On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Analytic Parameterization of Stabilizing Controllers for the Moore-Greitzer Compressor Model

This work presents an extension, simplification and application of a design procedure for dynamic output feedback design for systems with nonlinearities satisfying quadratic constraints (QC). Our method was motivated by the challenges of output feedback control design for the three-state Moore-Greitzer (MG) compressor model. The classical three-state MG model is a nonlinear dynamical system that is widely used in stall/surge analysis and control design. First, we find the parameter set of the stabilizing dynamic output feedback controllers for the surge subsystem by using conditions for stability of a transformed system and the associated matching conditions. Second, we choose the optimal control parameters from the stabilizing set with respect to different desired criteria. We show the set of parameters of the stabilizing controllers for the surge subsystem and the set of parameters of the stabilizing controllers with extended integral part for MG compressor. We present simplified sufficient conditions for stabilization, new constraints for the corresponding parameters and examples of optimal problem for the surge subsystem of the Moore-Greitzer compressor model. We discuss the degree of robustness and clarify an alternative proof of stability of the closed-loop system with the surge subsystem and the stabilizing dynamic output feedback controller without an integral state. In addition, we show the derivation of a quadratic function by using CVX

Robust sliding mode‐based extremum‐seeking controller for reaction systems via uncertainty estimation approach

"This paper deals with the design of a robust sliding mode‐based extremum‐seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input–output linearizing method with variable‐structure feedback, such that the closed‐loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum‐seeking control algorithms, the control scheme includes a dynamic modelling‐error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient‐based optimization algorithm. Practical stabilizability for the closed‐loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme.

Dynamic modelling and nonlinear model predictive control of a fluid catalytic cracking unit

The paper presents the application of two nonlinear model predictive control (NMPC) approaches: quasi-infinite-horizon nonlinear MPC (QIHNMPC) and moving horizon estimator nonlinear MPC (MHE-NMPC) to the Fluid Catalytic Cracking Unit (FCCU). A complex dynamic model of the reactor–regenerator–fractionator system is developed and subsequently used in the controller. The novelty of the model consists in that besides the complex dynamics of the reactor–regenerator system, it also includes the dynamic model of the fractionator, as well as a five lumps kinetic model for the riser. Tight control is achieved using the QIHNMPC approach. The MHE-NMPC considers important features of a real-time control algorithm, resulting in a framework for practical NMPC implementation, such as: state and parameter estimation and efficient solution of the optimisation problem. In the NMPC approach, only measurements available in practice are considered, whereas the rest of the states are estimated together with uncertain model parameters, via MHE technique. Using an efficient numerical implementation based on the multiple shooting algorithm real-time feasibility of the approach is achieved. The incentives of the proposed approaches are assessed on the simulated industrial FCCU

Real-time embedded system of super twisting-based integral sliding mode control for quadcopter UAV

This paper presents the development of set-point weighting-based integral super-twisting sliding mode control (SISTASMC) with full-order state observers to overcome the control challenges encountered with nonlinear and underactuated systems. Quadcopter UAV form is a good example of underactuated systems, and this is selected in this research for validating the developed control. A comparative assessment through experimental validation is conducted between SISTASMC and Set-point weighting-based Integral Sliding Mode Control to demonstrate the performance of both controllers. Based on predetermined performance criteria, the results obtained demonstrate good performance of SISTASMC in dealing with uncertainty

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Global Stabilization for a Class of Coupled Nonlinear Systems with Application to Active Surge Control

We propose here a new procedure for output feedback design for systems with nonlinearities satisfying quadratic constraints. It provides an alternative for the classical observer-based design and relies on transformation of the closed-loop system with a dynamic controller of particular structure into a special block form. We present two sets of sufficient conditions for stability of the transformed block system and derive matching conditions allowing such a representation for a particular challenging example. The two new tests for global stability proposed for a class of nonlinear systems extend the famous Circle criterion applied for infinite sector quadratic constraints. The study is motivated and illustrated by the problem of output feedback control design for the well-known finite dimensional nonlinear model qualitatively describing surge instabilities in compressors. Assuming that the only available measurement is the pressure rise, we suggest a constructive procedure for synthesis of a family of robustly globally stabilizing feedback controllers. The solution relies on structural properties of the nonlinearity of the model describing a compressor characteristic, which includes earlier known static quadratic constraints and a newly found integral quadratic constraint. Performance of the closed-loop system is discussed and illustrated by simulations