Iterative Optimal and Adaptive Control of a Near Isothermal Liquid Piston Air Compressor in a Compressed Air Energy Storage System Farzad A. Shirazi, Mohsen Saadat, Bo Yan, Perry Y. Li, and Terry W. Simon Abstract— The power density and efﬁciency of high compres- sion ratio (∼200:1) air compressors/expanders are crucial for the economical viability of a Compressed Air Energy Storage (CAES) system such as the one proposed in [1]. There is a trade-off between power density and efﬁciency that is strongly dependent on the heat transfer capability within compres- sor/expander. In previous papers, we have shown that the compression or expansion trajectory can be optimized so that for a given power, the efﬁciency can be optimized and vice versa. Theoretically, for high compression ratios, the improvement over ad-hoc trajectories can be signiﬁcant- for example, at the same efﬁciency of 90%, the power can be increased by 3-5 folds [2], [3], [4], [5]. Yet, the optimal trajectories depend on the heat transfer coefﬁcient proﬁle that is often unknown. In this paper, we focus on the experimental study of an iterative control algorithm to track a compression trajectory that optimizes the efﬁciency-power trade-off in a liquid piston air compressor. First, an adaptive controller is developed to track any desired compression trajectory characterized by the temperature-volume proﬁle. The controller adaptively estimates the unknown heat transfer coefﬁcient. Second, the estimated heat transfer coefﬁcient from one iteration is then used to esti- mate the optimal compression trajectory for the next iteration. As the estimate of the heat transfer coefﬁcient improves from one iteration to the next, the quality of the estimated optimal trajectory also improves. This leads to successively improved efﬁciency. The experimental results of optimal trajectories show up to 2% improvement in compression efﬁciency compared to linear trajectories in a same power density. I. I NTRODUCTION Gas compression and expansion has many applications in pneumatic and hydraulic systems, including in the Com- pressed Air Energy Storage (CAES) system for offshore wind turbine that has recently been proposed in [2], [5]. In the proposed CAES system, high pressure (∼20-30MPa) compressed air is stored in a dual chamber storage vessel with both liquid and compressed air. Since the air com- pressor/expander (C/E) is responsible for the majority of the storage energy conversion, it is critical that it is efﬁcient and sufﬁciently powerful. This is challenging because compress- ing/expanding air 200-300 times heats/cools the air greatly, resulting in poor efﬁciency, unless the process is sufﬁciently slow which reduces power [3], [6]. There is therefore a trade- off between efﬁciency and power. Most attempts to improve the efﬁciency or power of the air C/E aim at improving the heat transfer between the air and its environment [2]. To improve the efﬁciency of the C/E The authors are with Mechanical Engineering Department, University of Minnesota, Minneapolis, MN 55455. Email: fshirazi@umn.edu with few compression stages, it is necessary to enhance the heat transfer during the compression/expansion process. One approach is to use multi-stage processes with inter-cooling [7]. Efﬁciency increases as the number of stages increase. A liquid piston compression/expansion chamber with porous material inserts has been studied in [3]. The porous material greatly increases the heat transfer area and the liquid piston prevents air leakage [8]. Numerical simulation studies of ﬂuid ﬂow and enhanced heat transfer in round tubes ﬁlled with rolled copper mesh are studied in [9]. In addition, the compression/expansion trajectory can be optimized and controlled to increase the efﬁciency for a given power or to increase power for a given efﬁciency. For high compression/expansions ratios 200:1-350:1, such Pareto op- timal trajectories have been shown, theoretically, to increase the power of the C/E by 200-500% at the same efﬁciency, over ad-hoc trajectories such as linear and sinusoidal trajec- tories [3], [4], [5]. In [3], [4], the optimal trajectories were derived analytically based on simple heat transfer models and by considering thermodynamic losses alone. For example in [3], the product of the heat transfer coefﬁcient and heat transfer surface area hA is assumed to be constant; and in [4], hA is allowed to vary with air volume to take into account the decrease in surface area as the porous material is submerged in the liquid piston. In both cases, the optimal trajectories consist of fast adiabatic portions at the beginning and at the end. For the constant hA case [3], the middle portion is isothermal resulting in an Adiabatic-Isothermal-Adiabatic (AIA) trajectory, whereas for the volume-dependent hA(V ) case [4], the temperature difference from the ambient is inversely proportional to  hA(V ) leading to an Adiabatic- Pseudo-Isothermal-Adiabatic (APIA) trajectory. Optimal trajectories have also been numerically obtained for cases with varying heat transfer coefﬁcient, and consid- ering the effect of liquid friction and ﬂow rate constraints of the system [5]. Application of such optimal trajectories has been veriﬁed for a liquid piston C/E using CFD and the results have been compared with AIA and APIA trajectories. While the theoretical improvement in power/efﬁciency with the optimal trajectories for air compression over con- ventional linear and sinusoidal trajectories has been vali- dated analytically and numerically, this paper provides the experimental validation of the usefulness of such optimal trajectories. One issue with implementing the optimal trajec- tories experimentally is the uncertainty of the heat transfer model. The transient heat transfer coefﬁcient depends in reality on many factors. Even if a constant heat transfer 2013 American Control Conference (ACC) Washington, DC, USA, June 17-19, 2013 978-1-4799-0176-0/$31.00 ©2013 AACC 2940