Recursive computation of limited lookahead supervisory controls for discrete event systems

We continue the study of limited lookahead policies in supervisory control of discrete event systems undertaken in a previous paper. On-line control of discrete event systems using limited lookahead policies requires, after the execution of each event, the calculation of the supremal controllable sublanguage of a given language with respect to another larger language. These two languages are finite and represented by their tree generators, where one tree is a subtree of the other. These trees change dynamically from step to step, where one step is the execution of one event by the system. We show in this paper how to perform this calculation in a recursive manner, in the sense that the calculation for a new pair of trees can make use of the calculation for the preceding pair, thus substantially reducing the amount of computation that has to be done on-line. In order to make such a recursive procedure possible from step to step, we show how the calculation for a single step (i.e., for a given pair of trees) can itself be performed recursively by means of a backward dynamic programming algorithm on the vertices of the larger tree. These two nested recursive procedures are also extended to the limited lookahead version of the “supervisory control problem with tolerance.”Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45118/1/10626_2005_Article_BF01439177.pd

Limited Lookahead Supervisory Control with Buffering in Discrete Event Systems

The Supervisory Control Theory (SCT) of Discrete Event Systems (DES) provides systematic approaches for designing control command sequences for plants that can be modeled as DES. The design is done "offline" (before supervisor becomes operational) and is based on the plant and design specification DES models. These models are typically large, resulting in DES supervisors that require large computer memory - often unavailable in embedded mobile systems such as space vehicles. An alternative is to use the Limited Lookahead Policies (LLP) in which only models of individual plant components and specifications are stored (which take far less memory). The supervisory control command sequences are then calculated "online" during plant operation. In this way, "online" memory requirement can be reduced at the expense of higher "online" computational operations. In this thesis, the implementation issues of LLP supervisors are studied. The design of LLP supervisors is based on assumptions some of which may not hold in practice. Notably it is assumed that after every event, the supervisory control command can be calculated and applied before the next event occurs. This assumption usually does not hold. To address this issue, a novel technique is proposed in which supervisory control commands are calculated in advance (and online) for a predefined window of events in the future and buffered. When the window starts, the commands would be ready after each event. This eliminates the delay due to online calculations and reduces the delay in responding to new events to levels close to those of standard supervisors (designed "offline"). In an effort to assess the proposed methodology and better understand the implementation issues of SCT, a two degree-of-freedom solar tracker with two servo motors is selected as the plant. Previously, a standard supervisor had been designed for this solar tracker to guide the tracker and perform a sweep to find a sufficiently bright direction to charge the battery and other parts of the system (from its Photo Voltaic cell). The design of the standard supervisor and its software implementation is improved and polished in this thesis. Next the LLP with buffering is implemented. Several experimental results confirm that the plant under the supervision of LLP supervisor with buffering can match the behavior of the plant under the supervision of standard supervisor

PRODUCTION SEQUENCING AND STABILITY ANALYSIS OF A JUST-IN-TIME SYSTEM WITH SEQUENCE DEPENDENT SETUPS

Just-In-Time (JIT) production systems is a popular area for researchers but real-world issues such as sequence dependent setups are often overlooked. This research investigates an approach for determining stability and an approach for mixed product sequencing in production systems with sequence dependent setups and buffer thresholds which signal replenishment of a given buffer. Production systems in this research operate under JIT pull production principles by producing only when demand exists and idle when no demand exists. In the first approach, an iterative method is presented to determine stability for a multi-product production system that operates with replenishment signals and may have sequence dependent setups. In this method, a network of nodes representing machine states and arcs representing the buffer inventory levels is used to find a stable trajectory for the production system via an iterative procedure. The method determines suitable buffer levels for the production system that ensure that a trajectory originating from any point within a buffer region will always map to a point contained on another buffer region for all future mappings. This iterative method for determining the stability of a production system was implemented using an algorithm to calculate the buffer inventory regions for all arcs in a given arc-node network. The algorithm showed favorable results for two and three product systems in which sequence dependent setups may exist. In the second approach, a product sequencing algorithm determines a product sequence for a production system based on system parameters – setup times, buffer levels, usage rates, production rates, etc. The algorithm selects a product by evaluating the goodness of each product that has reached the replenishment threshold at the current time. The algorithm also incorporates a lookahead function that calculates the goodness for some time interval into the future. The lookahead function considers all branches of the tree of potential sequences to prevent the sequence from travelling down a dead-end branch in which the system will be unable to avoid a depleted buffer. The sequencing algorithm allows the user to weight the five terms of the goodness equations (current and lookahead) to control the behavior of the sequence