Switching tube-based MPC: characterization of minimum dwell-time for feasible and robustly stable switching

We study the problem of characterizing mode dependent dwell-times that guarantee safe and stable operation of disturbed switching linear systems in an MPC framework. We assume the switching instances are not known a-priori, but instantly at the moment of switching. We first characterize dwell-times that ensure feasible and stable switching between independently designed robust MPC controllers by means of the well established exponential stability result available in the MPC literature. Then, we employ the concept of multi-set invariance to improve on our previous results, and obtain an exponential stability guarantee for the switching closed-loop dynamics. The theoretical findings are illustrated via a numerical example

Mixed-integer optimal control under minimum dwell time constraints

AbstractTailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to $$\epsilon$$ ϵ -optimality by solving one continuous nonlinear program and one mixed-integer linear program (MILP). Within this work, we analyze the integrality gap of MIOCPs under MDT constraints by providing tight upper bounds on the MILP subproblem. We suggest different rounding schemes for constructing MDT feasible control solutions, e.g., we propose a modification of Sum Up Rounding. A numerical study supplements the theoretical results and compares objective values of integer feasible and relaxed solutions

Model predictive control for linear systems: adaptive, distributed and switching implementations

Thanks to substantial past and recent developments, model predictive control has become one of the most relevant advanced control techniques. Nevertheless, many challenges associated to the reliance of MPC on a mathematical model that accurately depicts the controlled process still exist. This thesis is concerned with three of these challenges, placing the focus on constructing mathematically sound MPC controllers that are comparable in complexity to standard MPC implementations. The first part of this thesis tackles the challenge of model uncertainty in time-varying plants. A new dual MPC controller is devised to robustly control the system in presence of parametric uncertainty and simultaneously identify more accurate representations of the plant while in operation. The main feature of the proposed dual controller is the partition of the input, in order to decouple both objectives. Standard robust MPC concepts are combined with a persistence of excitation approach that guarantees the closed-loop data is informative enough to provide accurate estimates. Finally, the adequacy of the estimates for updating the MPC's prediction model is discussed. The second part of this thesis tackles a specific type of time-varying plant usually referred to as switching systems. A new approach to the computation of dwell-times that guarantee admissible and stable switching between mode-specific MPC controllers is proposed. The approach is computationally tractable, even for large scale systems, and relies on the well-known exponential stability result available for standard MPC controllers. The last part of this thesis tackles the challenge of MPC for large-scale networks composed by several subsystems that experience dynamical coupling. In particular, the approach devised in this thesis is non-cooperative, and does not rely on arbitrarily chosen parameters, or centralized initializations. The result is a distributed control algorithm that requires one step of communication between neighbouring subsystems at each sampling time, in order to properly account for the interaction, and provide admissible and stabilizing control

Towards an access economy model for industrial process control

With the ongoing trend in moving the upper levels of the automation hierarchy to the cloud, there has been investigation into supplying industrial automation as a cloud based service. There are many practical considerations which pose limitations on the feasibility of the idea. This research investigates some of the requirements which would be needed to implement a platform which would facilitate competition between different controllers which would compete to control a process in real-time. This work considers only the issues relating to implementation of the philosophy from a control theoretic perspective, issues relating to hardware/communications infrastructure and cyber security are beyond the scope of this work. A platform is formulated and all the relevant control requirements of the system are discussed. It is found that in order for such a platform to determine the behaviour of a controller, it would need to simulate the controller on a model of the process over an extended period of time. This would require a measure of the disturbance to be available, or at least an estimate thereof. This therefore increases the complexity of the platform. The practicality of implementing such a platform is discussed in terms of system identification and model/controller maintenance. A model of the surge tank from SibanyeStillwater’s Platinum bulk tailings treatment (BTT) plant, the aim of which is to keep the density of the tank outflow constant while maintaining a steady tank level, was derived, linearised and an input-output controllability analysis performed on the model. Six controllers were developed for the process, including four conventional feedback controllers (decentralised PI, inverse, modified inverse and H¥) and two Model Predictive Controllers (MPC) (one linear and another nonlinear). It was shown that both the inverse based and H¥ controllers fail to control the tank level to set-point in the event of an unmeasured disturbance. The competing concept was successfully illustrated on this process with the linear MPC controller being the most often selected controller, and the overall performance of the plant substantially improved by having access to more advanced control techniques, which is facilitated by the proposed platform. A first appendix presents an investigation into a previously proposed switching philosophy [15] in terms of its ability to determine the best controller, as well as the stability of the switching scheme. It is found that this philosophy cannot provide an accurate measure of controller performance owing to the use of one step ahead predictions to analyse controller behaviour. Owing to this, the philosophy can select an unstable controller when there is a stable, well tuned controller competing to control the process. A second appendix shows that there are cases where overall system performance can be improved through the use of the proposed platform. In the presence of constraints on the rate of change of the inputs, a more aggressive controller is shown to be selected so long as the disturbance or reference changes do not cause the controller to violate these input constraints. This means that switching back to a less aggressive controller is necessary in the event that the controller attempts to violate these constraints. This is demonstrated on a simple first order plant as well as the surge tank process. Overall it is concluded that, while there are practical issues surrounding plant and system identification and model/controller maintenance, it would be possible to implement such a platform which would allow a given plant access to advanced process control solutions without the need for procuring the services of a large vendor.Dissertation (MEng)--University of Pretoria, 2020.Electrical, Electronic and Computer EngineeringMEngUnrestricte