Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process

Condition-based design of variable impedance controllers from user demonstrations

This paper presents an approach to ensure conditions on Variable Impedance Controllers through the off-line tuning of the parameters involved in its description. In particular, we prove its application to term modulations defined by a Learning from Demonstration technique. This is performed through the assessment of conditions regarding safety and performance, which encompass heuristics and constraints in the form of Linear Matrix Inequalities. Latter ones allow to define a convex optimisation problem to analyse their fulfilment, and require a polytopic description of the VIC, in this case, obtained from its formulation as a discrete-time Linear Parameter Varying system. With respect to the current state-of-art, this approach only limits the term definition obtained by the Learning from Demonstration technique to be continuous and function of exogenous signals, i.e. external variables to the robot. Therefore, using a solution-search method, the most suitable set of parameters according to assessment criteria can be obtained. Using a 7-DoF KinovaGen3 manipulator, validation and comparison against solutions with relaxed conditions are performed. The method is applied to generate Variable Impedance Controllers for a pulley belt looping task, inspired by the Assembly Challenge for Industrial Robotics in World Robot Summit 2018, to reduce the exerted force with respect to a standard (constant) Impedance Controller. These controllers fulfil a set of safety constraints, namely stability, bounds on task variables and maximum response overshooting; and their performance is determined by the User Preference heuristic, which allows to intuitively define the desired compliant behaviour along the task. In the context of the task, this is used to generate new controllers for one-off modifications of the nominal belt looping task setup without new demonstrations.This work is partially supported by MCIN/ AEI /10.13039/501100011033 and by the ”European Union NextGenerationEU/PRTR” under the project ROB-IN (PLEC2021-007859); and by MCIN/ AEI /10.13039/ 501100011033, Spain, under the project CHLOE-GRAPH (PID2020- 119244GB-I00). Authors also want to thank Adriá Colomé and Edoardo Caldarelli for their comments and help throughout this work.Peer ReviewedPostprint (published version

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc

Issues in the design of switched linear systems : a benchmark study

In this paper we present a tutorial overview of some of the issues that arise in the design of switched linear control systems. Particular emphasis is given to issues relating to stability and control system realisation. A benchmark regulation problem is then presented. This problem is most naturally solved by means of a switched control design. The challenge to the community is to design a control system that meets the required performance specifications and permits the application of rigorous analysis techniques. A simple design solution is presented and the limitations of currently available analysis techniques are illustrated with reference to this example

The role of closed-loop attitude dynamics in adaptive UAV position control

This paper presents the design and the stability analysis of an adaptive position controller for Unmanned Aerial Vehicles (UAVs). Considering a hierarchical control scheme, the novelty of this work is the definition of a systematic approach to design a position controller based on Model Reference Adaptive Control (MRAC) theory taking into account not-fast closed-loop attitude dynamics. After having reformulated the problem considering the attitude dynamics as pseudo-actuator, the authors exploit an existing Linear Matrix Inequality (LMI) based hedging framework designed such that the adaptation performance is not affected by the presence of actuator dynamics. Results from simulations and from experiments on a platform designed to replicate the longitudinal motion of quadrotors are provided to illustrate the performance of the proposed control scheme

Novel control design and strategy for load frequency control in restructured power systems

In restructured electric power systems, a number of generation companies and independent power producers compete in the energy market to make a profit. Furthermore, a new marketplace for ancillary services is established, providing an additional profit opportunity for those power suppliers. These services are essential since they help support the transmission of power from energy sources to loads, and maintain reliable operation of the overall system. This dissertation addresses regulation , a major ancillary service also known as the load frequency control (LFC) problem, and presents novel control designs and strategies for the LFC in restructured power systems.;A power system is an interconnection of control areas, which are operated according to control performance standards established by the North American Electric Reliability Council (NERC). LFC is a necessary mechanism in each control area because it maintains a balance between power demand and power generation while assuring compliance with NERC standards.;This dissertation first develops three new control designs that yield effective and robust load frequency control actions. All controllers developed here require only local measurements. The first control design is based on decoupling each area thru modeling of the interconnection effects of other control areas. The second control design relies on the robust H infinity theory in terms of linear matrix inequalities (LMIs). The third control design is achieved by the collaboration between genetic algorithms (GAs) and LMIs. The first two control designs result in high-order dynamic controllers. The third design requires only a simple proportional-integral (PI) controller while yielding control performance as good as those resulting from the previous two designs. Consequently, the third control design is the most preferable due to its simplicity and suitability for industry practice. Furthermore, a stability analysis method based on perturbation theory of eigenvalues is developed to assess the stability of the entire power system being equipped by the proposed controllers.;Second, to comply with NERC standards, two LFC strategies are developed to direct LFC\u27s actions. One strategy employs fuzzy logic to mimic a skillful operator\u27s actions so that all decisions are made efficiently. The other strategy treats the compliance with NERC standards as constraints while minimizing the operational and maintenance costs associated with LFC actions. Three new indices are introduced to assess economic benefits from the strategy compared to the conventional methods. Simulation is performed to demonstrate performances of all proposed methods and strategies

Integrated Robust Optimal Design (IROD) via sensitivity minimization

A novel Integrated Robust Optimal Design (IROD) methodology is presented in this work which combines a traditional sensitivity theory with relatively new dvancements in Bilinear Matrix Inequality (BMI) constrained optimization problems. IROD provides the least conservative approach for robust control synthesis. The proposed methodology is demonstrated using numerical examples of integrated control-structure design problem for combine harvester header and excavator linkages. The IROD methodology is compared with the state of the art sequential design method using the two application examples, and the results show that the proposed methodology provides a viable alternative for robust controller synthesis and often times offers even a better performance than competing methods. Although this method requires linearization of nonlinear system at each system parameter optimization step, a technique to linearized Differential Algebraic Equations (DAE) is presented which allows use of symbolic approach for linearization. This technique avoids repetitive linearizations. For the nonlinear systems with parametric uncertainties which can not be linearized at operating points, a new methodology is proposed for robust feedback linearization using sensitivity dynamics-based formulation. The feedback linearization approach is used for systems with augmented sensitivity dynamics and used to refine control input to improve robustness. The method is demonstrated using an example of a position tracking control of a hydraulic actuator. The robustness of controller design is demonstrated by considering variations in fluid density parameter. The results show that the proposed methodology improves robustness of the feedback linearization to parametric variations

Mixed H2/H∞ control for infinite dimensional systems

The class of infinite dimensional systems often occurs when dealing with distributed parameter models consisting of partial differential equations. Although forming a comprehensive description, they mainly become manageable by finite dimensional approximations which likely neglect important effects, but underlies a certain structure. In contrast to common techniques for controlling infinite dimensional systems, this work focuses on using robust control methods. Thus, the uncertainty structure that occurs due to the discretization shall be taken into account particularly. Additionally, optimal performance measures can be included into the design process. The mixed H2/H∞ control approach handles the inclusion of disturbances and inaccuracies while guaranteeing specified energy or magnitude bounds. In order to include various of these system requirements, multi-objective robust control techniques based on the linear matrix inequality framework are utilized. This offers great flexibility concerning the formulation of the control task and results in convex optimization problems which can be solved numerically efficient by semi-definite programming. A flexible robot arm structure serves as the major application example during this work. The model discretization leads to an LTI system of specified order with an uncertainty model which is obtained by considering the concrete approximation impact and frequency domain tests. A structural analysis of the system model relates the neglected dynamics to a robust characterization. For the objective selection, stability shall be ensured under all expected circumstances while the aspects of optimal H2 performance, passive behavior and optimal measurement output selection are included. The undesirable spillover effect is thoroughly investigated and thus avoided.Tesi