Multivariable Iterative Learning Control Design Procedures: from Decentralized to Centralized, Illustrated on an Industrial Printer

Iterative Learning Control (ILC) enables high control performance through learning from measured data, using only limited model knowledge in the form of a nominal parametric model. Robust stability requires robustness to modeling errors, often due to deliberate undermodeling. The aim of this paper is to develop a range of approaches for multivariable ILC, where specific attention is given to addressing interaction. The proposed methods either address the interaction in the nominal model, or as uncertainty, i.e., through robust stability. The result is a range of techniques, including the use of the structured singular value (SSV) and Gershgorin bounds, that provide a different trade-off between modeling requirements, i.e., modeling effort and cost, and achievable performance. This allows control engineers to select the approach that fits the modeling budget and control requirements. This trade-off is demonstrated in a case study on an industrial flatbed printer

Survey of robust control for rigid robots

Current approaches to the robust control of the motion of rigid robots are surveyed, and the available literature is summarized. The five major design approaches discussed are the linear-multivariable approach, the passivity approach, the variable-structure approach, the saturation approach, and the robust-adaptive approach. Some guidelines for choosing a method are offered

Contributions à l’estimation robuste et à la commande prédictive robuste par méthodes ensemblistes

Dans le contexte de la commande prédictive robuste, ces travaux s’articulent autour de l’élaboration d’approches ensemblistes pour la prise en compte des incertitudes. Trois axes principaux sont proposés.Un premier axe s’intéresse à l’élaboration de lois de commande prédictives robustifiées vis-à-vis de plusieurs types d’incertitudes (par exemple des incertitudes structurées formulées à l’aide d’ensembles polytopiques), plus spécifiquement via la paramétrisation de Youla-Kučera. Un logiciel a été à cette occasion développé afin de simplifier l’implantation de ces structures de commande. Plusieurs applications dans des domaines très variés (robot médical, hélicoptère, système de gestion de la production, centrale électrique au charbon) illustrent les résultats obtenus.Une deuxième direction est liée aux méthodes ensemblistes pour l’estimation d’état des systèmes soumis à des incertitudes par intervalles et à des perturbations bornées. Une technique d’estimation ensembliste zonotopique fondée sur la minimisation du P-rayon d’un zonotope est tout d’abord proposée. Une deuxième étape vise ensuite à l’élaboration d’une loi de commande prédictive robuste reprenant explicitement l’estimation ensembliste.Une troisième partie est dédiée à la commande prédictive des systèmes multi-agents sous contraintes dynamiques. Plusieurs aspects sont examinés, faisant appel également aux techniques ensemblistes : la génération de trajectoire, l’allocation des tâches, le suivi de trajectoire par la formation, en respectant des contraintes d’évitement de collision entre les agents et avec présence éventuelle d’obstacles. Dans ce contexte, plusieurs approches de commande prédictive centralisée, distribuée et décentralisée ont été développées. Une application à des drones est présentée afin de valider certains de ces concepts

Robust on-off pulse control of flexible space vehicles

The on-off reaction jet control system is often used for attitude and orbital maneuvering of various spacecraft. Future space vehicles such as the orbital transfer vehicles, orbital maneuvering vehicles, and space station will extensively use reaction jets for orbital maneuvering and attitude stabilization. The proposed robust fuel- and time-optimal control algorithm is used for a three-mass spacing model of flexible spacecraft. A fuel-efficient on-off control logic is developed for robust rest-to-rest maneuver of a flexible vehicle with minimum excitation of structural modes. The first part of this report is concerned with the problem of selecting a proper pair of jets for practical trade-offs among the maneuvering time, fuel consumption, structural mode excitation, and performance robustness. A time-optimal control problem subject to parameter robustness constraints is formulated and solved. The second part of this report deals with obtaining parameter insensitive fuel- and time- optimal control inputs by solving a constrained optimization problem subject to robustness constraints. It is shown that sensitivity to modeling errors can be significantly reduced by the proposed, robustified open-loop control approach. The final part of this report deals with sliding mode control design for uncertain flexible structures. The benchmark problem of a flexible structure is used as an example for the feedback sliding mode controller design with bounded control inputs and robustness to parameter variations is investigated

Utilization of Differential Thrust for Lateral/Directional Stability of a Commercial Aircraft with a Damaged Vertical Stabilizer

This thesis investigates the utilization of differential thrust to help a commercial aircraft with a damaged vertical stabilizer regain its lateral/directional stability. In the event of an aircraft losing its vertical stabilizer, the consequential loss of the lateral/directional stability is likely to cause a fatal crash. In this thesis, the damaged aircraft model is constructed, and the lateral/directional dynamic stability and frequency domain analyses are conducted. The propulsion dynamics of the aircraft are modeled as a system of differential equations with engine time constant and time delay terms to study the engine response time with respect to a differential thrust input. The novel differential thrust control module is presented to map the rudder input to differential thrust input. Then, the differential thrust based control strategies such as linear quadratic regulator (LQR), model reference adaptive system (MRAS), and H∞ loop-shaping based robust control system are proposed to be utilized to help maintain stability and control of the damaged aircraft. For each type of control system design, robustness and sensitivity analysis is also conducted to test the performance of each control system in the presence of noise and uncertainty. Results demonstrate successful applications of such control methodologies as the damaged aircraft can achieve stability under feasible control efforts and without any actuator saturation. Finally, a comparison study of three control systems is conducted to investigate the merits and limits of each control system. Overall, the H∞ loop-shaping based robust control system was found to have the most remarkable results for stabilizing and saving the damaged aircraft

Adaptive optimal control of under-actuated robotic systems using a self-regulating nonlinear weight-adjustment scheme: Formulation and experimental verification

This paper formulates an innovative model-free self-organizing weight adaptation that strengthens the robustness of a Linear Quadratic Regulator (LQR) for inverted pendulum-like mechatronic systems against perturbations and parametric uncertainties. The proposed control procedure is devised by using an online adaptation law to dynamically adjust the state weighting factors of LQR's quadratic performance index via pre-calibrated state-error-dependent hyperbolic secant functions (HSFs). The updated state-weighting factors re-compute the optimal control problem to modify the state-compensator gains online. The novelty of the proposed article lies in adaptively adjusting the variation rates of the said HSFs via an auxiliary model-free online self-regulation law that uses dissipative and anti-dissipative terms to flexibly re-calibrate the nonlinear function's waveforms as the state errors vary. This augmentation increases the controller's design flexibility and enhances the system's disturbance rejection capacity while economizing control energy expenditure under every operating condition. The proposed self-organizing LQR is analyzed via customized hardware-in-loop (HIL) experiments conducted on the Quanser's single-link rotational inverted pendulum. As compared to the fixed-gain LQR, the proposed SR-EM-STC delivers an improvement of 52.2%, 16.4%, 55.2%, and 42.7% in the pendulum's position regulation behavior, control energy expenditure, transient recovery duration, and peak overshoot, respectively. The experimental outcomes validate the superior robustness of the proposed scheme against exogenous disturbances

Reference Governors for MIMO Systems and Preview Control: Theory, Algorithms, and Practical Applications

The Reference Governor (RG) is a methodology based on predictive control for constraint management of pre-stablized closed-loop systems. This problem is motivated by the fact that control systems are usually subject to physical restrictions, hardware protection, and safety and efficiency considerations. The goal of RG is to optimize the tracking performance while ensuring that the constraints are satisfied. Due to structural limitations of RG, however, these requirements are difficult to meet for Multi-Input Multi-Output (MIMO) systems or systems with preview information. Hence, in this dissertation, three extensions of RG for constraint management of these classes of systems are developed. The first approach aims to solve constraint management problem for linear MIMO systems based on decoupling the input-output dynamics, followed by the deployment of a bank of RGs for each decoupled channel, namely Decoupled Reference Governor (DRG). This idea was originally developed in my previous work based on transfer function decoupling, namely DRG-tf. This dissertation improves the design of DRG-tf, analyzes the transient performance of DRG-tf, and extends the DRG formula to state space representations. The second scheme, which is called Preview Reference Governor, extends the applicability of RG to systems incorporated with the preview information of the reference and disturbance signals. The third subject focuses on enforcing constraints on nonlinear MIMO systems. To achieve this goal, three different methods are established. In the first approach, which is referred to as the Nonlinear Decoupled Reference Governor (NL-DRG), instead of employing the Maximal Admissible set and using the decoupling methods as the DRG does, numerical simulations are used to compute the constraint-admissible setpoints. Given the extensive numerical simulations required to implement NL-DRG, the second approach, namely Modified RG (M-RG), is proposed to reduce the computational burden of NL-DRG. This solution consists of the sequential application of different RGs based on linear prediction models, each robustified to account for the worst-case linearization error as well as coupling behavior. Due to this robustification, however, M-RG may lead to a conservative response. To lower the computation time of NL-DRG while improving the performance of M-RG, the third approach, which is referred to as Neural Network DRG (NN-DRG), is proposed. The main idea behinds NN-DRG is to approximate the input-output mapping of NL-DRG with a well-trained NN model. Afterwards, a Quadratic Program is solved to augment the results of NN such that the constraints are satisfied at the next timestep. Additionally, motivated by the broad utilization of quadcopter drones and the necessity to impose constraints on the angles and angle rates of drones, the simulation and experimental results of the proposed nonlinear RG-based methods on a real quadcopter are demonstrated

Evolutionary design of digital trajectory-tracking controllers for robotic manipulators

The design of digital trajectory-tracking controllers for robotic manipulators is a challenging task, since such manipulators are multivariable non-linear plants. In addition, in many applications of robotic manipulators, it is required that very high-accuracy trajectory-tracking performance be achievable even in the presence of unpredictable payload variations. These requirements can all be met to some extent by application of the previously developed fast-sampling digital PID controllers to robotic manipulators. Indeed, for such controllers, it is possible to prove a series of very reassuring robustness results using only the Markov parameters associated with locally linearised representations of robotic manipulators.However, these theoretical optimisation results for digital PID controllers are only valid as sampling periods become vanishingly small. In practice, of course, the sampling periods of digital controllers remain non-zero; but, in such cases, no theoretical optimisation results are available. There is, therefore, a great need for some alternative optimisation procedure that will facilitate the non- asymptotic design of digital PID controllers for robotic manipulators.This design need is addressed in this thesis. In particular, the following evolutionary optimisation techniques are used to design digital trajectorytracking controllers for robotic manipulators:(i) genetic algorithms,(ii) non-adaptive evolution strategies(iii) adaptive evolution strategies.It is shown that, with increasing effectiveness, these techniques are very useful in the design of high-accuracy digital PID controllers. These techniques are illustrated by the presentation of simulation results for a typical three-link robotic manipulator performing a range of demanding trajectory-tracking tasks in the presence of unpredictable payload variations. In addition, these evolutionary optimisation techniques are also used in the design of unconstrained digital PID controllers, in which all elements of the controller matrices are used as the design parameters.In order to validate these evolutionary design techniques in practice, an experimental laboratory investigation is also undertaken. This involves the practical implementation, in the case of a direct-drive two-link robotic manipulator, of digital PID trajectory-tracking controllers designed using evolutionary techniques. The results thus obtained indicate that such optimisation techniques greatly facilitate the tuning of digital PID controllers for robotic manipulators under practical non-asymptotic conditions