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Feedback linearization based control of a rotational hydraulic drive Control Engineering Practice,?Volume 15, Issue 12,?December 2007, Pages 1495-1507 Jaho Seo, Ravinder Venugopal and Jean-Pierre Kenné Abstract The technique of feedback linearization is used to design controllers for displacement, velocity and differential pressure control of a rotational hydraulic drive. The controllers, which take into account the square-root nonlinearity in the system's dynamics, are implemented on an experimental test bench and results of performance evaluation tests are presented. The objective of this research is twofold: firstly, to present a unified method for tracking control of displacement, velocity and differential pressure; and secondly, to experimentally address the issue of whether the system can be modeled with sufficient accuracy to effectively cancel out the nonlinearities in a real-world system. Keywords: Nonlinear control; Feedback linearization; Hydraulic actuators; Real-time systems 1. Introduction Electro-hydraulic hydraulic servo-systems (EHSS) are extensively used in several industries for applications ranging from hydraulic stamping and injection molding presses to aerospace flight-control actuators. EHSS serve as very efficient drive systems because they posses a high power/mass ratio, fast response, high stiffness and high load capability. To maximize the advantages of hydraulic systems and to meet increasingly exacting performance specifications in terms of robust tracking with high accuracy and fast response, high performance servo-controllers are required. However, traditional linear controllers ([Anderson, 1988] and [Merritt, 1967]) have performance limitations due to the presence of nonlinear dynamics in EHSS, specifically, a square-root relationship between the differential pressure that drives the flow of the hydraulic fluid, and the flow rate. These limitations have been well documented in the literature; see Ghazy (2001), Sun and Chiu (1999), for example. Several approaches have been proposed to address these limitations, including the use of variable structure control (Ghazy, 2001; Mihajlov, Nikolic, & Antic, 2002), back-stepping (Jovanovic, 2002; [Kaddissi et al., 2005] and [Kaddissi et al., 2007]; Ursu & Popescu, 2002) and feedback linearization ([Chiriboga et al., 1995] and [Jovanovic, 2002]). Variable structure control in its basic form is prone to chattering (Guglielmino & Edge, 2004) since the control algorithm is based on switching; however, several modifications have been proposed to address this problem ([Ghazy, 2001], [Guglielmino and Edge, 2004] and [Mihajlov et al., 2002]). Back-stepping is a technique that is based on Lyapunov theory and guarantees asymptotic tracking ([Jovanovic, 2002], [Kaddissi et al., 2005], [Kaddissi et al., 2007] and [Ursu and Popescu, 2002]), but finding an appropriate candidate Lyapunov function can be challenging. The controllers obtained using this method are typically complicated and tuning control parameters for transient response is non-intuitive. Other Lyapunov based techniques address additional system nonlinearities such as friction, but are also prone to the same drawbacks as those listed for back-stepping (Liu & Alleyne, 1999). Feedback linearization, in which the nonlinear system is transformed into an equivalent linear system by effectively canceling out the nonlinear terms in the closed-loop, provides a way of addressing the nonlinearities in the system while allowing one to use the power of linear control design techniques to address transient response requirements and actuator limitations. The use of feedback linearization for control of EHSS has been described in Chiriboga et al. (1995) and Jovanovic (2002). In Br?cker and Lemmen (2001) disturbance rejection for tracking control of a hydraulic flexible robot is considered, using a decoupling technique similar to the feedback linearization approach proposed herein. However, this approach requires measurements of the disturbance forces and their time derivatives, which are unlikely to be readily available in a practical application. In contrast to the above mentioned techniques, which are all full-state feedback based approaches, Sun and Chiu (1999) describe the design of an observer-based algorithm specifically for force control of an EHSS. An adaptive controller which uses an iterative approach to update control parameters and addresses frictional effects with minimal plant and disturbance knowledge is proposed in Tar, Rudas, Szeghegyi, and Kozlowski (2005) based on the model described in Br?cker and Lemmen (2001). Most of the literature on the subject shows simulation results; notable exceptions with actual experimental results are Liu and Alleyne (1999), Niksefat and Sepehri (1999), Sugiyama and Uchida (2004), and Sun and Chiu (1999). The focus of this study is on presenting a controller design approach that is comprehensive, that is, one that covers displacement, velocity and differential pressure control, addresses the nonlinearities present in EHSS and considers practical issues such as transient response and real-time implementation. Thus, a significant portion of the paper is dedicated to the experimental aspects of the study. In addition, this paper is intended to serve as a clear guide for the development and implementation of feedback linearization based controllers for EHSS. The paper is organized as follows: Section 2 describes the rotational hydraulic drive that is used as an experimental test bench. In this section, the mathematical model of the system is also reviewed and validated using experimental data. Section 3 describes the design of PID controllers for this system with simulation and experimental results that serve as a baseline for evaluating the performance of the feedback linearization controllers; Section 4 describes the design and implementation of the feedback linearization controllers and finally, concluding remarks are provided in Section 5. 2. Modeling System description The electro-hydraulic system for this study is a rotational hydraulic drive at the LITP (Laboratoire d’intégration des technologies de production) of the University of Québec école de technologie supérieure (éTS). The set-up is generic and allows for simple extension of the results herewith to other electro-hydraulic systems, for example, double-acting cylinders. Referring to the functional diagram in Fig. 1, a DC electric motor drives a pump, which delivers oil at a constant supply pressure from the oil tank to each component of the system. The oil is used for the operation of the hydraulic actuator and is returned through the servo-valve to the oil tank at atmospheric pressure. An accumulator and a relief valve are used to maintain a constant supply pressure from the output of the pump. The electro-hydraulic system includes two Moog Series 73 servo-valves which control the movement of the rotary actuator and the load torque of the system. These servo-valves are operated by voltage signals generated by an Opal-RT real-time digital control system. Fig.?1.?Functional diagram of electro-hydraulic system. The actuator and load are both hydraulic motors connected by a common shaft. One servo-valve regulates the flow of hydraulic fluid to the actuator and the other regulates the flow to the load. The actuator operates in a closed-loop while the load operates open-loop, with the load torque being proportional to the command voltage to the load servo-valve. While the actuator and load chosen for this study are rotary drives, the exact same set-up could be used with a linear actuator and load, and thus, they are represented as generic components in Fig. 1. The test set-up includes three sensors, two Noshok Series 200 pressure sensors with a 0–10?V output corresponding to a range of 20.7?MPa (3000 PSI) that measure the pressure in the two chambers of the rotational drive, as well as a tachometer to measure the angular velocity of the drive. In order to reduce the number of sensors used (a common preference for commercial application), angular displacement is obtained by numerically integrating the angular velocity measurement. Fig. 2 shows the layout of the system and the Opal-RT RT-LAB digital control system. Fig.?2.?Layout of LITP test bench. The RT-LAB system consists of a real-time target and a host PC. The real-time target runs a dedicated commercial real-time operating system (QNX), reads sensor signals using an analog-to-digital (A/D) conversion board and generates output voltage signals for the servo-valves using a digital-to-analog (D/A) conversion board. The host PC is used to generate code for the target using MATLAB/Simulink and Opal-RT's RT-LAB software and also to monitor the system. Controller parameters can also be adjusted on-the-fly from the host in RT-LAB. 3. Conclusions The goal of this research is to review the nonlinear dynamics of a rotational hydraulic drive, study how these dynamics lead to limitations in PID controller performance, and to design and implement servo-controllers appropriate for displacement, velocity and pressure control. Feedback linearization theory is introduced as a nonlinear control technique to accomplish this goal in this study, and the controllers designed using this method are validated using experimental tests. From these tests, it can be seen that for hydraulic systems that have nonlinear characteristics, feedback linearization theory provides a powerful control strategy that clearly improves on PID control in terms of tracking precision and transient response. The results show that the system can be modeled with sufficient accuracy to effectively implement the controllers. This study is limited to the control of a rotational hydraulic drive. The application of feedback linearization theory to the control of more complex integrated rotational and linear drives, as well as other effects such as friction, may be considered as future extensions of this work.