**Tracking Position Control of Electrohydraulic System**

with Minimum Number of Sensors

with Minimum Number of Sensors

**Lilia SIDHOM ^{1}, Mohamed SMAOUI^{2}, Xavier BRUN^{2}**

^{1 }Research Laboratory LA.R.A, ENIT,

BP 37, Le Belvédère, Tunis, 1002 Tunisia

lilia.sidhom@gmail.com

** ^{2 }**AMPERE Laboratory UMR 5005, INSA of Lyon,

20 Avenue Albert Einstein, Villeurbanne, Lyon, F 69621, France

xavier.brun@insa-lyon.fr, Mohamed.smaoui@insa-lyon.fr

**Abstract: **In general, feedback controllers require measurements of velocity and acceleration for feedback. To avoid the complexity of overall system with minimizing the sensor number implements on a test bench, a new estimation algorithm of the successive derivatives of measured signal is proposed. The differentiator design is a very difficult task because the important problem in real time differentiation signal is to combine differentiation exactness with robustness in respect of measurements errors and input noises. For this target, a higher order sliding modes differentiator with dynamic gains is proposed. The experimental validation highlights the performances of the differentiator/controller design of a high dynamic electrohydraulic servo-system. For this validation, two controllers are implemented on the test bench for position tracking objective. Moreover, two kinds of differentiators are also tested: the proposed one and some classic algorithm.

**Keywords:** Differentiator design, Dynamic gains, High order sliding mode, Experimental results, Electrohydraulic servo-actuator.

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**CITE THIS PAPER AS**:

Lilia SIDHOM, Mohamed SMAOUI, Xavier BRUN, **Tracking Position Control of Electrohydraulic System with Minimum Number of Sensors**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 25(4), pp. 479-488, 2016.

**Introduction**

Despite a large use of hydraulic system in industry applications, their control problem still remains an interesting challenge. Indeed, the dynamic behaviour of electrohydraulic systems is highly nonlinear which makes targets difficult to achieve. In practice, the most common type of control used for hydraulic servo-systems is a linear controller which is designed basing on the linear approximated model at an equilibrium point, [20], [17]. However in such work, some important dynamic information may be lost. Therefore, it is judiciously to choose a nonlinear control method to benefit greatly from the application of advanced control techniques, [7]. In recent years, a various studies of modern control technique have been applied on electrohydraulic actuators. Some number of them has rested on feedback linearization techniques, [23]. Other nonlinear approaches based on neural or fuzzy algorithms are also applied, [30], an adaptive controller is considered too for an electrohydraulic system [9], [15], [31]. An alternative approach have been investigated which is based on classic sliding mode which is added to the adaptive technique, [2]. For strict-feedback model system, a nonlinear controller can be designed with a Backstepping technique, [8]. This approach has been used in this paper in the context of electrohydraulic application.

All of the previous mentioned feedback controllers require generally measurements of velocity and acceleration for feedback. However, accelerometers are seldom used in practical drive systems. Indeed, the use of accelerometers adds cost, energy consumption, increases the complexity of the overall system, and reduces its reliability. Then all controllers are highly sensitive to noisy, inaccurate or delayed velocity and acceleration estimates. Nowadays, the problem of differentiation signal given in real time is an old and well-known problem, but it still remains an important challenge. Sometimes the synthesis of a differentiator requires a good knowledge of the model system. In this case the differentiator synthesis is reduced to an observation and a filtration problem. Many structures for state variables estimation are based on nonlinear observer theory, such as high gain observer [10], sliding mode observer [24] and Backstepping observer [14]. However, the lack information or insufficient knowledge on the dynamics of the system makes the implementation of a nonlinear state observer difficult. Another attractive method for estimation of the state variables, particularly for mechanical systems, is the numerical algorithms. In [12] the properties and the limitations of two different structures for linear differentiation have been discussed. For example, a predictive algorithm applied to angular acceleration measurements is presented in [28].

In other cases, the construction of a differentiator is inevitable. Indeed, differentiators are very useful tools to determine and estimate signals without basing on the dynamics system. The design of differentiator unit is a traditional aim for signal processing theory. For instance, using differentiator unit, the velocity and acceleration can be computed only from the position measurements. But, the design of an ideal differentiator is a hard and challenging task. For construction a differentiator, some features of the signal and the noise must be considered. However, in some cases the structure of the signal may be unknown except some differential inequalities, differentiators that are based on algebraic parametric estimation techniques can be well employed, [21]. Although the algebraic algorithms allow a good capability to attenuate efficiently the noise, they are sensitive to the truncation order also to the size of the sliding window estimation and essentially to the setting of its parameters.

Alternative methods based on the higher order sliding mode technique can be used [27]. In [18], a robust first order differentiator via second order sliding modes is proposed. Other works, [19]; employs an arbitrary-order robust exact differentiator with finite-time convergence. The main advantage of such differentiators is the easiness of its implementation in real time.

Even though large applications of these kinds of differentiators have been performed, its major drawback concerns the tuning of its gains in real time. This adjustment requires the exactly knowledge beforehand of the Lipschitz constant of the derivative signal. Moreover, it is so difficult to obtain in advance the value of this constant in real time since we do not necessarily know the signal to estimate. In the prior researches, different new schemes of sliding modes differentiators have been proposed to improve the performance of basic schemes. Some works that can be cited are: [1], [6], [31]. In these last, a new forms of the first-order differentiator are proposed.

In the current paper, we are going to develop the results from [19] in order to propose novel scheme of second-order differentiator which is based on third-order sliding mode. A dynamic are added to the differentiator gains to adjust them in real time and to avoid the condition of knowledge of the Lipschitz constant of Levant’s differentiator. Moreover, in all the previous works, generally, all contributions that have been made relate to the first order estimator which is based on the second order sliding mode and as for the made real-time applications. Our contributions consist to: **1)** Present a new extended form of the 2^{nd}-order sliding modes differentiator to estimate simultaneous the velocity and the acceleration of the electro-hydraulic system, not the 1^{st}-order what is usually done in the literature. **2)** Synthesis and implement a Backstepping controller on high dynamic electro-hydraulic system for a tracking position trajectory. **3)** Discuses experimental results with different desired trajectories of position to show the performance of the proposed algorithm with compare it to some classical numerical differentiation algorithm.

The paper is organized as follows. The first section outlines the 2^{nd}-order Adaptive Differentiator (ARD) is developed. Section2 describes the model of the electrohydraulic actuator.

Section 3 presents the controller design via a Backstepping technique for position tracking trajectory. Section 4 is devoted to the experimental results.

**REFERENCES**

- ANGULO, M. T., J. A. MORENO, L. FRIDMAN,
**The Differentiation Error of Noisy Signals Using the Generalized Super-Twisting Differentiator**, 51st IEEE Conf. on Dec. & Ctrl., Maui, 2012. - ALLEYNE, A., R. LUI,
**Systematic control of a Class of Nonlinear Systems with Application to Electrohydraulic Cylinder Pressure Control**, IEEE Trans. on Ctrl. Syst. Tech., 6(4), 2000, 623-634. - ARMSTRONG-HELOUVRY, B., P. DUPONT, C. CANUDAS De WIT, C.
**A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines with Friction**, Automatica, 30 (7), 1994, 1083-1138. - BLACKBURN, J. F., G. REETHOF, J. L. SHEARER,
**Fluid Power Control**, 1960. M.I.T Technology Press, and Wiley. - BOURI, M., D. THOMASSET,
**Sliding Control of an Electro-pneumatic Actuator Using an Integral Switching Surface**, IEEE Trans. on Ctrl. Syst. Tech., 9(2), 2001, 368-375. - CHAWDA, V., O. CELIK, M. K. O’MALLEY,
**Application of Levant’s Differentiator for Velocity Estimation and Increased Z-Width in Haptic Interfaces**, IEEE World Haptics Conf., June, Istanbul, 2011. - EDGE, K. A.
**The Control of Fuid Power Systems Responding to the Challenge**, J. Syst. & Ctrl Eng., 211(12), 1997, 91-110. - FREEMAN, R. A., P. KOKOTOVIC,
**Desgin****of Softer Robust Nonlinear Control Laws**, Automatica, 29, 1993, 1425-1437. - GUAN, C., S. PAN, S.
**Adaptive Sliding Mode Control of Electrohydraulic System With Nonlinear Unknown Parameters**, Ctrl Eng. Prac., 2008, 16, 1275-1284. - GAUTHIER, J. P., H. HAMMOURI, S. OTHMAN,
**A Simple Observer for Nonlinear Systems Applications to Bioreactors**, IEEE Trans. Aut. Ctrl., 37(37), 1992, 875-880. - IBRIR, S.,
**New Differentiators for Control and Observation Applications**, Am. Ctrl. Conf., 2001, 2522-2527. - IBRIR, S.
**Linear Time-Derivative Trackers**, Automatica, 2004, 40, 397-405. - KANELLAKOPOULOS, I., P. KOKOTVIC, MORSE,
**Systematic Design of Adaptive Controllers for Feedback Linearizable Systems**, IEEE Trans. Aut. Ctrl., 36, 1991, 1241-1253. - KRENER, A. J., W. KANG,
**Locally Convergent Nonlinear Observers**, Siam J. Ctrl. Optim., 42(1), 2003, 155-177. - KRSTIÇACUTE, M., L. KANELLAKOPOULOS, KOKOTOVIÇCUTE,
**Non-linear and Adaptive Control Design**, John Wiley & Sons, Inc., 1995, p. 563. - LAGHROUCHE, S., M. SMAOUI, F. PLESTAN, X. BRUN,
**Higher Order Sliding Mode Control Based on Optimal Approach of an Electropneumatic Actuator**, J. Ctrl, 79, 2006, 119-131. - LAVAL, L., N. K. M’SIRDI, J.-C. CADION,
*H*_{∞}**Force Control of a Hydraulic Servo-Actuator With Environmental Uncertainties**, IEEE Inter. Conf. on Rob. & Aut., 2, 1996, 156-1571. - LEVANT, A.,
**Robust Exact Differentiation via Sliding Mmode Technique**, Automatica, 34, 1998, 379-384. - LEVANT, A.,
**Higher Order Sliding Modes,****Differentiation and Output Feedback Control**, Int. J. Ctrl, 76, 2003, 924-941. - MERRITT, H. E.,
**Hydraulic Control Systems**. John Wiley & Sons, 1967, p. 368. - MBOUP, M., C. JOIN, M. FLIESS,
**Numerical Differentiation with Annihilators in Noisy Environment**, Num. Alg., 50(4), 2009, 439-467. - NIKSEFAT, N., N. SEPEHRI,
**Design and Experimental Evaluation of a Robust Force Controller for an Electro-hydraulic Actuator via Quantitative Feedback Theory**, Eng. Prac., 8, 2000, 1335-1345. - PLUMMER, A. R., N. D. VAUGHAN,
**Robust Adaptive Control for Hydraulic Servosystems**, Dyn. Syst., Meas. & Ctrl, 1996, 118, 237-244. - SLOTINE, J. E., W. LI,
**Applied Non-linear Control**, Prentice Hall, 1991, p. 461. - SIDHOM, L., X. BRUN, M. SMAOUI, E. BIDEAUX, D. THOMASSET,
**Dynamic Gains Differentiator for Hydraulic System Control**, J. Dyn. Syst., Meas., & Ctrl., 137(4), 2015, 017-041. - TUSTIN, S.,
**The Effects of Backlash and of Speed-Dependent Friction on the Stability of Closed-Cycle Controls System**, Inst. El. Eng., 94, 1947, 143-151. - WANG, H., W. ZHANG, Y. TIAN, Q. QU,
**Sliding Mode Control for Diesel Engine Using Extended State Observer**, Studies in Informatics and Control, 24(4), 2015, 439-448. - VALIVIITA, S., S. J. OVASKA,
**Delayless Recursive Differentiator With Efficient Noise Attenuation for Control Instrumentation**, Sign. Proc., 34, 1998, 379-384. - YAO, B., F. BU, J. REEDY, G. CHIU,
**Adaptive Robust Motion Control of Single-Rod Hydraulic Actuators: Theory and Experiments**, IEEE/ASME Trans. Mech., 5, 2000, 79-91. - ZAMOUM B., R., B. CHETATE, Y. ZAMOUM
**,****Artificial Neural Network Control of the Recycle Compression System****,**J. St. Inf. & Ctrl, 24(3), 2015, 301-308. - SKENDER, M. R., A. TLEMCANI,
**Implementation of a New Super Twisting Mode Algorithm Controlled by Dspace: Application to Series Multicell Converter**, Studies in Informatics and Control, 25(2), 2016, 255-264.