Stabilising Model Predictive Control for Discrete-time Fractional-order Systems

In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an asymptotically stable equilibrium point of the controlled system. We employ a finite-dimensional approximation of the original infinite-dimensional dynamics for which the approximation error can become arbitrarily small. We use the approximate dynamics to design a tube-based model predictive controller which steers the system state to a neighbourhood of the origin of controlled size. We finally derive stability conditions for the MPC-controlled system which are computationally tractable and account for the infinite dimensional nature of the fractional-order system and the state and input constraints. The proposed control methodology guarantees asymptotic stability of the discrete-time fractional order system, satisfaction of the prescribed constraints and recursive feasibility

Genetic Algorithm based Model Predictive Control of Fractional Order Systems

International audienceFractional calculus is a generalization of integration and derivative operators to no integer order. In the Last decades fractional systems receives a great attention in the research community, the reason lies in the fact that many real systems can be described accurately using dynamic models of fractional order. In our work a design of genetic algorithm based fractional order model predictive controller is simulated and applied to a given fractional order model plant

Robust model predictive control for discrete-time fractional-order systems

In this paper we propose a tube-based robust model predictive control scheme for fractional-order discrete-time systems of the Grunwald-Letnikov type with state and input constraints. We first approximate the infinite-dimensional fractional-order system by a finite-dimensional linear system and we show that the actual dynamics can be approximated arbitrarily tight. We use the approximate dynamics to design a tube-based model predictive controller which endows to the controlled closed-loop system robust stability properties

A Case Study of Fractional-Order Control

This thesis concerns fractional-order (non-integer) methods for control system design. Although fractional-order calculus has a long history in mathematics and engineering, the uptake of relevant fractional-order concepts in control systems research has been relatively slow, and interest in the topic remains comparatively low—albeit with some important exceptions, as highlighted by the literature review of this thesis. The first part of the thesis considers fractional-order methods for modelling and control in quite broad terms, before later focusing on one particular approach from the control systems literature, namely Fractional-order Generalised Predictive Control (FGPC). The FGPC approach is of particular interest here because of its relationship with the well-known, conventional control algorithm, namely Generalised Predictive Control (GPC). Both algorithms have a relatively straightforward implementation form, making them attractive to practitioners. Hence, one contribution of the thesis is to use worked examples in MATLAB as an introduction to GPC and FGPC design methods, in part for tutorial reasons. More significantly, the thesis demonstrates how fractional-order methods are utilised to increase control design flexibility. In this regard, the thesis investigates both conventional GPC and FGPC methods using various simulation examples. The robustness of control systems is investigated via Monte Carlo simulation, with consideration of model mismatch and unmeasured disturbances. These results Abstract II are utilised to develop recommendations for how to optimise the extra design coefficients introduced in the fractional-order case. The comparative study is extended to a laboratory example, namely the control of airflow in a 1 m by 2 m by 2 m forced ventilation environmental test chamber. To facilitate further uptake of FGPC methods in the future, the algorithms developed are prepared as a MATLAB toolbox, i.e. a collection of functions that calculate and implement the FGPC approach and subsequently measure the performance of the controller

The potential of fractional order distributed MPC applied to steam/water loop in large scale ships

The steam/water loop is a crucial part of a steam power plant. However, satisfying control performance is difficult to obtain due to the frequent disturbance and load fluctuation. A fractional order model predictive control was studied in this paper to improve the control performance of the steam/water loop. Firstly, the dynamic of the steam/water loop was introduced in large-scale ships. Then, the model predictive control with an extended prediction self adaptive controller framework was designed for the steam/water loop with a distributed scheme. Instead of an integer cost function, a fractional order cost function was applied in the model predictive control optimization step. The superiority of the fractional order model predictive control was validated with reference tracking and load fluctuation experiments

A survey on fractional order control techniques for unmanned aerial and ground vehicles

In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade

Fractional order impedance models as rising tools for quantification of unconscious analgesia

This research focuses on modeling the diffusion process that occurs in the human body when an analgesic drug is taken up, by using fractional-order impedance models (FOIMs). We discuss the measurement of a suitable feedback signal that can be used in a model-based control strategy. With this knowledge an early dawn concept of a pain sensor is presented. The major challenges that are encountered during this development consist of identification of the patient model, validation of the pain sensor and validation of the effect of the analgesic drug