The paper addresses the problem of design of a robust controller for a class of nonlinear uncertain systems to guarantee the prescribed decay rate of exponential stability. The bounded deterministic uncertainties are considered both in a studied system and its input part. The proposed approach does not employ matching conditions.
In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium μ is not well known. On the other hand, when also the substrate concentration in the feed stream sin is unknown, we provide an observer of system and propose a design of robust feedback control in...
In this paper, a method for observer design for linear systems with multiple delays in state and output variables is proposed. The designing method involves attenuating of the disturbance to a pre-specified level. The observer design requires solving certain algebraic Riccati equation. An example is given in order to illustrate the proposed method.
The paper deals with the problem of obtaining a robust PI-D controller design procedure for linear time invariant descriptor uncertain polytopic systems using the regional pole placement and/or criterion approach in the form of a quadratic cost function with the state, derivative state and plant input (QSR). In the frame of Lyapunov Linear Matrix Inequality (LMI) regional pole placement approach and/or quadratic cost function based on Bellman-Lyapunov equation, the designed novel design procedure...
Considerable safety benefits are achieved by robustly decoupling the lateral and yaw motions of a car with active steering. Robust unilateral decoupling requires an actuator to generate an additional front wheel steering angle. However, introducing actuators to closed loop systems may cause limit cycles due to actuator saturation and rate limits. Such limit cycles are intolerable w.r.t. safety and comfort. By introducing a simple nonlinear modification of the control law, this paper proposes a remedy...
In the paper the design of an aircraft motion controller based on the Dynamic Contraction Method is presented. The control task is formulated as a tracking problem for Euler angles, where the desired decoupled output transients are accomplished under assumption of high-level, high-frequency sensor noise and incomplete information about varying parameters of the system and external disturbances. The resulting controller has a simple form of a combination of a low-order linear dynamical system and...
In this paper, a robust sampled-data observer is proposed for Lipschitz nonlinear systems. Under the minimum-phase condition, it is shown that there always exists a sampling period such that the estimation errors converge to zero for whatever large Lipschitz constant. The optimal sampling period can also be achieved by solving an optimal problem based on linear matrix inequalities (LMIs). The design methods are extended to Lipschitz nonlinear systems with large external disturbances as well. In...
This article addresses the problem of distributed-parameter control for a class of infinite-dimensional manufacturing processes with scanned thermal actuation, such as scan welding. This new process is implemented on a robotic GTAW laboratory setup with infrared pyrometry, and simulated by a flexible numerical computation program. An analytical linearized model, based on convolution of Green’s fields, is expressed in multivariable state-space form, with its time-variant parameters identified in-process....
Problems of the system identification using orthonormal functions are discussed and algorithms of computing parameters of the discrete time state- space model of the plant based on the generalized orthonormal functions and the Laguerre functions are derived. The adaptive LQ regulator and the predictive controller based on the Laguerre function model are also presented. The stability and the robustness of the closed loop using the predictive controller are investigated.
The handling of various input constraints in the self-tuning generalized predictive control (STGPC) problem of ARIMAXARMAX systems is considered. The methods based on the Lagrange multipliers and Lemke's algorithm are used to solve the constrained optimization problem. A self-tuning controller is implemented in an indirect way, and the considered constraints imposed on the control input signal are of the rate, amplitude and energy types. A comparative simulation study of self-tuning control system...
A design technique for the stabilization of linear systems by one constant output-feedback controller is developed. The design equations are functions of the state and the control weighting matrices. An example of the stabilization of an aircraft at different operating points is given.
This paper presents sufficient conditions for the sliding mode control of a system with disturbance input. The behaviour of the sliding dynamics in the presence of unmatched uncertainty is also studied. When a certain sufficient condition on the gain feedback matrix of the discontinuous controller and the disturbance bound holds, then the disturbance does not affect the sliding system. The design of asymptotically stable sliding observers for linear multivariable systems is presented. A sliding...
In this paper new necessary and sufficient conditions for static output feedback stabilizability for continuous and discrete time linear time invariant systems have been proposed. These conditions form the basis for the procedure of static output feedback controller design proposed in this paper. The proposed LMI based algorithms are computationally simple and tightly connected with the Lyapunov stability theory and LQ optimal state feedback design. The structure of the output feedback gain matrix,...
The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem...
An observer for a system with polynomial nonlinearities is designed. The system is assumed to exhibit a time delay whose value is supposed to be constant and known. The design is carried out using the sum-of-squares method. The key point is defining a suitable Lyapunov-Krasovskii functional. The resulting observer is in form of a polynomial in the observable variables. The results are illustrated by two examples.
A new methodology for the design of filters that permits failure detection and isolation of dynamic systems is presented. Assuming that the normal and the faulty behavior of a process can be modeled by two linear systems subject to inequality bounded perturbations, a method for the on-line implementation of a test signal, guaranteeing failure detection, is proposed. To improve the fault detectability of the dynamic process, appropriate test signals are injected into the system. All the computations...