Stable inversion based output tracking control of robotic systems

This thesis addresses stable inversion based output tracking control and its applications to robotic systems. It considers the non-causal invertibility (stable inversion) problem of control systems in its various aspects including properties of stable inverses and algorithms for constructing stable inverses. Then, the stable inversion approach is applied to solve a control problem of long-standing interest: output tracking control for non-minimum phase nonlinear systems;A minimum energy property of stable inverses is firstly established. The property claims that given any desired output trajectory, out of infinitely many possible inverse solutions, the one provided by the stable inversion process is the only one that has finite energy. Based on this property, a numerical procedure is developed to provide an efficient approach to construct stable inverses;Secondly, a new output tracking control design is developed. The design incorporates stable inverses and assumes a controller structure of feed-forward plus feedback. It achieves high precision tracking together with closed-loop stability. Furthermore, when system uncertainties are considered and assumed to satisfy the so-called matching conditions , a modified controller structure is presented and the corresponding robust tracking performance is discussed;Finally, the stable inversion based tracking control design is applied to three flexible robotic systems. The first study is output tracking control of a flexible-joint robot. The application demonstrates how the new design deals with the undesirable non-minimum phase property and achieves desired output tracking. The second application is tip trajectory tracking for a two-flexible-link manipulator. This thesis, for the first time, addresses the problem of stable tip trajectory tracking without any transient or steady-state errors for such non-minimum phase systems. In the third application, a new optimal motion control strategy for a flexible space robot is presented. The space robot system is assumed to consist of a two-link flexible manipulator attached to rigid space-craft. Optimality is in the sense that a performance index measured by maneuvering time, control effort, and structural vibrations is minimized while the interference from the manipulator to spacecraft is kept satisfactorily small;Studies on three applications demonstrate that the stable inversion based control design is very effective on output tracking for various robotic systems. This approach is expected to perform equivalently well for many other realistic non-minimum phase nonlinear systems

Control Theory: On the Way to New Application Fields

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently, deep interactions are emerging with new application areas, such as systems biology, quantum control and information technology. In order to address the new challenges posed by the new application disciplines, a special focus of this workshop has been on the interaction between control theory and mathematical systems biology. To complement these more biology oriented focus, a series of lectures in this workshop was devoted to the control of networks of systems, fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control

Finite element-based observer design for nonlinear systems with delayed measurements

summary:This paper presents a computational procedure for the design of an observer of a nonlinear system. Outputs can be delayed, however, this delay must be known and constant. The characteristic feature of the design procedure is computation of a solution of a partial differential equation. This equation is solved using the finite element method. Conditions under which existence of a solution is guaranteed are derived. These are formulated by means of theory of partial differential equations in $L^2$-space. Three examples demonstrate viability of this approach and provide a comparison with the solution method based on expansions into Taylor polynomials

Digital Control and Monitoring Methods for Nonlinear Processes

The chemical engineering literature is dominated by physical and (bio)-chemical processes that exhibit complex nonlinear behavior, and as a consequence, the associated requirements of their analysis, optimization, control and monitoring pose considerable challenges in the face of emerging competitive pressures on the chemical, petrochemical and pharmaceutical industries. The above operational requirements are now increasingly imposed on processes that exhibit inherently nonlinear behavior over a wide range of operating conditions, rendering the employment of linear process control and monitoring methods rather inadequate. At the same time, increased research efforts are now concentrated on the development of new process control and supervisory systems that could be digitally implemented with the aid of powerful computer software codes. In particular, it is widely recognized that the important objective of process performance reliability can be met through a comprehensive framework for process control and monitoring. From: (i) a process safety point of view, the more reliable the process control and monitoring scheme employed and the earlier the detection of an operationally hazardous problem, the greater the intervening power of the process engineering team to correct it and restore operational order (ii) a product quality point of view, the earlier detection of an operational problem might prevent the unnecessary production of o-spec products, and subsequently minimize cost. The present work proposes a new methodological perspective and a novel set of systematic analytical tools aiming at the synthesis and tuning of well-performing digital controllers and the development of monitoring algorithms for nonlinear processes. In particular, the main thematic and research axis traced are: (i) The systematic integrated synthesis and tuning of advanced model-based digital controllers using techniques conceptually inspired by Zubov’s advanced stability theory. (ii) The rigorous quantitative characterization and monitoring of the asymptotic behavior of complex nonlinear processes using the notion of invariant manifolds and functional equations theory. (iii) The systematic design of nonlinear state observer-based process monitoring systems to accurately reconstruct unmeasurable process variables in the presence of time-scale multiplicity. (iv) The design of robust nonlinear digital observers for chemical reaction systems in the presence of model uncertainty

Full-Body Torque-Level Non-linear Model Predictive Control for Aerial Manipulation

Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.Comment: Submitted to Transactions on Robotics. 17 pages, 16 figure