Control of Constrained Dynamical Systems with Performance Guarantees: With Application to Vehicle motion Control

In control engineering, models of the system are commonly used for controller design. A standard control design problem consists of steering the given system output (or states) towards a predefined reference. Such a problem can be solved by employing feedback control strategies. By utilizing the knowledge of the model, these strategies compute the control inputs that shrink the error between the system outputs and their desired references over time. Usually, the control inputs must be computed such that the system output signals are kept in a desired region, possibly due to design or safety requirements. Also, the input signals should be within the physical limits of the actuators. Depending on the constraints, their violation might result in unacceptable system failures (e.g. deadly injury in the worst case). Thus, in safety-critical applications, a controller must be robust towards the modelling uncertainties and provide a priori guarantees for constraint satisfaction. A fundamental tool in constrained control application is the robust control invariant sets (RCI). For a controlled dynamical system, if initial states belong to RCI set, control inputs always exist that keep the future state trajectories restricted within the set. Hence, RCI sets can characterize a system that never violates constraints. These sets are the primary ingredient in the synthesis of the well-known constraint control strategies like model predictive control (MPC) and interpolation-based controller (IBC). Consequently, a large body of research has been devoted to the computation of these sets. In the thesis, we will focus on the computation of RCI sets and the method to generate control inputs that keep the system trajectories within RCI set. We specifically focus on the systems which have time-varying dynamics and polytopic constraints. Depending upon the nature of the time-varying element in the system description (i.e., if they are observable or not), we propose different sets of algorithms.The first group of algorithms apply to the system with time-varying, bounded uncertainties. To systematically handle the uncertainties and reduce conservatism, we exploit various tools from the robust control literature to derive novel conditions for invariance. The obtained conditions are then combined with a newly developed method for volume maximization and minimization in a convex optimization problem to compute desirably large and small RCI sets. In addition to ensuring invariance, it is also possible to guarantee desired closed-loop performance within the RCI set. Furthermore, developed algorithms can generate RCI sets with a predefined number of hyper-planes. This feature allows us to adjust the computational complexity of MPC and IBC controller when the sets are utilized in controller synthesis. Using numerical examples, we show that the proposed algorithms can outperform (volume-wise) many state-of-the-art methods when computing RCI sets.In the other case, we assume the time-varying parameters in system description to be observable. The developed algorithm has many similar characteristics as the earlier case, but now to utilize the parameter information, the control law and the RCI set are allowed to be parameter-dependent. We have numerically shown that the presented algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting parameter information.Lastly, we demonstrate how we can utilize some of these algorithms to construct a computationally efficient IBC controller for the vehicle motion control. The devised IBC controller guarantees to meet safety requirements mentioned in ISO 26262 and the ride comfort requirement by design

Survey of Gain-Scheduling Analysis & Design

The gain-scheduling approach is perhaps one of the most popular nonlinear control design approaches which has been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide application of gain-scheduling controllers and a diverse academic literature relating to gain-scheduling extending back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in interest in gain-scheduling in the literature with many new results obtained. An extended review of the gainscheduling literature therefore seems both timely and appropriate. The scope of this paper includes the main theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition of nonlinear design into linear sub-problems) control with the aim of providing both a critical overview and a useful entry point into the relevant literature

A gain-scheduled LPV control for oxygen stoichiometry regulation in PEM fuel cell systems

The article addresses the LPV control of a Polymer Electrolyte Membrane Fuel Cell (PEMFC). In order to optimize efficiency, PEMFCs require reliable control systems ensuring stability and performance, as well as robustness to model uncertainties and external perturbations. On the other hand, PEMFCs present a highly nonlinear behavior that demands nonlinear and/or adaptive control strategies to achieve high performance in the entire operating range. Here, a linear parameter varying (LPV) gain scheduled control is proposed. The control is based on a piecewise affine LPV representation of the PEMFC, a model that can be available in practice. In order to deal with the saturation of the control action, an LPV anti-windup compensation is also proposed. The complete control strategy is applied to several experimental practical situations in a laboratory fuel cell system to evaluate its performance and the reliability of the proposed algorithms.The research of F.D. Bianchi was supported by the European Regional Development Funds (ERDF, FEDER Programa Competitivitat de Catalunya 2007-2013). The research of C. Kunusch has been supported by the Seventh Framework Programme of the European Community through the Marie Curie actions (GA: PCIG09-GA-2011-293876) and project Puma-Mind (GA: FCH-JU-2011-1-303419), as well as by the CICYT project DPI2011-25649 (MICINN-Spain). The research of C. Ocampo-Martinez has been supported by the project MACPERCON (Ref. 201250E027) of the CSIC. The research of R.S. Sánchez Peña has been supported by CONICET and grant PICT2008-290 from the PRH Program of the Ministry of Science, Technology and Innovation of Argentina.Peer Reviewe

Model-based control for automotive applications

The number of distributed control systems in modern vehicles has increased exponentially over the past decades. Today’s performance improvements and innovations in the automotive industry are often resolved using embedded control systems. As a result, a modern vehicle can be regarded as a complex mechatronic system. However, control design for such systems, in practice, often comes down to time-consuming online tuning and calibration techniques, rather than a more systematic, model-based control design approach. The main goal of this thesis is to contribute to a corresponding paradigm shift, targeting the use of systematic, model-based control design approaches in practice. This implies the use of control-oriented modeling and the specification of corresponding performance requirements as a basis for the actual controller synthesis. Adopting a systematic, model-based control design approach, as opposed to pragmatic, online tuning and calibration techniques, is a prerequisite for the application of state-of-the-art controller synthesis methods. These methods enable to achieve guarantees regarding robustness, performance, stability, and optimality of the synthesized controller. Furthermore, from a practical point-of-view, it forms a basis for the reduction of tuning and calibration effort via automated controller synthesis, and fulfilling increasingly stringent performance demands. To demonstrate these opportunities, case studies are defined and executed. In all cases, actual implementation is pursued using test vehicles and a hardware-in-the-loop setup. • Case I: Judder-induced oscillations in the driveline are resolved using a robustly stable drive-off controller. The controller prevents the need for re-tuning if the dynamics of the system change due to wear. A hardware-in-the-loop setup, including actual sensor and actuator dynamics, is used for experimental validation. • Case II: A solution for variations in the closed-loop behavior of cruise control functionality is proposed, explicitly taking into account large variations in both the gear ratio and the vehicle loading of heavy duty vehicles. Experimental validation is done on a heavy duty vehicle, a DAF XF105 with and without a fully loaded trailer. • Case III: A systematic approach for the design of an adaptive cruise control is proposed. The resulting parameterized design enables intuitive tuning directly related to comfort and safety of the driving behavior and significantly reduces tuning effort. The design is validated on an Audi S8, performing on-the-road experiments. • Case IV: The design of a cooperative adaptive cruise control is presented, focusing on the feasibility of implementation. Correspondingly, a necessary and sufficient condition for string stability is derived. The design is experimentally tested using two Citroën C4’s, improving traffic throughput with respect to standard adaptive cruise control functionality, while guaranteeing string stability of the traffic flow. The case studies consider representative automotive control problems, in the sense that typical challenges are addressed, being variable operating conditions and global performance qualifiers. Based on the case studies, a generic classification of automotive control problems is derived, distinguishing problems at i) a full-vehicle level, ii) an in-vehicle level, and iii) a component level. The classification facilitates a characterization of automotive control problems on the basis of the required modeling and the specification of corresponding performance requirements. Full-vehicle level functionality focuses on the specification of desired vehicle behavior for the vehicle as a whole. Typically, the required modeling is limited, whereas the translation of global performance qualifiers into control-oriented performance requirements can be difficult. In-vehicle level functionality focuses on actual control of the (complex) vehicle dynamics. The modeling and the specification of performance requirements are typically influenced by a wide variety of operating conditions. Furthermore, the case studies represent practical application examples that are specifically suitable to apply a specific set of state-of-the-art controller synthesis methods, being robust control, model predictive control, and gain scheduling or linear parameter varying control. The case studies show the applicability of these methods in practice. Nevertheless, the theoretical complexity of the methods typically translates into a high computational burden, while insight in the resulting controller decreases, complicating, for example, (online) fine-tuning of the controller. Accordingly, more efficient algorithms and dedicated tools are required to improve practical implementation of controller synthesis methods