Hybrid Systems and Hybrid Bond Graph Models
A hybrid system consists of interacting continuous and discrete dynamics—a system that can both flow and jump. Hybrid systems emerge from manufacturing system, automotive engine control, chemical process, aerospace engineering as well as embedded control
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Hybrid Systems and Hybrid Bond Graph Models
2.1 Hybrid Systems In general, the term “hybrid” refers to heterogeneous in nature and “hybrid system” means a system which consists of interacting continuous and discrete dynamics [1, 2]. The discrete states are usually represented by modes. Figure 2.1 shows a diagram of hybrid systems. Discrete events (transitions) trigger the system to undergo from one mode to another. At each mode, the system is governed by continuous dynamics, and different modes correspond to different continuous dynamic models. For continuous dynamic systems, the state variables continuously change through time and hence are considered as time-driven. The possible values of these continuous state variables are real number, and differential equations are the general tools to model continuous systems. In contrast to continuous dynamic systems, discrete event dynamic systems are discrete-state, event-driven systems where the state evolution depends entirely on the occurrence of instantaneous discrete events. These systems contain solely of discrete state spaces and event-driven state transition mechanisms [3, 4]. The state variables of discrete event dynamic systems remain constant between events and are evolved in a discontinuous way by the occurrence of discrete events. Examples of instantaneous events like switching on and off a valve or acquisition roll contacting the paper of a printer. The possible values of discrete state variables take from an enumerable set of values. Hybrid dynamical systems possess state variables of both continuous and discrete values, i.e., state changes either continuously or discretely. In other words, hybrid dynamical systems can be treated as both time-driven and eventdriven [5, 6]. The transition in hybrid dynamical systems could happen autonomously as a result of the continuous evolution of system variables or due to a discrete event such as a control command (a jump from one mode to another). In real world applications, there are many examples of hybrid systems such as high speed printer, automotive, switched mode power converter and so forth [7, 8]. For example, the feeding motor of a printer can be in a ramp-up mode, a rotational constant velocity mode, a ramp-down mode, or an idle mode [9, 10]. Each of these modes is governed by a different time-driven continuous model. On the other hand, D. Wang et al., Model-based Health Monitoring of Hybrid Systems, DOI: 10.1007/978-1-4614-7369-5_2, © Springer Science+Business Media New York 2013
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2 Hybrid Systems and Hybrid Bond Graph Models
Fig. 2.1 Diagram of hybrid systems
the system is also characterized by discrete events, some of which can be attributed to control events and others are caused by continuous state variables crossing threshold values. For instance, the transition from idle mode to ramp-up mode for the motor is caused by a “turn_motor_on” control event. However, a transition that represents the acquisition roll contacting the paper is autonomous, and must be estimated using model and sensor dat
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