Microcontroller Based Supervisory Control of a Solar Tracker

The Supervisory Control theory (SCT) of Discrete-Event Systems is concerned with the design of supervisors that can generate appropriate control command sequences that meet the plant design specifications. Examples of these sequences include the startup and shut-down command sequences of a spacecraft engine. This thesis addresses the implementation of Supervisory Controller (SC) executing on microcontroller hardware. The plant studied is a 2 degree-of-freedom solar tracker. Existing implementations of Supervisory Control Theory focus on Programmable Logic Controller (PLC) based systems. PLCs are mainly used in process control and manufacturing applications. These implementations have proven advantages but suffer from numerous drawbacks. The hardware is large, expensive and over engineered for many embedded system applications. Additionally, a number of disconnects between Supervisory Control Theory and their practical application exist. These include but are not limited to: the Avalanche Effect, Inexact Synchronization and Simultaneous Events. This thesis extends the application of SCT to the field of microcontroller-based embedded systems. Methods to minimize or remove the effects of Avalanche Effect, Inexact Synchronization, and Simultaneous Events are analyzed in a microcontroller-based environment. Additionally, design procedures for the modelling and implementation of a supervisory controller executing within a microcontroller are explored. To this end, a physical implementation of a real system was created and documented. An offline computation of the system supervisor is derived in MATLAB and stored in the system’s onboard memory as a State Transition Table (STT). An optimized storage method is developed that allows for fast execution of state transitions and a low memory footprint

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

Lower Bound for the Duration of Event Sequences of Given Length in Timed Discrete Event Systems

The Supervisory Control Theory (SCT) of Discrete Event Systems (DES) provides a framework for synthesizing a DES supervisor to ensure a DES plant satisfies its design specification. In SCT, supervisor synthesis is performed offline before the functioning of the plant. Generally, the size of the plant and the specifications models are large resulting in supervisors that need huge computer memory for storage -- usually unavailable in embedded systems. A solution to this problem proposed in the literature is Limited Lookahead Policy (LLP). In LLP, the supervisory control commands are calculated online during the plant operation. After the occurrence of each event, the next control command is calculated based on the plant behaviour over a limited number of events into the future. In practice such frequent LLP computation would not be feasible as multiple events can occur consecutively over a short duration, not leaving enough time for LLP computation between them. To tackle this issue, a method is proposed called LLP with Buffering where the supervisory control commands are calculated online and buffered in advance for a predefined window of events in future. Determining the correct size of the buffer is crucial in order to achieve a trade-off between the on-board memory requirement and the computational resources and also ensuring that new supervisor commands are computed before the buffer runs out empty. The size of the buffer primarily depends on (1) the execution time of the code for supervisor calculation and (2) the (fastest) rate of event generation in the plant. This thesis focuses on the second factor. Previously, the minimum execution duration of event sequences has been calculated experimentally. The experimental approach is not exhaustive and thus results in an overestimate in the value of the minimum execution duration of event sequences. In this thesis, a model-based approach to the computation of the minimum duration is proposed which begins by transforming the untimed model of the plant under supervision into a timed automaton (TA) by incorporating timing information of the events. Next, an exhaustive symbolic matrix-based search algorithm is proposed where all the event sequences from every mode of the TA model are traversed to determine the minimum execution duration of the event sequences. The proposed method avoids the reachability analysis of TA needed to determine the reachable clock regions for each mode. The number of these regions is exponential in the number of events. Instead, the method uses reachability on the graph of the untimed model (polynomial in the number of events). This algorithm runs faster but provides an underestimate for the minimum execution duration of event sequences. Next, a two-degree-of-freedom solar tracker system is used as a plant to analyse the timing behaviour of the events and the implementation of LLP with buffering. In this study, the model-based and experimental methods have been used together to choose a suitable buffer size. The resulting LLP supervisor with buffering has been successfully implemented