In this paper, we propose, discuss, and validate an online Nonlinear Model Predictive Control (NMPC) method for multi-rotor aerial systems with arbitrarily positioned and oriented rotors which ...simultaneously addresses the local reference trajectory planning and tracking problems. This work brings into question some common modeling and control design choices that are typically adopted to guarantee robustness and reliability but which may severely limit the attainable performance. Unlike most of state of the art works, the proposed method takes advantages of a unified nonlinear model which aims to describe the whole robot dynamics by explicitly including a realistic physical description of the actuator dynamics and limitations. As a matter of fact, our solution does not resort to common simplifications such as: (1) linear model approximation, (2) cascaded control paradigm used to decouple the translational and the rotational dynamics of the rigid body, (3) use of low-level reactive trackers for the stabilization of the internal loop, and (4) unconstrained optimization resolution or use of fictitious constraints. More in detail, we consider as control inputs the derivatives of the propeller forces and propose a novel method to suitably identify the actuator limitations by leveraging experimental data. Differently from previous approaches, the constraints of the optimization problem are defined only by the real physics of the actuators, avoiding conservative – and often not physical – input/state saturations which are present, e.g., in cascaded approaches. The control algorithm is implemented using a state-of-the-art Real Time Iteration (RTI) scheme with partial sensitivity update method. The performances of the control system are finally validated by means of real-time simulations and in real experiments, with a large spectrum of heterogeneous multi-rotor systems: an
under-actuated
quadrotor, a
fully-actuated
hexarotor, a multi-rotor with
orientable
propellers, and a multi-rotor with an unexpected
rotor failure
. To the best of our knowledge, this is the first time that a predictive controller framework with all the valuable aforementioned features is presented and extensively validated in real-time experiments and simulations.
A robust model predictive control algorithm solving the tracking and the infeasible reference problems for constrained systems subject to bounded disturbances is presented in this technical note. The ...proposed solution relies on three main concepts: 1) the reformulation of the system in the so-called velocity form to obtain offset-free tracking when constant disturbances are present, 2) the use of a tube-based approach to cope with non-constant but bounded disturbances, 3) the use of reference outputs as arguments of the optimization problem to cope with infeasible references. Convergence results are derived by suitably defining the auxiliary control law and the terminal set used in the problem formulation.
Air pollution has a negative impact on human health. For this reason, it is important to correctly forecast over-threshold events to give timely warnings to the population. Nonlinear models of the ...nonlinear autoregressive with exogenous variable (NARX) class have been extensively used to forecast air pollution time series, mainly using artificial neural networks (NNs) to model the nonlinearities. This work discusses the possible advantages of using polynomial NARX instead, in combination with suitable model structure selection methods. Furthermore, a suitably weighted mean square error (MSE) (one-step-ahead prediction) cost function is used in the identification/learning process to enhance the model performance in peak estimation, which is the final purpose of this application. The proposed approach is applied to ground-level ozone concentration time series. An extended simulation analysis is provided to compare the two classes of models on a selected case study (Milan metropolitan area) and to investigate the effect of different weighting functions in the identification performance index. Results show that polynomial NARX are able to correctly reconstruct ozone concentrations, with performances similar to NN-based NARX models, but providing additional information, as, e.g., the best set of regressors to describe the studied phenomena. The simulation analysis also demonstrates the potential benefits of using the weighted cost function, especially in increasing the reliability in peak estimation.
This paper deals with the development of a simplified, control-oriented mathematical model of an offshore variable speed wind turbine with tension leg platform. First, the model is derived with the ...goal of describing the most relevant physical phenomena of the turbine/platform dynamics, while limiting its complexity. The unknown model parameters are identified and a model validation phase is carried out using Fatigue, Aerodynamics, Structures, and Turbulence (FAST), an accurate reference model available in the literature. Then, an H∞ controller is designed for above-rated power operating conditions. The ability of the controller to attenuate the effect of wind variations and waves is tested in simulation both on the small-scale simulation model and on the FAST simulator.
This paper presents a novel Distributed Predictive Control (DPC) algorithm for linear discrete-time systems. This method enjoys the following properties: (i) state and input constraints can be ...considered; (ii) under mild assumptions, convergence of the closed loop control system is proved; (iii) it is not necessary for each subsystem to know the dynamical models of the other subsystems; (iv) the transmission of information is limited, in that each subsystem only needs the reference trajectories of the state variables of its neighbors. A simulation example is reported to illustrate the main characteristics and performance of the algorithm.
In the past ten years many Stochastic Model Predictive Control (SMPC) algorithms have been developed for systems subject to stochastic disturbances and model uncertainties. These methods are ...motivated by many application fields where a-priori knowledge of the stochastic distribution of the uncertainties is available, some degree of constraint violation is allowed, and nominal operation should be defined as close as possible to the operational constraints for economic/optimality reasons. However, despite the large number of methods nowadays available, a general framework has not been proposed yet to classify the available alternatives. For these reasons, in this paper the main ideas underlying SMPC are first presented and different classifications of the available methods are proposed in terms of the dynamic characteristics of the system under control, the performance index to be minimized, the meaning and management of the probabilistic (chance) constraints adopted, and their feasibility and convergence properties. Focus is placed on methods developed for linear systems. In the first part of the paper, all these issues are considered, also with the help of a simple worked example. Then, in the second part, four algorithms representative of the most popular approaches to SMPC are briefly described and their main characteristics are discussed.
This paper presents a novel stochastic Model Predictive Control algorithm for linear systems characterized by multiplicative and possibly unbounded model uncertainty. Probabilistic constraints on the ...states and inputs are considered, and a quadratic cost function is minimized. The stochastic control problem, and in particular the probabilistic constraints, are reformulated in deterministic terms by means of the Cantelli inequality, so that the on-line computational burden of the algorithm is similar to the one of a standard MPC method. The properties of the algorithm, namely the recursive feasibility and the pointwise convergence of the state, are proven by suitably selecting the terminal cost and the constraints on the mean and the variance of the state at the end of the prediction horizon, and by considering as additional optimization variables also the mean and the covariance of the state at the beginning of the prediction horizon. An extension to deal with the case of expectation, rather than probabilistic, constraints is reported. The numerical issues related to the off-line selection of the algorithm’s parameters and its on-line implementation are discussed. Simulation results referred to a system with unbounded uncertainty are shown to compare the performances achievable with probabilistic and expectation constraints.
Research on system monitoring, fault detection, and fault isolation is extremely important for guaranteeing reliability, safety, integrity, and efficiency of plants, technical processes, and ...especially safety-critical systems. In this paper we first discuss, analyze, and compare two known centralized observer-based fault isolation schemes. Secondly we devise and discuss their distributed implementations. We finally evaluate and compare the potentialities of the different fault isolation schemes and their distributed implementations considering a benchmark case study.
In this paper we propose a novel algorithm based on linear matrix inequalities for the design of distributed controllers and state estimators for large-scale systems inspired by linear quadratic ...regulators and Kalman filters, respectively. With respect to similar state-of-the art methods, the scheme proposed here allows to reduce the conservativeness due to the approximations used for the covariance distributed iterative computation. The theoretical properties of the proposed scheme are thoroughly investigated.
The controllers and observers obtained using the proposed approach are applied to a simulated dynamical system and their performances are thoroughly compared to those obtained with state-of-the-art schemes, showing the potentialities of the scheme.
In this technical note, we consider a linear system structured into physically coupled subsystems and propose a decentralized control scheme capable to guarantee asymptotic stability and satisfaction ...of constraints on system inputs and states. The design procedure is totally decentralized, since the synthesis of a local controller uses only information on a subsystem and its neighbors, i.e. subsystems coupled to it. We show how to automatize the design of local controllers so that it can be carried out in parallel by smart actuators equipped with computational resources and capable to exchange information with neighboring subsystems. In particular, local controllers exploit tube-based Model Predictive Control (MPC) in order to guarantee robustness with respect to physical coupling among subsystems. Finally, an application of the proposed control design procedure to frequency control in power networks is presented.
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