Event-driven control in theory and practice : trade-offs in software and control performance

Feedback control algorithms are indispensable for the proper functioning of many industrial high-tech systems like copiers, wafer steppers and so on. Most research in digital feedback control considers periodic or time-driven control systems, where continuous-time signals are represented by their sampled values at a fixed frequency. In most applications, these digital control algorithms are implemented in a real-time embedded software environment. As a consequence of the time-driven nature of controllers, control engineers pose strong, non-negotiable requirements on the real-time implementations of their algorithms as the required control performance can be guaranteed in this manner. This might lead to non-optimal solutions if the design problem is considered from a broader multi-disciplinary system perspective. As an example, time-driven controllers perform control calculations all the time at a fixed rate, so also when nothing significant has happened in the process. This is clearly an unnecessary waste of resources like processor load and communication bus load and thus not optimal if these aspects are considered as well. To reduce the severe real-time constraints imposed by the control engineer and the accompanying disadvantages, this thesis proposes to drop the strict requirement of equidistant sampling. This enables the designers to make better balanced multidisciplinary trade-offs resulting in a better overall system performance and reduced cost price. By not requiring equidistant sampling, one could for instance vary the sample frequency over time and dynamically schedule the control algorithms in order to optimize over processor load. Another option is to perform a control update when new measurement data arrives. In this manner quantization effects and latencies are reduced considerably, which can reduce the required sensor resolution and thus the system cost price. As it is now an event (e.g. the arrival of a new measurement), rather than the elapse of time, that triggers the controller to perform an update, this type of feedback controllers is called event-driven control. In this thesis, we present two different event-driven control structures. The first one is sensor-based event-driven control in the sense that the control update is triggered by the arrival of new sensor data. In particular, this control structure is applied to accurately control a motor, based on an (extremely) low resolution encoder. The control design is based on transforming the system equations from the time domain to the angular position (spatial) domain. As controller updates are synchronous with respect to the angular position of the motor, we can apply variations on classical control theory to design and tune the controller. As a result of the transformation, the typical control measures that we obtain from analysis, are formulated in the spatial domain. For instance, the bandwidth of the controller is not expressed in Hertz (s¡1) anymore, but in rad¡1 and settling time is replaced by settling distance. For many high-tech systems these spatial measures directly relate to the real performance requirements. Moreover, disturbances are often more easily formulated in terms of angular position than in terms of time, which has clear advantages from a modeling point of view. To validate the theory, the controller is implemented on a high speed document printing system, to accurately control a motor based on an encoder resolution of only 1 pulse per revolution. By means of analysis, simulation and measurements we show that the control performance is similar to the initially proposed industrial controller that is based on a much higher encoder resolution. Moreover, we show that the proposed event-driven controller involves a significant lower processor load and hence outperforms the time-driven controller from a system perspective. The aim of the second type of event-driven controllers is to reduce the resource utilization for the controller tasks, such as processor load and communication bus load. The main idea is to only update the controller when it is necessary from a control performance point of view. For instance, we propose event-driven controllers that do not update the control value when the tracking/stabilization error is below a certain threshold. By choosing this threshold, a trade-off can be made between control performance and processor load. To get insight in this trade-off, theory is presented to analyze the control performance of these event-driven control loops in terms of ultimate bounds on the tracking/stabilization error. The theory is based on inferring properties (like robust positive invariance, ultimate boundedness and convergence indices) for the event-driven controlled system from discrete-time linear systems and piecewise linear systems. Next to the theoretical analysis, simulations and experiments are carried out on a printer paper path test-setup. It is shown that for the particular application the average processing time, needed to execute the controller tasks, was reduced by a factor 2 without significant degradation of the control performance in comparison to a timedriven implementation. Moreover, we developed a method to accurately predict the processor load for different processing platforms. This method is based on simulation models and micro measurements on the processing platform, such that the processor load can be estimated prior to implementing the controller on the platform. Next to these contributions in the field of event-driven control, a system engineering technique called "threads of reasoning" is extended and applied to the printer case study to achieve a focus on the right issues and trade-offs in a design. In summary, two types of event-driven controllers are theoretically analyzed and experimentally validated on a prototype document printing system. The results clearly indicate the potential benefits of event-driven control with respect to the overall system performance and in making trade-offs between control performance, software performance and cost price.