【文章內(nèi)容簡(jiǎn)介】 Lipschitz, we assume that the system is observable for any input. However, we have constructed the observer under rather general practical assumptions that consider Lipschitz nonlinearity condition is satisfied at least locally. Indeed, this is a kind of extended Luenberger observer. In other word, we weaken the concept of observability to consider only practical justi fication. Therefore, it may sufce to get measurable output for any inputs to consider the system as locally observable. Residual generation is also important for fault detection, as it makes known the state of the system. However, it does not provide sufcient information about the detection of the fault unless it is evaluated using a statistical decisionmaking method. Herein, we propose the evaluation of residuals using Wald_s sequential test, a robust statistical method for detecting the occurrence of a fault. One of the char acteristics of Wald_s method is that the number of observations required is not deter mined in advance of the experiment. The decision to terminate the experiment, therefore, depends at each stage, on the results of the observations previously made. Subsequently, the Wald sequential test frequently results in savings of about 110% in the number of observations over the most efcient of other test procedures based on fixed numbers of observations. If an individual sensor is detected as being temporarily or permanently defective, it should be automatically phased out of normal system operation, and if possible, replaced with one or more alternative sensors. Even though a number of publications do exist in this domain, the industrial application of the techniques, particularly in ?uid power systems, continues to be sparse. In addition, hydraulic systems are plex and can experience ponent failures。 in hydraulic manipulators, for instance, a drop in supply pump pressure that causes actuators to stall could have disastrous consequences. In this work, the above technical challenge are addressed for an electrohydraulic servopositioning system through the use of a specific type of supervision system, (i) employing a nonlinear observer, and (ii) incorporating the Wald sequential test to detect the occurrence of a fault. Experimental verifications were conducted to evaluate both the observer and the fault detection technique performances. This paper is organized as follows. The experimental test rig and its mathematical model are described in Section 2. Section 3 outlines a review of relevant literature, and the design and analysis of the nonlinear observer, followed by a description of the method for fault detection. Section 4 presents observer performance simulation re sults for piston velocity and pressure, and experimental results for incorrect pump pressure as well as sensor faults. 1040 H. Khan et al. / Mechatronics 15 (2005) 10371059 2. Experimental setup and mathematical modelling Fig. 1 shows the hydraulic test station used in conducting experiments. It consists of a pressure source and an electrohydraulic proportional valve connected to a hydraulic cylinder by ?exible hoses. The output ?ow of the pump can be set to a maximum ?ow rating of 28 l/min, at a nominal speed of 1800 rpm. The pump pressure can be regulated to up to 250 bar. The valve is a lowcost proportional valve. The positioning of the valve spool is based on the pulse width modulation principle. The reaction time of the valve from the neutral position to maximal spool travel is rated at 120 ms. Fig. 2 shows the schematic diagram of the test station shown in Fig. 1. With ref erence to this figure, the governing nonlinear equations describing the ?uid ?ow dis tribution in the valve are written in their simplest forms as follows [12]: ( x sp P 0 240。extension222。 xsp 0 240。retraction222。 q 188。 i k dwxsp k dwxsp k dwxsp k dwxsp ( pffffffffffffff P s _ P i pffffffffffffff P i _ P r pffffffffffffffff P o _ P r pffffffffffffffff P s _ P o 240。 1222。 q 188。 o x sp P 0 240。extension222。 xsp 0 240。retraction222。 240。 2222。 where q i and q o represent ?uid ?ows into and out of the valve, respectively。 k d is the metering coefcient, and w is the orifice area gradient that relates the spool displace ment, x sp to the orifice area. P s is the pump pressure, while P i and P o are the input and output line pressures, respectively, and P r is the return pressure. Continuity equations for oil ?ow through the cylinder, neglecting the leakage ?ow across the actuator_s piston are, [6] 8 q i 188。 V i240。x222。 b _ iP 254。 A iv 240。 3222。 : q 188。 _ o V o240。x222。 b _ oP 254。 A ov Fig. 1. Experimental hydraulic test station. H. Khan et al. / Mechatronics 15 (2005) 10371059 1041 U p 3 P i 4 U Po p r d Ai Ao X qi q o 1 Analog and Digital Interface Board u xsp Ps 2 M Pr Fig. 2. Schematic of hydraulic actuator: (1) proportional valve。 (2) pump with pressure regulator。 (3) pressure transducer and (4) incremental encoder. where v 188。 x_ is the actuator_s linear velocity. A i and A o are the piston efective areas, b is the efective bulk modulus of the hydraulic ?uid. V i(x) and V o(x) are the volumes of the ?uid trapped at the sides of the actuator, including hoses, and are functions of actuator displacement, x. Although higherorder nonlinear models of the mechanical behaviour of servo valves can be developed from the relationship between the