A Velocity Algorithm for the Implementation of Gain-scheduled Controllers

A new method is proposed to implement gain-scheduled controllers for nonlinear plants. Given a family of linear feedback controllers designed for linearizations of a nonlinear plant about constant operating points, a nonlinear gain-scheduled controller is derived that preserves the input-output properties of the linear closed loop systems locally, about each equilibrium point. The key procedures in the proposed method are to provide integral action at the inputs to the plant and differentiate some of the measured outputs before they are fed back to the scheduled controller. For a fairly general class of systems, the nonlinear gain-scheduled controllers are easy to obtain, and their structure is similar to that of the original linear controllers.Research Initiation Grant of the Naval Postgraduate SchoolNSF under Grant ECS-9096109AFOSR under Grant F49620-93-1-0246AR under Grant DAAH01-93-G-001

The State-of-Art of Underwater Vehicles - Theories and Applications

An autonomous underwater vehicle (AUV) is an underwater system that contains its own power and is controlled by an onboard computer. Although many names are given to these vehicles, such as remotely operated vehicles (ROVs), unmanned underwater vehicles (UUVs), submersible devices, or remote controlled submarines, to name just a few, the fundamental task for these devices is fairly well defined: The vehicle is able to follow a predefined trajectory. AUVs offer many advantages for performing difficult tasks submerged in water. The main advantage of an AUV is that is does not need a human operator. Therefore it is less expensive than a human operated vehicle and is capable of doing operations that are too dangerous for a person. They operate in conditions and perform task that humans are not able to do efficiently, or at all (Smallwood & Whitcomb, 2004; Horgan & Toal, 2006; Caccia, 2006)

Appropriate Realisation of MIMO Gain-Scheduled Controllers

The dynamic characteristics of a controller designed by the gain-scheduling approach can be strongly dependent on the realisation adopted; that is, the manner in which the local linear controller designs are combined to obtain a nonlocal controller. The purpose of the present paper is to investigate the choice of appropriate realisations for general MIMO gain-scheduled controllers. An extended local linear equivalence condition for MIMO gain-scheduled nonlinear controllers is proposed which minimises the controller nonlinearity. It is shown that, with few exceptions, it is possible to realise all gain-scheduled controllers as nonlinear controllers satisfying the extended local linear equivalence condition and requiring the controller to do so is not at all restrictive

Appropriate Realisation of MIMO Gain-Scheduled Controllers

The dynamic characteristics of a controller designed by the gain-scheduling approach can be strongly dependent on the realisation adopted; that is, the manner in which the local linear controller designs are combined to obtain a nonlocal controller. The purpose of the present paper is to investigate the choice of appropriate realisations for general MIMO gain-scheduled controllers. An extended local linear equivalence condition for MIMO gain-scheduled nonlinear controllers is proposed which minimises the controller nonlinearity. It is shown that, with few exceptions, it is possible to realise all gain-scheduled controllers as nonlinear controllers satisfying the extended local linear equivalence condition and requiring the controller to do so is not at all restrictive

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

Modélisation et commande d'un quadricoptère en présence de vent

RÉSUMÉ Les multicoptères sont utilisés à toutes sortes de fins, mais limités par ce que permet la technologie actuelle. Il incombe alors de développer des solutions qui vont permettre de repousser ces limites. Une des plus grandes limites à l’heure actuelle est le vent. Les drones sont souvent appelés à opérer dans des milieux extérieurs, pour l’inspection de structures notamment. Leur vulnérabilité face aux perturbations occasionnées par un environnement venteux en réduit toutefois les performances et limite leur spectre d’utilisation. Dans cet optique, on présente dans ce projet une solution pour améliorer la résistance d’un quadricoptère à ce type de perturbations et ainsi rendre l’utilisateur moins dépendant de son environnement lors de ses activités. L’approche suggérée vise à améliorer la résistance du quadricoptère au vent via une loi de commande plus robuste. Pour ce faire, on établit d’abord les équations non linéaires caractérisant la dynamique d’un quadricoptère dans le vent. À partir de ces équations, on peut établir l’expression du modèle d’état linéaire invariant dans le temps (Linear Time Invariant (LTI)) en fonction des valeurs d’équilibre du drone. On synthétise ensuite une loi de commande efficace en maintien de position. On compare alors deux techniques de synthèse différentes ; la synthèse Linear Quadratic Regulator (LQR) et la synthèse H1 structurée. On conclut que la synthèse H1 structurée est plus appropriée, puisqu’elle permet de traiter les problématiques de stabilité et de robustesse aux perturbations directement lors de la synthèse alors que la synthèse LQR ne le permet pas. Elle a aussi l’avantage d’offrir plus de flexibilité au niveau de l’architecture de la loi de commande. On étend finalement les performances de la synthèse H1 structurée, non seulement pour une position d’équilibre en vol stationnaire, mais pour un ensemble de points d’équilibre. En gardant la même technique, on développe, pour chacun de ces points d’équilibre, le modèle LTI associé et on cherche à faire en sorte que les performances soient rencontrées pour chacun des points. La dynamique du quadricoptère étant non linéaire, les modèles peuvent grandement varier et il devient difficile de rencontrer les performances sur l’ensemble avec des gains fixes. Pour pallier à ce problème, on utilise un séquencement des gains de la loi de commande (gain-scheduling). Les gains dépendent alors des variables d’état caractérisant l’attitude du quadricoptère. En augmentant ainsi les degrés de liberté du contrôleur, on arrive à imposer de meilleures performances sur un ensemble plus grand de points d’équilibre. Un problème survient toutefois en utilisant cette technique.----------ABSTRACT Multicopters are used for all kinds of purposes, but limited by what current technology allows. New solutions must be developped in order to push these limits. One of the biggest limitations at the moment is the wind. Drones are often called upon to operate in external environments, particularly for the inspection of structures. However, their vulnerability to disturbances caused by a windy environment reduces their performance and limits their range of use. With this in mind, this project presents a solution to improve the resistance of a quadricopter to this type of disturbance and thus make the user less dependent on his environment during his activities. The suggested approach aims to improve the wind resistance of the quadricopter’s through a more robust control law. To do this, we first establish the non-linear equations characterizing the dynamics of a quadricopter in the wind. From these equations, we can establish the expression of the time-invariant linear state model (LTI) as a function of the equilibrium values of the drone. An effective control law is then synthesized to hold position. We compare two different synthesis techniques ; the synthesis LQR and the structured synthesis H1W˙ e conclude that the structured synthesis H1 is more appropriate, since it allows to treat the problems of stability and robustness to disturbances directly during the synthesis while the LQR synthesis does not allow it. It also has the advantage of offering more flexibility in the architecture of the control law. Finally, the performance of the structured synthesis H1 is extended, not only for hovering, but for a set of equilibrium points. By keeping the same technique, we develop, for each of these equilibrium points, the associated LTI model and we try to ensure that the performances are met for each of the points. The dynamics of the quadricopter being non-linear, models can vary greatly and it becomes difficult to meet the performance on the whole set with fixed gains. To overcome this problem, we use a scheduling of the control law gains. The gains depend on the state variables characterizing the quadricopter’s attitude. By increasing the controller’s degrees of freedom in this way, better performance can be imposed on a larger set of equilibrium points. However, a problem arises when using this technique. Indeed, the scheduling function introduces a non-linearity into the control law, which takes the form of hidden coupling terms

From Fixed-Order Gain-Scheduling to Fixed-Structure LPV Controller Design

This thesis focuses on the development of some fixed-order controller design methods in the gain-scheduling/Linear Parameter Varying (LPV) framework. Gain-scheduled controllers designed using frequency-domain Single Input Single Output (SISO) models are considered first, followed by LPV controller design in the SISO transfer function setting and, finally, by Multiple Input Multiple Output (MIMO) LPV controller design in the state-space setting. In addition to the guarantee of closed-loop stability, each of the methods optimizes some classical performance measure, such as the $\mathscr{H}_\infty$ or $\mathscr{H}_2$ performance metrics. In the LPV state-space setting, the practical assumption of bounded scheduling parameter variations is taken into account in order to allow a higher performance level to be achieved. The fixed-order gain-scheduled controller design method is based on frequency-domain models dependent on the scheduling parameters. Based on the linearly parameterized gain-scheduled controllers and desired open-loop transfer functions, the $\mathscr{H}_\infty$ performance of the weighted closed-loop transfer functions is presented in the Nyquist diagram as a set of convex constraints. No a posteriori interpolation is needed, so the stability and performance level are guaranteed for all values of scheduling parameters considered in the design. Controllers designed with this method are successfully applied to the international benchmark in adaptive regulation. These low-order controllers ensure good rejection of the multisinusoidal disturbance with time-varying frequencies on the active suspension testbed. One issue related to the gain-scheduled controller design using the frequency response model is the computational burden due to the constraint sampling in the frequency domain. The other is a guarantee of stability and performance for all the values of scheduling parameters, not just those treated in design. To overcome these issues, a method for the design of fixed-order LPV controllers with the transfer function representation is proposed. The LPV controller parameterization considered in this approach leads to design variables in both the numerator and denominator of the controller. Stability and $\mathscr{H}_\infty$ performance conditions for all fixed values of scheduling parameters are presented in terms of Linear Matrix Inequalities (LMIs). With a problem of rejection of a multisinusoidal disturbance with time-varying frequencies in mind, LPV controller is designed for an LTI plant with a transfer function model. The extension of these methods from SISO to MIMO systems is far from trivial. The state-space setting is used for this reason, as there the transition from SISO to MIMO systems is natural. A method for fixed-order output-feedback LPV controller design for continuous-time state-space LPV plants with affine dependence on scheduling parameters is proposed. Bounds on the scheduling parameters and their variation rates are exploited in design through the use of affine Parameter Dependent Lyapunov Functions (PDLFs). The exponential decay rate, induced $\mathscr{L}_2$-norm and $\mathscr{H}_2$ performance constraints are expressed through a set of LMIs. The proposed method is applied to the 2DOF gyroscope experimental setup. In practice control is performed using digital computers, so some effort needs to be put into the LPV controller discretization. If the discrete-time LPV model of the system is available [...

Energy Efficient Control of Hydrostatic Drive Transmissions: A Nonlinear Model-Based Approach

The high standard of living in industrial countries is based on the utilization of machines. In particular, the tasks performed with hydraulic work machines (HWMs) are essential in numerous industrial fields. Agriculture, mining, and construction are just a few examples of the lines of business that would be inconceivable today without HWMs. However, rising oil prices and competing technologies are challenging the manufacturers of these machines to improve their fuel economy.Despite the fact that energy efficiency research of hydraulic systems has been active for more than a decade, there seems to be a significant gap between industry and academia. The manufacturers of HWMs have not adopted, for example, novel system layouts, prototype components, or algorithms that require powerful control units in their products.The fuel economy of HWMs can be increased by utilizing system information in control algorithms. This cost-effective improvement enables operation in challenging regions and closer to the operating boundaries of the system. Consequently, the information about the system has to be accurate. For example, reducing the rotational speed of the engine has proven effective in improving the energy efficiency, but it increases the risk of even stalling the engine, for instance in situations where the power generation cannot meet the high transient demand. If this is considered in the controller with low uncertainty, fuel economy can be improved without decreasing the functionality of the machine.This thesis studies the advantages of model-based control in the improvement of the fuel economy of HWMs. The focus is on hydrostatic drive transmissions, which is the main consumer of energy in certain applications, such as wheel loaders.We started by developing an instantaneous optimization algorithm based on a quasi-static system model. The control commands of this fuel optimal controller (FOC) were determined based on cost function, which includes terms for fuel economy, steady-state velocity error, and changes in the control commands.Although the use of quasi-static models is adequate for steady-state situations, the velocity tracking during transients and under load changes has proven to be inadequate. To address this issue, a high-performance velocity-tracking controller was devised. Full state feedback was assumed, and we resorted to a so-called D-implementation, which eliminates, for example, the need for the equilibrium values of pressure signals. The nonlinearities of the system were considered with the state-dependent parameters of the linear model.In the next step, a nonlinear model predictive controller combined fuel economy control and velocity tracking. To the best of the author’s knowledge, this is the first time that the model predictive control scheme has been utilized with such a detailed system model that also considers the hydraulic efficiencies and torque generation of the engine. This enables utilizing the controller as a benchmark of control algorithms for non-hybrid hydrostatic drive transmissions that do not require information about the future.The initial tests of all the controllers were conducted with a validated simulation model of a research platform machine, a five-ton municipal tractor. In addition, the FOC and velocity-tracking controller were implemented into the control system of the machine. The practical worth of the FOC was proven with a relatively unique field experiment set-up that included, for example, an online measurement system of fuel consumption and autonomous path following. The fuel economy improved up to 16.6% when compared with an industrial baseline controller. The devised velocity-tracking concept was also proven as a significant reduction of error was observed in comparison with classic literature solutions, namely state feedback and proportional-integral-derivative controllers