Jaime Alvarez-Gallegos

Robust Structure-Control Design Approach for Mechatronic Systems

In this paper, a robust formulation for the structure-control design of mechatronic systems is developed. The proposed robust approach aims at minimization of the sensitivity of the nominal design objectives with respect to uncertain parameters. The robust integrated design problem is established as a nonlinear multiobjective dynamic optimization one, which in order to consider synergetic interactions uses mechanical and control nominal design objectives. A planar parallel robot and its controller are simultaneously designed with the proposed approach when the nominal design objectives are the tracking error and the manipulability measure. The payload at the end-effector is considered as the uncertain parameter. Experimental results show that a robustly designed parallel robot presents lower sensitivity of the nominal design objectives under the effects of changes at the payload than a nonrobustly designed one.

Two-time scale sliding-mode control for a class of nonlinear systems

The paper deals with the robust asymptotic stabilization of a class of nonlinear singularly perturbed systems using sliding-mode control techniques. The approach consists of decomposing the original system into two reduced order systems, for which stabilizing sliding-mode controllers are applied and combined in a two-time scale sliding-mode control for the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. An example illustrates the design procedure and performance of the proposed control scheme.

Differential evolution techniques for the structure-control design of a five-bar parallel robot

The present work deals with the use of a constraint-handling differential evolution algorithm to solve a nonlinear dynamic optimization problem (NLDOP) with 51 decision variables. A novel mechatronic design approach is proposed as an NLDOP, where both the structural parameters of a non-redundant parallel robot and the control parameters are simultaneously designed with respect to a performance criterion. Additionally, the dynamic model of the parallel robot is included in the NLDOP as an equality constraint. The obtained solution will be a set of optimal geometric parameters and optimal PID control gains. The optimal geometric parameters adjust the dynamic and the kinematic parameters, optimizing then, the link shapes of the robot. The proposed mechatronic design approach is applied to design simultaneously both the mechanical structure of a five-bar parallel robot and the PID controller.

Parametric reconfiguration improvement in non-iterative concurrent mechatronic design using an evolutionary-based approach

Parametric reconfiguration plays a key role in non-iterative concurrent design of mechatronic systems. This is because it allows the designer to select, among different competitive solutions, the most suitable without sacrificing sub-optimal characteristics. This paper presents a method based on an evolutionary algorithm to improve the parametric reconfiguration feature in the optimal design of a continuously variable transmission and a five-bar parallel robot. The approach considers a solution-diversity mechanism coupled with a memory of those sub-optimal solutions found during the process. Furthermore, a constraint-handling mechanism is added to bias the search to the feasible region of the search space. Differential Evolution is utilized as the search algorithm. The results obtained in a set of five experiments performed per each mechatronic system show the effectiveness of the proposed approach.

Sign and stability of equilibria in quasi-monotone positive nonlinear systems

The paper deals with the problem of finding the extension of a well-established connection between sign and stability of nontrivial equilibria in positive linear systems to the class of quasi-monotone positive nonlinear systems. The mathematical framework to provide the sufficient conditions guaranteeing such a relationship is the stability theory for nonlinear systems, especially the comparison principles and the method of vector Lyapunov functions. As an illustration of our results we present an example of a double-effect evaporator to study the sign-stability property of its only equilibrium point.

Experimental Analysis and Control of a Chaotic Pendubot

Applying attractor reconstruction techniques and other chaotic measurements, it is shown that the long-term dynamics of a vertical, underactuated, two-degrees-of-freedom robot called Pendubot may exhibit complex dynamics including chaotic behavior. These techniques use only the measurement of some available variable of the system, and the resulting reconstruction allows us to identify unstable periodic orbits embedded in the chaotic attractor. In this paper, we also propose a parameter-perturbation-like control algorithm to stabilize the behavior of the Pendubot to force its dynamics to be periodic. We control this device using only the measurement of one of its angular position coordinates and consider that the system may be seen as five-dimensional (a non-autonomous, four-dimensional system), taking the amplitude of a sinusoidal external torque as the perturbation parameter. We change this parameter to stabilize one of the equilibrium points in the so-called Lorenz map. The main advantage of the method proposed here is that it can be implemented directly from time series data, irrespective of the overall dimension of the phase space. Also, reconstructions of the attractor based on the measurements are shown, as well as some experimental results of the controlled system.

Kinematic Dexterity Maximization of an Omnidirectional Wheeled Mobile Robot: A Comparison of Metaheuristic and SQP Algorithms

Mobile robots with omnidirectional wheels are expected to perform a wide variety of movements in a narrow space. However, kinematic mobility and dexterity have not been clearly identified as an objective to be considered when designing omnidirectional redundant robots. In light of this fact, this article proposes to maximize the dexterity of the mobile robot by properly locating the omnidirectional wheels. In addition, four hybrid differential evolution (DE) algorithm based on the synergetic integration of different kinds of mutation and crossover are presented. A comparison of metaheuristic and gradient-based algorithms for kinematic dexterity maximization is also presented.

Evolutionary dynamic optimization of a continuously variable transmission for mechanical efficiency maximization

This paper presents a dynamic optimization approach based on the differential evolution (DE) strategy which is applied to the concurrent optimal design of a continuously variable transmission (CVT). The structure-control integration approach is used to state the concurrent optimal design as a dynamic optimization problem which is solved using the Constraint Handling Differential Evolution (CHDE) algorithm. The DE strategy is compared with the sequential approach. The results presented here demonstrate that the DE strategy is less expensive than the sequential approach from the computational implementation point of view.

Modeling and controller design of a magnetic levitation system

In this paper, the nonlinear mathematical model with five DOFs of a magnetic levitation system is developed and analyzed. Then a second order sliding mode controller is proposed to regulate the levitation to a desired position, stabilize the other 4 DOFs in the nonlinear system and compensate the unknown increments on the load. Simulation results are presented to show the effectiveness of the proposed controller.

Structure-control mechatronic design of the planar 5R 2DoF parallel robot

In this paper, a concurrent design methodology to formulate the mechatronic design problem of the planar five revolute two degrees of freedom (5R 2DoF) parallel robot and its PID controller is presented. This methodology involves a synergetic design of the mechanical structure and the control system. A nolinear dynamic optimization problem is stated for this approach and two optimization techniques, one based on a nonlinear programming technique and the other based on a novel evolutionary approach, are used to solve it. Finally, the optimal mechanical structure and controller parameters show the effectiveness of the proposed approach via simulation and experimental results.