Abstract This thesis presents that the closed-loop sensitivity function shaping combined with -synthesis applies to design the controller with structured uncertainties. The sensitivity function shaping is directly based on the indices of the closed-loop performances. The closed-loop frequency response and the robust stability for the system could approach the designed performances by adjusting weighting functions. Since the robust performance of the closed-loop systems bases on the index of the open-loop function in the loop shaping, it may not accomplish the requirement of the designer. The loop shaping can¡¦t be applied to design controllers for the system with structured uncertainties. Therefore, using the closed-loop sensitivity function shaping to design controller will contain the system with structured uncertainties and satisfy the closed-loop performance.

This thesis mainly proposes a new method to design Hinf Loop Shaping Robust Controller by choosing Weighting Function. In the paper, the author first introduces the concept of SISO Loop Shaping design. It utilizes Small Gain Theorem to achieve robust stability of the system and develops the relationship of Open Loop Transfer Function(L) to Robust Performance and to Robust Stability of the system.. These concepts can be extended to Hinf Loop Shaping method. As to Hinf loop shaping method, the author first introduces the problem of Robust Stability under the framework of Coprime Factor and the theory of Hinf Loop Shaping, and then discusses the relationship between stability margin and the different pole-zero system. Generally speaking, the control theories of the Loop Shaping are mainly used for making appropriate adjustments between the stability and performance of the system. Because the system can conform to the performance requirement through the choice of Weighting Function, the author proposes a new method toward MIMO system to design Hinf Loop Shaping Controller by choosing Weighting Function under the framework of Hinf Loop Shaping. Moreover, at the end of the paper,the author compares the result of the new method with that of the literature.

Robust control design has become a major research area during the last twenty years and there are nowadays several robust design methods available. One example of such a method is the robust loop shaping method that was developed by K. Glover and D. C. MacFarlane in the late 1980s. The idea of this method is to use decentralized controller design to give the singular values of the loop gain a desired shape. This step is called Loop Shaping and it is followed by a Robust Stabilization procedure, which aims to give the closed loop system a maximum degree of stability margins. In this thesis, the robust loop shaping method is used to design a gain scheduled controller for a missile. The report consists of three parts, where the first part introduces the Robust Loop Shaping theory and a Gain Scheduling approach. The second part discusses the missile and its characteristics. In the third part a controller is designed and a short analysis of the closed loop system is performed. A scheduled controller is implemented in a nonlinear environment, in which performance and robustness are tested. Robust Loop Shaping is easy to use and simulations show that the resulting controller is able to cope with model perturbations without considerable loss in performance. The missile should be able to operate in a large speed interval. There, it is shown that a single controller does not stabilize the missile everywhere. The gain scheduled controller is however able to do so, which is shown by means of simulations.

This paper presents the results of servo designs for optical disk drives which consist of a dual-input/single-output (DISO) actuator; both a sledge actuator and a voice coil motor contribute to a radial movement of the spot on the disk. DISO systems are subset of multi-input/multi-output (MIMO) systems and thus the servo engineer can apply the design methods developed for MIMO controller design to the DISO compensator problems. These techniques include H2 , H¡Û and £g-synthesis. However, in order to obtain insights into the controller elements, in this study we prefer the H¡Û loop-shaping approach. Here, the focus is on stability and disturbance rejection. The method is presented for a master-slave control scheme in tracking servo, a parallel scheme in seeking servo, and a unit-feedback scheme in focusing servo. The maximum stability margin can be obtained in H¡Û loop-shaping algorithm. Furthermore, a robust controller guarantees to stabilize it would be carried out. Finally, computer simulation results are provided to show that the shaking disturbance due to the run-out of disk can be significantly attenuated and a good tracking performance can be achieved by the developed controller.

<p>Robust control design has become a major research area during the last twenty years and there are nowadays several robust design methods available. One example of such a method is the robust loop shaping method that was developed by K. Glover and D. C. MacFarlane in the late 1980s. The idea of this method is to use decentralized controller design to give the singular values of the loop gain a desired shape. This step is called Loop Shaping and it is followed by a Robust Stabilization procedure, which aims to give the closed loop system a maximum degree of stability margins. In this thesis, the robust loop shaping method is used to design a gain scheduled controller for a missile. The report consists of three parts, where the first part introduces the Robust Loop Shaping theory and a Gain Scheduling approach. The second part discusses the missile and its characteristics. In the third part a controller is designed and a short analysis of the closed loop system is performed. A scheduled controller is implemented in a nonlinear environment, in which performance and robustness are tested. Robust Loop Shaping is easy to use and simulations show that the resulting controller is able to cope with model perturbations without considerable loss in performance. The missile should be able to operate in a large speed interval. There, it is shown that a single controller does not stabilize the missile everywhere. The gain scheduled controller is however able to do so, which is shown by means of simulations.</p>

In this work, we introduce several novel approaches to feedback controller design, known collectively as the “Robust Bode” methods, which adapt classical control principles to a modern robust control (H∞) framework. These methods, based on specially modified Bode diagrams extend familiar frequency-domain controller design techniques to linear and nonlinear, single–input/single– output (SISO) and multi–input/multi–output (MIMO) systems with parametric and/or unstructured uncertainties. In particular, we introduce the Contoured Robust Controller Bode (CRCBode) plots which show contours (level-sets) of a robust metric on the Bode magnitude and phase plots of the controller. An iterative loop shaping design procedure is then employed in an attempt to eliminate all intersections of the controller frequency response with certain forbidden regions indicating that a robust stability and performance criteria is satisfied. For SISO systems a robust stability and performance criterion is derived using Nyquist arguments leading to the robust metric used in the construction of the CRCBode plots. For open-loop unstable systems and for non-minimum phase systems the Youla parametrization of all internally stabilizing controllers is used to develop an alternative Robust Bode method (QBode). The Youla parametrization requires the introduction of state-space methods for coprime factorization, and these methods lead naturally to an elegant connection between linear-quadratic Gaussian (LQG) optimal control theory and Robust Bode loop-shaping controller design. Finally, the Robust Bode approach is extended to MIMO systems. Utilizing a matrix norm based robustness metric on the MIMO CRCBode plots allows cross-coupling between all input/output channels to be immediately assessed and accounted for during the design process, making sequential MIMO loop-shaping controller design feasible.

The primary objective of this thesis is to leverage on the framework of H∞ loop-shaping control to formulate efficient and powerful optimization algorithms in LMI framework for the synthesis of performance loop-shaping weights. The H∞ loop-shaping design procedure is an efficient controller synthesis technique that combines classical loop-shaping concepts with H∞ synthesis. This procedure establishes a good tradeoff between robust stability and robust performance of a closed-loop system in a systematic manner. However, the selection of pre- and/or post-compensators, a crucial step in the design procedure, is nontrivial as factors such as the right half plane poles/zeros of the nominal plant, roll-off rate around the crossover frequency, strength of cross-coupling in multi-input multi-output systems, expected bandwidth, etc. must be adequately considered.Firstly, a frequency-dependent weight optimization framework is formulated in state-space form in order to remove the dependency on frequency while retaining the objective of maximizing the robust stability margin of a closed-loop system. This formulation facilitates the synthesis of low-order controllers, which is desirable from an implementation perspective.A weight optimization framework that incorporates smoothness constraints in order to prevent the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, is subsequently formulated. The proposed formulation is intuitive from a design perspective as the smoothness constraints are expressed as gradient constraints on a log-log scale in dB/decade, consistent with the notation used in Bode plot for single-input single-output systems and singular value plots for multi-input multi-output systems.Thereafter, an optimization framework that maximizes the robust performance of a closed-loop system is presented. The philosophy in this framework is in line with practical design objectives that give the best achievable robust performance on a particular problem once a level of robust stability margin is demanded.Lastly, a novel unmanned vehicle is proposed. The vehicle uses a full six-degree-of-freedom tri-rotor actuation, capable of fully decoupled thrust and torque vectoring in all the 3D space. This vehicle can act as an unmanned ground vehicle or unmanned aerial vehicle, but the objective herein is restricted to the upright stability of the vehicle while operating on the ground as this is a precursor to rolling motion. The full nonlinear model of the vehicle is derived and linearized for subsequent controller synthesis, and this is thereafter validated by means of numerical simulations.

La stabilisation inertielle de ligne de visée est essentiellement un problème de rejet de perturbations : il faut rendre la ligne de visée de la caméra embarquée dans le viseur insensible aux mouvements du porteur. Les méthodes de commande robuste du type H-infini sont bien adaptées à la résolution de ce type de problème, et plus particulièrement l’approche Loop-Shaping qui repose sur des concepts de réglage de l’automatique fréquentielle classique. Cependant, les correcteurs obtenus via cette approche sont généralement d’ordre élevé et donc difficilement implémentables sur le calculateur embarqué du viseur.Dans cette thèse, nous avons proposé des méthodologies de synthèse de correcteurs robustes d’ordre réduit et/ou de structure fixée. Pour cela, nos travaux ont été axés sur :- L’optimisation pour la synthèse H-infini à ordre et/ou structure fixée. Tout d’abord nous avons exploré les possibilités offertes par l’optimisation sous contraintes LMI (Linear Matrix Inequalities). Celles-ci se sont avérées limitées, bien que de nombreux algorithmes aient été proposés dans ce cadre depuis le début des années 90. Ensuite, nous avons opté pour l’optimisation non lisse. En effet des outils numériques récemment développés rendent accessible cette approche, et leur efficacité s’est avéré indéniable.- L’adaptation au cadre particulier du critère H-infini Loop-Shaping.La structure particulière de ce critère de synthèse a été exploitée afin de mieux prendre en compte les pondérations, et d’améliorer la réduction d’ordre du correcteur final. Enfin, une approche basée uniquement sur le réglage graphique d’un gabarit de gain fréquentiel en boucle ouverte est proposée. Ces différentes méthodologies sont illustrées, tout au long de la thèse, sur un viseur dont le modèle a été identifié à partir de mesures expérimentales. / Inertial line of sight stabilization is a disturbance rejection problem: the goal is to hold steady in the inertial space, the line of sight of a camera, which is carried on a mobile vehicle. H-infinity robust control techniques are well suited for this type of problem, in particular the Loop-Shaping approach which relies on classical frequency domain concepts. However, this approach results in high order controllers which are hardly implementable on the real time embedded electronic unit of the sight system.In this thesis, fixed order and fixed structure controller design methodologies are proposed. This development follows two main axis: - Fixed order H-infinity Optimization. First, fixed order controllers have been investigated through the LMI (Linear Matrix Inequalities) optimization framework. However the numerical efficiency of this approach is still limited, despite the large amount of research in this area since the 90’s. Then, we used recently developed and more efficient tools that recast the fixed order H-infinity synthesis problem as a nonsmooth optimization problem.- Adaptation to the H-infinity Loop-Shaping frameworkWe adapted the 4 block H-infinity criterion in order to include the weighting filters in the fixed order controller optimization, which enhance the final controller order reduction. Then, we proposed a fixed order controller design approach, based only on graphically tuning a target open loop frequency gain.

abstract: Proportional-Integral-Derivative (PID) controllers are a versatile category of controllers that are commonly used in the industry as control systems due to the ease of their implementation and low cost. One problem that continues to intrigue control designers is the matter of finding a good combination of the three parameters - P, I and D of these controllers so that system stability and optimum performance is achieved. Also, a certain amount of robustness to the process is expected from the PID controllers. In the past, many different methods for tuning PID parameters have been developed. Some notable techniques are the Ziegler-Nichols, Cohen-Coon, Astrom methods etc. For all these techniques, a simple limitation remained with the fact that for a particular system, there can be only one set of tuned parameters; i.e. there are no degrees of freedom involved to readjust the parameters for a given system to achieve, for instance, higher bandwidth. Another limitation in most cases is where a controller is designed in continuous time then converted into discrete-time for computer implementation. The drawback of this method is that some robustness due to phase and gain margin is lost in the process. In this work a method of tuning PID controllers using a loop-shaping approach has been developed where the bandwidth of the system can be chosen within an acceptable range. The loop-shaping is done against a Glover-McFarlane type &#8459;&#8734; controller which is widely accepted as a robust control design method. The numerical computations are carried out entirely in discrete-time so there is no loss of robustness due to conversion and approximations near Nyquist frequencies. Some extra degrees of freedom owing to choice of bandwidth and capability of choosing loop-shapes are also involved and are discussed in detail. Finally, comparisons of this method against existing techniques for tuning PID controllers both in continuous and in discrete-time are shown. The results tell us that our design performs well for loop-shapes that are achievable through a PID controller. / Dissertation/Thesis / M.S. Electrical Engineering 2011

Cette thèse porte sur le problème de commande des systèmes non-linéaires à paramètres variants rencontrés souvent (mais non seulement) dans le domaine aéronautique, avec la technique de séquencement de gains par linéarisation. Une stratégie innovante, appelée extended - Loop Shaping Design Procedure (e-LSDP), qui facilite et systématise la tache du scientique pour le calcul d'une loi de commande séquencée pour ce type de systèmes, est ici proposée.<br />Cette stratégie est basée sur une pré-compensation (loop shaping) faite à partir des systèmes linéarisés du système non-linéaire autour d'un petit nombre de points de fonctionnement en utilisant des compensateurs de structure simple (e.g. PID), et de plus en utilisant une compensation additionnelle/corrective type retour de sortie H1 statique. Les points de fonctionnement de la deuxième compensation sont calculés à l'aide d'un algorithme de choix de points de synthèse basé sur la connexion des théories de la gap métrique et de la commande H1 par loop shaping. La loi de commande globale non-linéaire séquencée est finalement obtenue en utilisant une interpolation de tous les gains des com-pensateurs impliqués pendant la phase de synthèse.<br />La méthode proposée ici est validée sur deux exemples d'application : le pilotage autour de l'axe de tangage d'un missile fortement manœuvrant et d'un véhicule de rentrée atmosphérique. Les deux autopilotes sont testés de façon intensive en utilisant des simulations non-linéaires, une analyse Monte Carlo et linéaire à temps figé afin de démontrer leurs excellentes caractéristiques en termes de performance et de robustesse.