maximum switching frequency of 120 Hz and a flow rate of 22.7 L/min. The leakage of the valve is very low (0.065 L/min), when tested at the pressure difference of 194bar and at the rotating speed of the input shaft of the crank-slider of less than 0.32rad/s [64]. This mechanism was able to recuperate the energy with a flywheel and avoided the bang-bang actuation with a solenoid, or the throttling process with a servo valve, thus minimized the energy needed in the pilot stage and greatly simplified the control strategy. A possible problem is that the crank-slider mechanism makes the valve bulky.

Valve effects and comparison between the valves
A high-speed switching valve is the key component of an SIHC and significantly affects the SIHC performance. The valve bandwidth determines the highest switching frequency that the SIHC can achieve, as well as the length of the inertance tube required. A shorter inertance tube can be used if a very high-speed switching valve is available, which can reduce hydraulic resistance and improve efficiency. The valve resistance and leakage highly depend on the design and manufacturing accuracy of the valve. Different designs lead to a variety of flow-pressure drop characteristics, and leakage directly corresponds to a power loss in the valve.
DS-19-1197, Pan 19 The development of SIHCs is currently limited by the performance of high-speed valves. The valve needs to deliver high flow rates with low pressure drop, switch fast, have low leakage and require low driving energy. The valve is also expected to provide good controllability and have reasonable manufacturing costs. Table 1 summarizes the designs and performance of some of the high-speed switching valves developed in recent years. The advantages and limitations of the designs have been discussed.
In a spool valve, it is relatively easy to perform position control of a spool driven by solenoids, a hydraulic pilot stage or piezoelectric actuators. In addition, manufacture of a spool and its housing with good accuracy is standard practice. It is possible to achieve good performance such as a high flowrate and a low pressure drop using a spool design. A good example is the solenoid-driven linear spool valve developed by Winkler [60], which successfully achieved 90 L/min at only 5 bar pressure drop. But the mass of the spool makes it difficult and energy-consuming to be driven at a high frequency and maintain a relatively large stroke. One design to solve this problem is to have multiple smaller orifices on the spool [26]. Therefore, a small displacement of the spool such as 0.1mm is enough to switch between the ports and maintain a high flow rate. The other approach is to introduce more efficient actuation, for example, a crank-slider mechanism is used to recuperate the energy needed in moving the spool [64], at the expense of flexibility in spool positioning.

Examples
Manhartsgrub er et al [58] Kudzma et al [26] Koktavy et al [64] Ouyang et al [59] Winkler et al [60] Lantela et al [63] Katz et al [55] Tu et al [53] DS-19-1197, Pan 20 Using a poppet valve could simplify the actuation stage because it is easier to open or close with a small initial force. Piezoelectric actuators could be used to strike the poppet in both directions making it possible to switch at a high frequency. This idea was first proposed by Yokota [57] in 1991 and later similar idea was used by Ouyang to build a high-speed switching valve in [59] and the valve could be operated at 250 Hz with a flow rate of 15L/min in simulation.
For a rotary valve, it is easy to drive at a high frequency by increasing the speed of the motor [10,55]. There are two common problems in the rotary valve: one is the friction loss during the rotation and the other is the energy loss due to flow throttling and fluid compressibility. These problems limit the switching frequency and the flow rate of the rotary valve. Further improvements on the design are needed to minimize these effects. The models show generally good agreement with experimental results, but there are still some inaccuracies. For example, the flow loss is effectively reduced by varying switching frequency with different switching ratios as the optimal curves show in Fig. 21. However, the optimal curve for the delivery flow rate of 20 L/min and 0 L/min are expected to have similar trends but there is an unexpected deviation between them as the red arrow shows in Fig. 21. This deviation could be caused by the transition dynamics with a large delivery flow rate, the variation of the operating temperature, valve dynamics or system cavitation, and should be a matter for future research. The previous work into modelling the SIHC characteristic and the valve design shows that there is plenty of room for improvement in terms of design parameters of systems and components, and research to optimise these is ongoing. Pan used a genetic algorithm to find the optimal tube diameter and tube length of a SIHC based on the analytical models given in [23,24]. The optimisation starts with setting the initial values of the diameter and tube length and then the switching frequency and period are calculated under the optimal condition in [22]. The genetic algorithm is used to search for the optimal value of the two tube parameters to minimize the cost function of power loss which is given in [23]. The result indicated that the length of 0.62m and the diameter of 9.5mm gives the lowest power loss which is almost half of that at the length of 3m. However, this set of parameters needs a high switching frequency (544 Hz) which is difficult to achieve. Ven der Buhs et al also optimised the shape of the inertance tube and found the optimal arrangement of various tapered tubes is 6% better in efficiency compared with the uniform tubes when used in a SIHC [65]. The optimised shape of the inertance tube includes a uniform section of the tube and a diverging tapered section followed by another uniform section at larger diameter and with lower resistance as in Fig. 22. However, in general there is not much research into design optimization of SIHCs and this needs to be more investigated thoroughly in the future.

CONCLUSIONS
The switched inertance hydraulic converter is a very promising concept to achieve high energy efficiency compared with conventional Future research should be carried out into the design, control and optimisation of linear and rotary high-speed switching valves. Faster, high flow, low leakage valves can further improve the efficiency of SIHCs. Analytical models can be enhanced by including cavitation, valve dynamics and loading resonance effects on SIHCs, and can be used for investigating the influence of valve switching transition in more detail. The investigation of SIHCs in a variety of configurations is desired to complete systematic models as current work is mainly based on switched buck converters (flow boosters). Configurations such as switched booster converters (pressure boosters) and fourport SIHCs need to be investigated and evaluated for efficiency. Control of the high-speed switching valves is also a good area to explore.
The accuracy and robustness of the valve switching can significantly affect SIHC performance. Experimental investigations using higher operating pressures and flow rates are necessary for practical hydraulic applications that include robotics, transportation, oil and gas, and machinery for industry, construction and agriculture. The cyclic switching mechanism of SIHCs generates periodic pressure pulsation which also needs to be addressed to eliminate noise problems associated with this new technology. [65] Wiens, T. K., Chen, D. X., Bergstrom, D. J., and Chowdhury, N. A., 2018, "Investigation and Optimization of Hydraulic Step-down Switched Inertance Converters with Non-uniform Inertance Tubes". Thesis (M.A.), University of Saskatchewan, Saskatoon. Tab. 1 Summary of high-speed switching valve design