A Radial Basis Function Method for Approximating the Optimal Event-Based Sampling Policy

In networked control systems it is desirable to have efficient wireless communication (saving energy and bandwidth) while still ensuring good control performance. By abandoning periodic sampling, communication can be made more efficient by sampling and updating the control signal only "when required" based on the system’s behaviour. This is the concept of event-based control. In this work we consider the classic LQG problem with an added penalty on the average sampling rate, and derive a numerical method using radial basis functions (RBFs) to approximate the optimal sampling policy. The method is validated numerically, and we prove guaranteed uniqueness and existence of the optimal RBF weights

An Improved Stochastic Send-on-Delta Scheme for Event-Based State Estimation

Event-based sensing and communication holds the promise of lower resource utilization and/or better performance for remote state estimation applicationsin e.g networked control systems (NCS). However, the problem of designing an optimal event-based state estimator often becomes untractable due to nonlinear measurements. This complexity is avoided with stochastic event-triggering. In this work, we extend the previous work on stochastic triggering by proposing a simple predictor in the sensor to further improve the estimation performance

Development of a Solution for Start-up Optimization of a Thermal Power Plant

This thesis covers optimizing the first phase of the start-up of a thermal power plant using Nonlinear Model Predictive Control (NMPC) and state estimation using an Unscented Kalman Filter (UKF). The start-up has been optimized in regards to time and fuel usage. The thesis is done as a joint project between Vattenfall and Modelon. Both NMPC and UKF are nonlinear methods and require a model of the power plant. The model used in this thesis has been developed in the language Modelica in a previous master thesis and has been extended and improved upon during this thesis. The optimization and simulation of the model required by the NMPC and UKF was done within the framework of JModelica.org. Another, more detailed, model of the power plant, developed by Vattenfall, was originally planned to be used as the process to be controlled. State estimation using the UKF has been successful, with a maximum mean absolute error of 0.7 % when estimating the states of the detailed model in a reference startup. When using the NMPC to control the optimization model itself, the simulated start-up time is 70 minutes faster compared to a reference start-up using the detailed model. This is more than half the time of the first phase of the start-up. The total firing power, which relates to the fuel amount, is also considerably less, with the optimized value being about 40 % of that in the reference soft start with the detailed model. Due to difficulties in initializing the detailed model, it was not possible to run it online together with the NMPC and UKF. Running the NMPC and UKF together on the optimization model worked, but the NMPC failed to find an optimal trajectory 8 out of 10 iterations. The conclusion is that the start-up has potential for optimization, but requires more robust models to work with

Event-Based State Estimation Using an Improved Stochastic Send-on-Delta Sampling Scheme

Event-based sensing and communication holds the promise of lower resource utilization and/or better performance for remote state estimation applications found in e.g. networked control systems. Recently, stochastic event-triggering rules have been proposed as a means to avoid the complexity of the problem that normally arises in event-based estimator design. By using a scaled Gaussian function in the stochastic triggering scheme, the optimal remote state estimator becomes a linear Kalman filter with a case dependent measurement update. In this paper we propose a modified version of the stochastic send-on-delta triggering rule. The idea is to use a very simple predictor in the sensor, which allows the communication rate to be reduced while preserving estimation performance compared to regular stochastic send-on-delta sampling. We derive the optimal mean-square error estimator for the new scheme and present upper and lower bounds on the error covariance. The proposed scheme is evaluated in numerical examples, where it compares favorably to previous stochastic sampling approaches, and is shown to preserve estimation performance well even at large reductions in communication rate

On LQG-Optimal Event-Based Sampling

Event-based control is a promising concept for the design of resource-efficient feedback systems, where events such as sampling, actuation, and data transmissions are triggered reactively based on monitored control performance rather than a periodic timer. In this thesis, we investigate how sampling and communication events should be triggered to fully exploit the potential of event-based control based on the classic linear–quadratic–Gaussian (LQG) framework.The design of the event trigger is formulated as a trade-off between a quadratic cost on control performance and the average event rate. The optimal event trigger is well-known for first-order systems, where it corresponds to a scalar symmetric threshold on the monitored control performance. In this thesis, we consider systems of higher order, where the shape of the optimal threshold is generally unknown. For two new system classes with previously unknown solutions, we prove that the optimal threshold is ellipsoidal for all system orders. Additionally, we propose two numerical methods for finding the optimal threshold shape for general systems.Suboptimal but simpler designs in the form of event-based proportional–integral–derivative (PID) control are also considered. Inspired by results from LQG-optimal sampled-data control, we derive an “ideal” (in the LQG sense) sampled-data PID implementation, from which a range of design options of varying complexity for event-based PID control is proposed. Based on numerical evaluations, we present a proposal implementation that strikes a balance between performance and simplicity. Finally, this thesis also considers stochastic triggering, where events are triggered according to a certain probability. Two policies for stochastic triggering are proposed for a remote state estimation problem, both featuring predictions in the sensor for improved estimation performance. Both policies compare well to other proposals from the literature, and one of the policies also offers significantly simpler performance analysis

LQG-Optimal versus Simple Event-Based PID Controllers

In this paper, we study event-based PID control from an optimal stochastic control perspective. The purpose is to better understand what implementation features are critical for achieving good event-based PID performance. For this end, we formulate an LQG control design problem for a double integrator process with an integral disturbance, where the solution is an ideal PID controller. We then consider the trade-off between LQG cost and average sampling rate and give an interpretation of the optimal sampled-data controller and event-based sampling policy in terms of PID control. Based on insights from the optimal solution, we finally discuss how suboptimal but simple event-based PID controllers can be implemented. The proposed implementation is evaluated in a simulation study and compared to earlier work in event-based PID control. The results highlight the importance of considering both the triggering rule and the transmitted information in order to obtain an event-based PID controller with good performance

On Event-Based Sampling for LQG-Optimal Control

We consider the problem of finding an event-based sampling scheme that optimizes the trade-off between average sampling rate and control performance in a linear-quadratic-Gaussian (LQG) control problem setting with output feedback. Our analysis is based on a recently presented sampled-data controller structure, which remains LQG-optimal for any choice of sampling scheme. We show that optimization of the sampling scheme is related to an elliptic convection–diffusion type partial differential equation over a domain with free boundary, a so called Stefan problem. A numerical method is presented to solve this problem for second order systems, and thus obtain an optimal sampling scheme. The method also directly generalizes to higher order systems, although with a higher computational cost. For the special case of multidimensional integrator systems, we present the optimal sampling scheme on closed form, and prove that it will always outperform its periodic counterpart. Tight bounds on the improvement are presented. The improved performance is also demonstrated in numerical examples, both for an integrator system and a more general case

Cloud Application Predictability through Integrated Load-Balancing and Service Time Control

Cloud computing provides the illusion of infinite capacity to application developers. However, data center provisioning is complex and it is still necessary to handle the risk of capacity shortages. To handle capacity shortages, graceful degradation techniques sacrifice user experience for predictability. In all these cases, the decision making policy that determines the degradation interferes with other decisions happening at the infrastructure level, like load-balancing choices. Here, we reconcile the two approaches, developing a load-balancing strategy that also handles capacity shortages and graceful degradation when necessary. The proposal is based on a sound control-theoretical approach. The design of the approach avoids the pitfalls of interfering control decisions. We describe the technique and provide evidence that it allows us to achieve higher performance in terms of emergency management and user experience

Modelling and simulation of a coal-fired power plant for start-up optimisation

The increased impact from fluctuating energy sources like wind and photovoltaics significantly affects the operational regime of conventional power plants. In the near future, even former base load power plants such as the large-scale lignite plants in Germany will need to start and shut down to balance the electricity system. As frequent starts were not in the focus of optimisation in the past, an extensive potential can be expected to reduce start-up costs and environmental impacts. In order to investigate such optimisation potentials, a comprehensive dynamic simulation model has been developed including process components such as boiler and water-steam cycle but also the power plants control system along with start-up sequence control. After successfully reproducing a reference start of the power plant, the model has been used to identify restrictions for faster start-ups, less fuel consumption and less emission while keeping the thermal and mechanical stress, caused by higher ramp rates, within acceptable bounds