An observer based approach for achieving fault diagnosis and fault tolerant control of systems modeled as hybrid Petri nets
Introduction
The concepts of fault detection and diagnosis (FDD) and fault tolerant control (FTC) have gained wide importance in the recent years in order to provide higher reliability and safety standards as well as improving the quality, cost and efficiency of most technical processes [1], [2].
The faults occurring in the system are either due to the malfunctions of the main processing equipment (leak in tanks, variations in process parameters like mass flow rate, heat transfer coefficient, gas storage rate etc.) or in the auxiliary equipment (bias/drift in sensors, actuators, pumps, controller outputs, stuck sensors, actuators and pumps) [3]. The general practice involved in many industries is to isolate the fault after diagnosis. But some faults which can be tolerated [4] under certain conditions have also been considered nowadays, whereby the productivity is not affected at any cost. For example, in process industries, the need for fault tolerant control can be explained by the way the measurement/control signals are transmitted usually using 4–20 mA signal lines. The significance for using 4 mA rather than 0 mA as the lower limit is to provide inherent FTC against broken wires. The other instance which can be considered are the circumstances where multiple pumps are designed and considered over a large pump to discharge the same capacity to avoid the problems occurring due to pump failures. Lastly, it can also be seen in process industries where multiple sensors and transmitters are placed in strategic points in the plant to measure the same possible critical variables to enhance FTC against sensor failures.
Numerous approaches have been dealt to achieve FDD in the past few years. Ramirez-Trevino, et al. in [5] dealt with achieving on-line FDD of discrete event systems based on modeling the system using Interpreted Petri nets (IPN). A unique procedure has been used by developing an online diagnosis which efficiently monitors the output of the system as well as handles the normal behavior model for detecting and locating faults. FDD achieved using the scheme of structured residual approach for a multi input multi output (MIMO) process has been proposed by Asokan and Sivakumar in [6]. Here, techniques such as residual generation and evaluation have been considered for detecting multiple faults based on a state space model derived from first principles. The concept of achieving FDD for nonlinear systems using an observer based approach was given by Rincon, et al. in [7] wherein two schemes of nonlinear observers were used for reconstructing faulty signals for determining fault diagnosability with minimum number of measurements from the system. FDD along with isolation based on model checking technique using a timed automaton was described by Simeu, et al. in [8]. The concepts of fault detection, isolation, estimation and control compensation using analytical redundancy were described by Theillol, et al. in [9].
From a detailed study, it was found that the techniques described and proposed earlier were either based on state models developed from first principles using a timed automaton or using discrete event systems, wherein the system was analyzed based on its continuous or discrete behaviors, considered individually. In this paper, a hybrid dynamic system (HDS), which describes both discrete and continuous behaviors along with their interdependencies are considered. Petri nets as a modeling tool are useful for the study of HDS [10] because they combine discrete and structural aspects with continuous evolution. Continuous Petri nets [11] are particularly suitable for modeling flows: liquid flow or continuous production of a machine. However, a flow may be suddenly interrupted; for example, closing of a valve or a machine breakdown. This is equivalent to having another continuous Petri net. This situation can instead be modeled by a hybrid Petri net containing both continuous and discrete places and transitions. In addition, in a hybrid Petri net, discrete marking may be converted into a continuous marking, and vice versa. Hence, for these reasons, hybrid Petri nets are considered for modeling the system. For achieving FDD and FTC, observer based techniques have been considered.
The concept, properties and analysis of hybrid Petri nets are utilized for modeling a three tank system initially. The three tank system considered for modeling is the system which was considered in [12], wherein the system was modeled using continuous Petri nets. But here, the semantics of timed Hybrid Petri nets are applied (instead of D-elementary Petri nets considered in [10]) and improved results are obtained. After modeling the system, a detailed analysis is done for achieving FDD and FTC using estimation techniques. For this purpose, an algorithm is proposed and analytical results are obtained. Finally, performance measures are evaluated, and the results are compared.
Section snippets
Background of Petri nets
The definitions and notations for discrete, continuous and hybrid Petri nets are as follows.
System description
The system of three connected tanks as shown in Fig. 1 comprises tanks T1 and T2, which are supplied by liquid flowing continuously through pumps 1 and 2 connected to valves V1 and V2. Tanks T1 and T3 are connected by means of valve V3. Similarly, tanks T2 and T3 are connected by valve V4. After considerable amount of time, the collected liquid in tank T3 is drained out through valve V5. The details of specifications for the system are listed in Table 1. The reason for choosing different
Observer concept
Observer based FDD [16] is obtained under two considerations that (1) the initial marking and sequence of transitions (word) are known initially, and (2) the initial marking is not known. Moreover, the observer concept has been utilized for estimating the continuous part of the model developed separately based on a model based event feedback system as shown in Fig. 6. Here, denotes the vector of event markings and is the control signal sent from the controller.
It is also true that, when the
Results and discussions
The proposed algorithm along with the simulation results and analysis for achieving FDD along with FTC are as follows:
Conclusions
In this paper, an estimation technique for achieving FDD and FTC is proposed. For this purpose, a three tank system is considered for study, and modeled using hybrid Petri nets. Based on the model developed, algorithms are proposed to achieve FDD and FTC of the systems separately, and the results are obtained. The main aspects of this paper are as follows:
- 1.
An algorithm for achieving FDD of a hybrid system is proposed based on considering the continuous part, rather than the discrete part [16].
- 2.
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