Tomando como ejemplo de aplicación, un vehículo aéreo no tripulado con dos brazos y cuatro rotores, en el presente trabajo se lleva cabo una comparación del desempeño de dos sistemas de control. Uno de estos controles fue diseñado mediante técnicas lineales de parámetros variantes, mientras que el otro se basa en la estrategia denominada PID inteligente, técnica adaptativa basada en controles libres de modelo. Ambos controles atacan el problema de tolerancia a fallas con diferentes enfoques para adaptarse a dos casos de fallas, en uno y en dos rotores. Las fallas consideradas son de tipo total y se conocen de ellas el momento en que se producen y el actuador en el cual ocurrió la falla. En este escenario, se lleva a cabo la comparación.

The design of a displacement velocity controller is presented for a six rotor aerial vehicle. H-infinity control is proposed in order to achieve robust performance in presence of dynamic model uncertainty. It is assumed that a considerable amount of uncertainty is due to time delays introduced by the algorithms employed. The estimation of the vehicle's displacement velocity is carried out on-board through an optical flow sensor implemented employing a camera and a high level processor as well as the H-infinity controller. Through experimental data, the system's identification procedure used to obtain a description of the plant as a family of models with global dynamic uncertainty is also presented as part of the design process. The implemented optical flow estimation methods are also presented as well as the tuning procedures employed which may affect the results of the system's identification and the control performance. Experimental results are presented with details regarding the implementation phase.

Se presenta el diseño del control para la velocidad de desplazamiento de un vehículo aéreo de seis rotores. La técnica de diseño utilizada es el control óptimo en H–infinito con el objetivo de conseguir rendimiento robusto ante la incertidumbre en el modelo de la dinámica de la velocidad de desplazamiento. Se considera que buena parte de la incertidumbre es atribuible a retardos de tiempo inciertos que introduce el propio algoritmo que se utiliza para estimar la velocidad de desplazamiento. El vehículo realiza a bordo la estimación de esta última a través de un sensor de flujo óptico implementado con una cámara y un procesador de alto nivel en el cual además se implementa la ley de control. Junto con el diseño del control, se muestra el procedimiento de identificación de sistemas utilizado para conseguir una descripción de la dinámica a través de una familia de plantas con incertidumbre dinámica global a través de la toma de datos experimentales. Finalmente se exhiben resultados experimentales con la implementación del sistema de control completo.

Power inverters are widely used in grid connected applications, specially with the increasing use of renewable energies, to improve power quality and increase efficiency. However some parameter associated to the grid and/or the inverters, such as the grid frequency, needs to be known or properly estimated. This estimation introduces an uncertainty in the system and suffer transients due to the estimator. Linear Parameter Varying (LPV) control can be used to account for those uncertainties. This paper presents a feedback control based on a LPV control law to improve the power quality of a grid connected Current Source Inverter (CSI), significantly reducing the total harmonic distortion (THD) of the grid generator current. A linear model of the interconnection is presented, where the frequency of the grid is assumed variable being estimated together with its phase through a Phase Locked Loop (PLL). The LPV control law is implemented through state feedback achieving both, harmonic suppression and reference tracking, using the estimation of the frequency of the PLL. Implicitly, this allows for the estimation of the magnitude and phase of the harmonic distortion canceling it up to the CSI current limit. An analytic proof of the filtering guarantees of the method is presented along with simulation results that show the practical viability of this technique. It is shown that this control approach is capable of an appealing adaptation to changes in the frequency of the power grid with a low computational burden being able to also cope with disturbances in the estimation of the frequency due to the PLL..

Within the Cluster Space robot formation control scheme, a new approach is presented where a cascaded control scheme is proposed. On one hand, a simple secondary (inner) loop is used to control the formation's velocity in Robot Space, while on the other hand a quasi-LPV (Linear Parameter Varying) approach is employed for the design of the main (outer) control loop where the geometry and kinematics of the problem are captured by the LPV formulation. Certain aspects of the design such as stability are tackled, and the use of parameter-dependent weighting functions is discussed through a design example tested in simulations in order to illustrate the use of the method.

Recently, it was shown that an hexagon shaped hexarotor vehicle with tilted rotors, is capable of fault tolerant attitude and altitude control. In this work, we propose a strategy to select the signals commanded to each rotor in order to achieve a desired torque and vertical force. The proposed strategy is optimal in the sense that minimizes the maximum force exerted by the rotors. A comparison with the commonly used strategy based upon the Moore-Penrose pseudoinverse is carried out. It is shown that, with the optimal strategy proposed here, maneuverability is improved, because the new method takes into account the actuators constraints. Although the optimal strategy is computationally more demanding than the classical method, the additional computational burden is not significant when both strategies are compared in a real application. To show this, both algorithms were programmed in an autopilot based on an ARM Cortex M3 microcontroller, and the experimental results are presented.

A proof is presented of how a hexagon-shaped hexacopter can be designed to keep the ability to reject disturbance torques in all directions while counteracting the effect of a failure in any of its motors. The method proposed is simpler than previous solutions, because it does not require change of the motor rotation direction or in-flight mechanical reconfiguration of the vehicle. It consists of tilting the rotor a small fixed angle with respect to the vertical axis. Design guidelines are presented to calculate the tilt angle to achieve fault-tolerant attitude control without losing significant vertical thrust. It is also formally proved that the minimum number of unidirectional rotating motors needed to have fault tolerance is 6 and that this can be achieved by tilting their rotors. This proof is essentially a control allocation analysis that recovers in a simple way a result already known: the standard configuration (without tilting the motors) is not fault tolerant. A simulation example illustrates the theory.

This work considers the problem of automatically controlling the glucose level in insulin dependent diabetes mellitus (IDDM) patients. The objective is to include several important and practical issues in the design: model uncertainty, time variations, nonlinearities, measurement noise, actuator delay and saturation, and real time implementation. These are fundamental issues to be solved in a device implementing this control. Two time-varying control procedures have been proposed which take into consideration all of them: linear parameter varying (LPV) and unfalsified control (UC). The controllers are implemented with low-order dynamics that adapt continuously according to the glucose levels measured in real time in one case (LPV) and by controller switching based on the actual performance in the other case (UC). Both controllers have performed adequately under all these practical restrictions, and a discussion on pros and cons of each method is presented at the end.

- -- - An LPV (Linear Parameter Varying) controller design example for a Magnetic Bearing System is presented. A linear model of the system including bending modes and imbalance is described. Simulations and experimental results show the usefulness of the LPV method with eigenvalue clustering constraints in spite of the limited rota tion rate range. The results show that this method facil itates simulation and allows implementation. Conclusions are drawn on the limited range for the rotati on rate the LPV controller allows for.

A formulation of an LPV control problem with regional pole placement constraints is presented, which is suitable for the application of a Full Block S-Procedure. It is demonstrated that improved bounds can be obtained on the induced L2 norm of closed loop systems, while satisfying pole placement constraints. An application consisting in the 6 degrees of freedom (DOF) control of a space vehicle is developed as an example, with hardware in the loop (HIL) simulation. This shows that the method is appealing from the practical point of view, considering that the synthesized control law can be implemented satisfactorily in standard flight control systems. Conclusions with remarks towards the practical use of the method are presented as well.

This paper considers the problem of automatically controlling the glucose level in a Diabetes type I patient. Three issues have been considered: model uncertainty, time-varying/nonlinear phenomena and controller implementation. To that end, the dynamical model of the insulin/glucose relation is framed as a Linear Parameter Varying system and a controller is designed based on it. In addition, this framework allows not only a better performance than other classical methods, but also provides stability and performance guarantees. Design computations are based on convex Linear Matrix Inequality (LMI) optimization. Implementation is based on a low order controller whose dynamics adapts according to the glucose levels measured in real-time.

A linear parameter varying (LPV) controller design example for the position and attitude control of a spacecraft is presented. The six degree-of freedom (DOF) model including the aerodynamics is described. Simulations with the nonlinear 6-DOF model show the usefulness of the design procedure. The practical problem of "fast dynamics" in the controller is solved by an ad hoc method based on the use of a single quadratic Lyapunov function with pole clustering constraints for each frozen linear time invariant (LTI) system in the parameter variation set. The results show that the method facilitates simulation and allows for addressing implementation aspects such as the sampling rate.

The objective of this work is to solve the problem of fast dynamics which appears in the synthesis of LPV controllers using a single quadratic Lyapunov function. This can be a serious problem for controller implementation or computer simulation. The solution is achieved by means of an extra LMI added to the set of LMI's used to design the controller. This LMI defines the region where the poles of the "frozen" LTI closed loop system will be.

An active magnetic bearing (AMB) system for the rotor of a rotating machine is considered as a test-bench to compare different control techniques. The plant can be modeled as a Linear Parameter Varying (LPV) system. The objective of this work is to compare time invariant vs. time varying and nominal vs. robust designs on this particular application. First, the nominal model has been simplified to a diagonal one and a controller has been designed via pole-placement. Next, using the complete model, a MIMO time invariant mu-synthesis controller has been designed. Finally a time varying LPV controller has been synthesized for the uncertain plant. Due to the recent development of the latter techniques (Packard, 1993; Becker and Packard, 1994) we have included a brief introduction to LPV controllers. Other designs which use different procedures (loop-shaping, H(infinity) optimal control) have been referenced. Simulation results are compared in terms of disturbance rejection and robustness. These results are also compared to previous works in this area.

Resumen—En este trabajo se propone el diseño lineal de parámetros variantes (LPV) para el control de un cuadricóptero cuyos brazos pueden moverse respecto del eje vertical del vehı́culo, cambiando su forma de acuerdo a requerimientos de misión. El trabajo presenta el desarrollo del simulador multicuerpo y del algoritmo de control junto con una introducción al método LPV, mostrando con su utilización. Además, se presenta una explicación detallada del prototipo construido hasta el momento para las pruebas. Palabras Clave—LPV, Foldable Drone