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The control law for theAFSMC was expressed asu ¼ ^ ufz þ ^ ur; ð48Þwhere~ ufz≡^ ufz−u fz ¼ ^ ufz−u eq þ ε;~ θ ¼ θ−θ ;~ E ¼ ^ E−E; ð49Þ~ ufz ¼ ~ θTξ−ε: ð50ÞTheorem. Consider the system presented in Eq. (34). If the adaptivecontroller was designed as in Eq. (48), where the parameters of the con-troller were^ ufz s; θ ðÞ¼ θTξ and ð51Þ^ ur ¼ −^ E sgn s ðÞ⋅ sgn g ðÞ; ð52Þwith the adaptation laws_θ ¼ −η1sξ sgn g ðÞ and ð53Þ_ ^ E ¼ η2 st ðÞ jj; ð54Þwhere ^ E is the estimated bound value of the approximation error and η1and η2 are the positive constants known as learning rates, then the sta-bility of the system was guaranteed.Proof. Define a Lyapunov function candidate as follows:V ¼ 12s2þ g jj2η1~ θT~ θ þ g jj2η2~ E2: ð55ÞUsing Eqs. (34), (36), and (42), we obtained a value for _ s. UsingEqs. (48)–(50) and _ s and differentiating V with respect to time, weobtained_V ¼ s_ s þ g jjη1~ θT _ ~ θ þ g jjη2~ E _ ~ E ¼ sg ~ θTξ−ε þ ^ ur þ g jjη1~ θT _ ~ θ þ g jjη2~ E _ ~ E¼ ~ θTsgξ þ g jjη1_ ~ θ −gsε þ gs^ ur þ g jjη2^ E−E _ ~ E¼ ~ θTsgξ þ g jjη1_ ~ θ −gsε−gs^ E sgn s ðÞ⋅ sgn g ðÞþ g jjη2^ E−E _ ~ E¼ ~ θTsgξ þ g jjη1_ ~ θ −gsε− g jjη2E _ ~ E þ g jj^ E −s sgn s ðÞþ 1η2_ ~ E ¼ −gsε− s jj g jjE≤ s jj g jj ε jj− s jj g jjE ¼ s jj g jj ε jj−E ðÞ≤0: ð56ÞAccording to Barbalat's lemma [21], we concluded that s(t)→0ast→∞. Thus, the system was asymptotically stable.4. Test bench system and experimental programs4.1. Test bench system setupTo validate the ability of the proposed system, a model systemwasdeveloped for use in a 2000 kg vehicle. The final reduction gear ratiowas 3.55:1, the radius of the wheel was 0.28 m, and the scale modelfactor of the recoverable energy was 15:1. The parameters of thetest bench are shown in Table 2.The schematic and photograph of the test bench are shown inFig. 8a and b, respectively. For the test bench, the hydraulicpump/motor HPV55-02 was employed. The hydraulic accumulatorswere Hyundai Oil Products, and the directional control valve wasfrom the Atos RPE4 series with the maximum flow rate of 120LPM,themaximumoperatingpressureof250barandthemaxi-mumbackpressureatportTof210bar.Thepressureand flow sen-sors were employed from Webster Instruments LPT and LTE series,respectively, and the tachometer and torque transducer wereSETech products.The control and data acquisition systems were controlled by a per-sonal computer and 1711 and 1720 ADC or DAC interface boards ofAdvantech products. The control system was designed in MatlabSimulink, where the sampling time was 2 ms.4.2. Experimental programs4.2.1. Flywheel test and estimation of the round-trip efficiencyA cycle of energy recovery was defined as follows. The kinetic en-ergy of the flywheel was transferred to the accumulator as potentialTable 2Parameters of the systems.Main parameters of SCL-CPS Value UnitMaximum displacements of PM1,2 55 cm3/revMoment of inertia of the flywheel 2.5 kg·m2Viscous friction coefficient 0.01 N m·s/radVolume of high pressure accumulator HA1 20 LVolume of low pressure accumulator HA2 40 LPre-charge pressures of HA1 120 barPre-charge pressures of HA2 2 barElectric motor power 25 hp energy in the form of a high-pressure fluid, which then transformedthe stored energy back into kinetic energy via the flywheel. Fromthe viewpoint of the component efficiencies, the theory round-trip ef-ficiency was defined as in (57),ηrt¼ ηfl;dηpηacηmηfl;a; ð57Þwhere ηfl, ηm/p, and ηac are the efficiencies of the flywheel, PM2, andthe accumulator, respectively. The efficiencies of the flywheel duringdeceleration (ηfl,d) or acceleration (ηfl,a) depended on the particularapplication. For the estimation of the round-trip efficiency of the sys-tem, the efficiency of the accumulator was assumed to be a constant0.95. The motor efficiency was in the interval [0.6 0.94] and thepump efficiency was in the interval [0.68 0.92].The key to energy recovery was the flywheel, so its characteristicsshould be taken into account when analyzing the regenerative cyclingdata. The kinetic energy of the flywheel was lost gradually due to thefriction of the particular simulated system. The test was conducted asfollows. The flywheel was powered to 1100 rpm, at which time pumpP1 shut off and the displacement of PM2 was controlled to zero.Whenthe displacement of PM2 is zero the speed of the flywheel also gradu-ally decreases due to friction torques at PM2 shaft. Those torquescaused by the hydraulic frictions as well as mechanical frictions gen-erated by the initial setting the slot of the braking system. Because thetest bench is fabricated to simulate a vehicle the speed of the flywheelmust decrease when it is not powered or the displacement of PM2 iszero. A few identical tests were conducted to test the repeatability.The results of the simulation and the experiment are shown inFig. 9, illustrating agreement between the result sets. Under the test conditions, the energy of the flywheel was significantly reduced foroperations longer than 10 s. However, the braking time in most appli-cations was only a few seconds, so the system could still be consid-ered suitable as a regenerative energy simulator system.The efficiencies of the flywheel were assumed to be constant andsimilar during both deceleration and acceleration. The determinationof the efficiency based on Fig. 9 is as follows. Assuming a decelerationtime of 3 s, the energy of the flywheel decreases from E0 ¼ 12 Jω20 toE3 ¼ 12 Jω23, so the efficiency ηfl is estimated using Eq. (31) to beηfl¼ E3E0¼ 0:9. As seen in Fig. 9, ηfl varied from 0.9 to 0.52 with respectto a deceleration time increase from 3 s to 10 s. Therefore, usingEq. (57), the round-trip efficiency of the test bench varied from 32%to 66% when the braking time was less than 10 s.4.2.2. Basis testThis test was used to evaluate the validity of the employed math-ematical model. The determination of the round trip efficiency of thesystem using Eq. (57) is difficult because the current efficiencies ofcomponents in the system are unknown. Hence, the round trip effi-ciency of the system is experimentally determined using Eq. (31),inwhich the speed of the flywheel was a measured value. The test wasconducted at four initial flywheel speeds, corresponding to four dis-placement ratios. For each test, when the speed of the flywheelreached the set value, pump P1 was deactivated and valve V12 was ac-tivated. When the speed of the flywheel was nearly zero, V12 wasdeactivated and V11 was activated and the speed of the flywheel increased again.