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

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.

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

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

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

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

On-line state and parameter estimation in nonlinear systems

On-line, simultaneous state and parameters estimation in deterministic, nonlinear dynamic systems of known structure is the problem considered. Available methods are few and fall short of user needs in that they are difficult to apply, their applicability is restricted to limited classes of systems, and for some, conditions guaranteeing their convergence don\u27t exist. The new methods developed herein are placed into two categories: those that involve the use of Riccati equations, and those that do not. Two of the new methods do not use Riccati equations, and each is considered to be a different extension of Friedland\u27 s parameter observer for nonlinear systems with full state availability to the case of partial state availability. One is essentially a reduced-order variant of a state and parameter estimator developed by Raghavan. The other is developed by the direct extension of Friedland\u27 s parameter observer to the case of partial state availability. Both are shown to be globally asymptotically stable for nonlinear systems affine in the unknown parameters and involving nonlinearities that depend on known quantities, a class restriction also true of existing state and parameter estimation methods. The two new methods offer, however, the advantages of improved computational efficiency and the potential for superior transient performance, which is demonstrated in a simulation example. Of the new methods that do involve a Riccati equation, there are three. The first is the separate-bias form of the reduced-order Kalman filter. The scope of this filter is somewhat broader than the others developed herein in that it is an optimal filter for linear, stochastic systems involving noise-free observations. To apply this filter to the joint state and parameter estimation problem, one interprets the unknown parameters as constant biases. For the system class defined above, the method is globally asymptotically stable. The second Riccati equation based method is derived by the application of an existing method, the State Dependent Algebraic Riccati Equation (SDARE) filtering method, to the problem of state and parameter estimation. It is shown to work well in several nonlinear examples involving a few unknown parameters; however, as the number of parameters increases, the method\u27s applicability is diminished due to an apparent loss of observability within the filter which hinders the generation of filter gains. The third is a new filtering method which uses a State Dependent Differential Riccati Equation (SDDRE) for the generation of filter gains, and through its use, avoids the “observability” shortcomings of the SDARE method. This filter is similar to the Extended Kalman Filter (EKF), and is compared to the EKF with regard to stability through a Lyapunov analysis, and with regard to performance in a 4th order stepper motor simulation involving 5 unknown parameters. For the very broad class of systems that are bilinear in the state and unknown parameters, and potentially involving products of unmeasured states and unknown parameters, the EKF is shown to possess a semi-global region of asymptotic stability, given the assumption of observability and controllability along estimated trajectories. The stability of the new SDDRE filter is discussed

Observer-based strict positive real (SPR) switching output feedback control

This paper considers switching output feedback control of linear systems and variablestructure systems. Theory for stability analysis and design for a class of observer-based feedback control systems is presented. It is shown how a circlecriterion approach can be used to design an observerbased state feedback control which yields a closedloop system with speci ed robustness characteristics. The approach is relevant for variable structure system design with preservation of stability when switching feedback control or sliding mode control is introduced in the feedback loop. It is shown that there exists a Lyapunov function valid over the total operating range and this Lyapunov function has also interpretation as a storage function of passivity-based control and a value function of an optimal control problem. The Lyapunov function can be found by solving a Lyapunov equation. Important applications are to be found in hybrid systems with switching control and variable structure systems with high robustness requirements

Novel Formulation and Application of Model Predictive Control.

Model predictive control (MPC) has been extensively studied in academia and widely accepted in industry. This research has focused on the novel formulation of model predictive controllers for systems that can be decomposed according to their nonlinearity properties and several novel MPC applications including bioreactors modeled by population balance equations (PBE), gas pipeline networks, and cryogenic distillation columns. Two applications from air separation industries are studied. A representative gas pipeline network is modeled based on first principles. The full-order model is ill-conditioned, and reduced-order models are constructed using time-scale decomposition arguments. A linear model predictive control (LMPC) strategy is then developed based on the reduced-order model. The second application is a cryogenic distillation column. A low-order dynamic model based on nonlinear wave theory is developed by tracking the movement of the wave front. The low-order model is compared to a first-principles model developed with the commercial simulator HYSYS.Plant. On-line model adaptation is proposed to overcome the most restrictive modeling assumption. Extensions for multiple column modeling and nonlinear model predictive control (NMPC) also are discussed. The third application is a continuous yeast bioreactor. The autonomous oscillations phenomenon is modeled by coupling PBE model of the cell mass distribution to the rate limiting substrate mass balance. A controller design model is obtained by linearizing and temporally discretizing the ODES derived from spatial discretization of the PBE model. The MPC controller regulate the discretized cell number distribution by manipulating the dilution rate and the feed substrate concentration. A novel plant-wide control strategy is developed based on integration of LMPC and NMPC. It is motivated by the fact that most plants that can be decomposed into approximately linear subsystems and highly nonlinear subsystems. LMPCs and NMPCs are applied to the respective subsystems. A sequential solution algorithm is developed to minimize the amount of unknown information in the MPC design. Three coordination approaches are developed to reduce the amount of information unavailable due to the sequential MPC solution of the coupled subsystems and applied to a reaction/separation process. Furthermore, a multi-rate approach is developed to exploit time-scale differences in the subsystems