Patricio Ordaz

The Furuta's pendulum stabilization without the use of a mathematical model: Attractive Ellipsoid Method with KL-adaptation

This paper presents a development of adaptive state estimator and output controller based on Attractive Ellipsoid Method (AEM) for the stabilization of the Furutas pendulum. The proposed method guaranties that the controlled system trajectories are stabilized within an ellipsoid of a “minimal size”. We expand the classical AEM without adaptation to a class of observer and controller compensator with time varying gain matrices K and L adjusted on-line by specific adaptation procedure, that guaranties the convergence of the trajectories to an ellipsoid of less size compared to one without adaptation. In the case of the considered pendulum the incorporated adaptation procedures provides a stabilization in the vertical position practically with negligible vibrations, or in other words, without any “chattering effect”.

Adaptive super-twist control with minimal chattering effect

The, so-called, adaptive super-twist controller is considered here. It contains the adaptive gain-parameter which adjusts the level of a scalar control action on-line based on direct measurements the “equivalent control” obtained by a first-order low-pass filter. It is shown that the problems of the finite time convergence and keeping a small chattering amplitude can be handled simultaneously if the gain magnitude is reduced to a minimal admissible level defined by the conditions for sliding mode to exist. The suggested methodology is compared numerically with another schemes of a gain-adaptation (including σ-adaptation) showing a high effectiveness under a significant level of uncertainties and external disturbances.

Modeling and Sliding Mode Control of a Micro Helicopter-Airplane System

This paper presents the regulation and trajectory tracking for a Micro Coaxial Rocket Helicopter (MCR UAV), as well as the control of a mini aircraft. The former vehicle has the characteristic of performing hover and forward flight while the latter vehicle is considered as an external air transporter for the MCR UAV. For control purposes, the helicopter stabilization is based on sliding mode controllers which avoid the chattering generated during the flight and allow the MCR UAV to perform tracking of smooth trajectories, Furthermore a PD controller stabilizes the aircraft in order to execute semi-autonomous flight. A flight computer for these aerial vehicles consists of a homemade embedded system, low-cost sensors, and signal conditioning circuits, analog filters and actuator. The proposed control algorithms are implemented on the embedded system. Simulation and experimental results show the good performance of the developed system during the flight.

Implementation of leader-follower linear consensus algorithm for coordination of multiple aircrafts

In this paper, we consider the tracking problem for leader-follower multi-agent systems under a linear consensus protocol. Our main goal is to study the real-time behavior of the algorithm when applied to a group of four holonomic Unmanned Aircraft Systems (UAS). A comprehensive analysis of the linear consensus protocol theory is presented. In our approach, the linear model of the agents are obtained by using the step response methodology, then, the models are approximated to a standard second-order model representation. The leader-follower consensus algorithm is designed and implemented for the heading and the altitude dynamics of the group of UAS. In order to prove the effectiveness of the proposed consensus algorithm we have implemented it both in simulation as well as in real-time experiments. Our work concludes with future directions of our research, which will address the issues found during the real-time tests.

‘KL’-gain adaptation for attractive ellipsoid method

This paper presents the development of an adaptive state estimator and an output controller based on the attractive ellipsoid method (AEM) for a class of uncertain non-linear systems (quasi-Lipschitz with external perturbations). The proposed method guarantees that, under a specific persistent excitation condition, the controlled system trajectories converge to an ellipsoid having a smaller trace of the corresponding inverse ellipsoidal matrix comparing to classical AEM without adaptation. An underactuated vertical double pendulum is considered as an experimental illustrative example of the suggested approach.

Nonlinear stabilization for a class of time delay systems via inverse optimality approach

This paper is devoted to obtain a stabilizing optimal nonlinear controller based on the well known Control Lyapunov-Krasovskii Functional (CLKF) approach, aimed to solve the inverse optimality problem for a class of nonlinear time delay systems. To determine sufficient conditions for the Bellmans equation solution of the system under consideration, the CLKF and the inverse optimality approach are considered in this paper. In comparison with previous results, this scheme allows us to obtain less conservative controllers, implying energy saving (in terms of average power consumption for a specific thermo-electrical process). Sufficient delay-independent criteria in terms of CLKF is obtained such that the closed-loop nonlinear time-delay system is guaranteed to be local Asymptotically Stable. To illustrate the effectiveness of the theoretical results, a comparative study with an industrial PID controller tuned by the Ziegler-Nichols methodology (Z-N) and a Robust-PID tuned by using the D-partition method is presented by online experimental tests for an atmospheric drying process with time delay in its dynamics.

Research on Swing up Control Based on Energy for the Pendubot System

In this paper, we present a class of nonlinear control scheme for swinging up and stabilization of an underactuated two-link robot called as Pendubot. The main objective of this paper is to present a switched control that swing up and stabilize for almost all combination of initial states given on the four equilibrium points of the double underactuated pendulum. The proposed methodology is based on two control strategies to swing up and stabilize the Pendubot system. The first one is based on Lagrangian dynamics, energy analysis, and stability theory, while the second one is based on linear quadratic regulator. Moreover, here we present a stability analysis of the switched control algorithm. In order to verify the proposed control strategy, experimental results were performed.

Robust bounded control for the flexible arm robot

This work presents an algorithm for designing the optimal robust saturated output feedback controller for the two-link planar robot with a spring between two links by the Attractive Ellipsoid Method serving for class of uncertain “quasi-Lipschitz” dynamics. The Attractive Ellipsoid Method (AEM) application permits to describe the class of nonlinear feedbacks containing a saturation operator that guarantees a boundedness of all possible trajectories around the origin. Here we consider more general types of nonlinear bounded feedbacks which can be corrected (adjusted) on-line during a control process. The optimization of feedback within this class of controllers is associated with the selection of the feedback parameters which provide the trajectory converges within an ellipsoid of a “minimal size”.

Nonlinear suboptimal control for a class of underactuated mechanical systems

This paper addresses to the problem of suboptimal control for a class of chained underactuated mechanical systems, whose dynamic linearization contains uncontrollable stable modes. In order to bring the system to its linearity domain and stabilize it without need of a switching control, a suboptimal control technique is proposed, based on the energy of the system and under the Bellmans Optimality Principle. A non-conventional, pendular-type underactuated dynamic system exhibiting particular features is studied to illustrate the presented approach; the swing-up and stabilization control of this numerical system about an unstable equilibrium point is shown.

Global stability of PD+ controller with velocity estimation

This paper addresses the demonstration of global asymptotic convergence for the PD+ compensator. The proposed strategy is developed for a Robotic Manipulator process, which is a typical Electro-Mechanical System (when only the joint positions are available to be measured). It is well known that in the case of robot manipulators, the optical incremental encoders are widely used to monitor joints positions information, however, joints velocities can only be measured by processing the position data (by filtering or by state estimation). The proposed feedback strategy is based on nonlinear state estimation with a Luenberger-like observer. The main result is based on the knowledge of the system dynamics for the design of a nonlinear observer in order to conclude with Global Asymptotic Convergence of the system trajectories by using a particular Lyapunov function.