# Automation of a Hybrid Control for Electrohydraulic Servo-Actuators with Residual Dynamics
###### Abstract
Recently, we have developed a hybrid position/force controller for a hydraulic actuator [32]. The idea here is defined by a global hybrid position/force control structure design based on a reduced state-space linear model. For such a design, the control parameters are determined separately as having the performances required in each configuration. In addition, autonomous switching is elaborated via a hysteresis relay where the switching is triggered by a hard stop. Despite the simplicity of the designed feedback controller, it is noteworthy to indicate the local character of such an algorithm, which leads to working on a limited domain of an operating range of the system. In addition, the control gain settings are determined via the standard pole placement for both position and force modes. Consequently, any change in the operating point requires a re-calculation of these gains. On the other hand, the stability proof remains locally limited to the operating points relating to the specific tests that are carried out. Although the tracking performance of the proposed controller is good, the force trajectory presents some overshoot at switching times. In Ref. [33], the authors circumvented the so-called stick-slip problem on the electroneumatic actuator with empirical switching controllers. To prove the stability, the closed-loop system was described in a piecewise-affine form to find a Lyapunov function for it. There are several tools in the literature for analyzing the stability of a switched system. A survey of basic problems on the stability and design of switched systems has been proposed in Refs. [34; 35]. In Refs. [36; 37], the authors introduced the concept of hybrid systems and some challenges associated with the stability of such systems. In Ref. [38], the stability condition with multiple Lyapunov functions for switched systems was considered. The stability proof using these methods is conditioned by the resident time of every subsystem that must be supposed relatively small. Otherwise, the stability can only be checked. It is well known that the choice of the switching signal is important regardless of the switching type. For the time-dependent switching controller, a close relationship exists between the switching times and the design of the desired trajectories imposed on the process. Usually, the switching occurrences are manually adjusted to commute between different subsystems, but, in real-time applications, some state problems may appear [28]. Such problems can be so dangerous as to harm some sensors on the test bench. Moreover, these problems become more serious in the presence of some residual dynamics. Supposing that these uncontrolled dynamics are stable, the problem amounts exactly to the convergence time of these dynamics. In most of the previous works, switching was defined by imposing either the instants of switching or conditions on the system states. Such a switching choice does not prevent the appearance of undesirable peaks during switching. Our work is different to previous works since it proposes a purely mathematical solution, which allows automatically updating the desired force trajectory by taking into account the time of convergence of the residual dynamics. In this paper, the problem of time-dependent switching hybrid controller position/force is considered for electrohydraulic servo-actuator systems with a flexible load. The presence of such a load makes it possible to have uncontrolled states on the dynamics of one subsystem. To avoid any damage at switching times, our proposed solution is to design a force trajectory generator that is based on the desired position trajectory, previous switching times and time convergence of residual dynamics where it is computed in real time. Thus, our contribution is to conceive a specified switching law to guarantee system commutation without any problems. The outline of this paper is as follows. Section 2 presents the system dynamics, including an electro-hydraulic servo-actuator.