Igor Boiko

Chattering in sliding mode control systems with boundary layer approximation of discontinuous control

It has been a widely accepted notion that approximation of discontinuous control by certain continuous function in a boundary layer results in chattering elimination in sliding mode control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the boundary layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided. An approach to robust stability of linear systems from the consideration of the saturating control is proposed.

Design of gain scheduling control strategy for artificial gas lift in oil production through modified relay feedback test

One of the major problems encountered in artificial gas lifting is the stability of production from wells were gas lift may show a highly oscillatory behavior, and hence production varies greatly with time. This paper presents methodology of design of a gain scheduling strategy based on a new physical model of artificial gas lift in oil wells. The model was preliminarily validated by comparing the states dynamics with other models from the literature which have been replicated. The Modified Relay-Feedback-Test (MRFT) method was used to calculate the PI controller parameters, and the model reached steady state for different operating points. Gain scheduling was then performed following the MRFT results to provide a simple PI controller tuning parameters for the automatic control and optimization of the production from the oil well, and to compensate for the casing-heading instability in the system.

On relative degree, chattering and fractal nature of parasitic dynamics in sliding mode control

Abstract With respect to relative degree and chattering in sliding mode (SM) control systems, the notion of fractal dynamics is introduced, and a conjecture is formulated that the character of parasitic dynamics of real control systems is fractal. A model of fractal dynamics is proposed. The characteristics of fractal dynamics are studied in the frequency and time domains. It is shown that with fractal parasitic dynamics SM control systems will always feature chattering and non-ideal closed-loop performance. An example of analysis is provided.

Non-parametric Tuning of PID Controllers

In Chap. 2, further to Introduction, two approaches in controller tuning, parametric and non-parametric, are considered. Non-parametric methods of tuning based on the continuous cycling principle are considered in this chapter in detail. The chapter starts with the Ziegler-Nichols closed-loop tuning method and progresses to the available methods of tuning, which involve the possibility of excitation of test oscillations at frequencies corresponding to phase lags of the process other than −180∘. The necessity of such functionality is supported by examples provided.

Interpolating sliding mode observer for a ball and beam system

ABSTRACT A principle of interpolating sliding mode observer is introduced in this paper. The observer incorporates multiple linear observers through interpolation of multiple estimates, which is treated as a type of adaptation. The principle is then applied to the ball and beam system for observation of the slope of the beam from the measurement of the ball position. The linearised model of the ball and beam system using multiple linearisation points is developed. The observer dynamics implemented in Matlab/Simulink Real Time Workshop environment. Experiments conducted on the ball and beam experimental setup demonstrate excellent performance of the designed novel interpolating (adaptive) observer.

Dynamic harmonic balance principle and analysis of rocking block motions

Abstract The harmonic balance (HB) principle is a powerful and convenient tool for finding periodic solutions in nonlinear systems. In the present paper, this principle is extended to transient processes in systems with one single-valued odd-symmetric nonlinearity and linear plant not having zeros in the transfer function, and named the dynamic HB. Based on the dynamic HB, first the equations for the amplitude, frequency, and amplitude decay of an oscillatory process in the Lure system are derived. It is then applied to analysis of rocking block decaying motions. An example is provided.

A data-driven subspace predictive controller design for artificial gas-lift process

The objective of artificial gas-lift technique is to improve the oil production in petroleum industry. However, in open-loop control, the stability issue may arise due to the so-called casing heading phenomenon. Artificial Gas-lift process is a nonlinear multivariable time varying system with slow dynamics. Therefore, model predictive control (MPC) can be considered as a good candidate for closed-loop control of such a process. In this work, we present a new design of subspace predictive controller (SPC) for gas-lift process. The SPC is a data driven algorithm, using linear predictor to predict future output based on process input and output data. The linear prediction model is derived offline. Thereby, the key future of the proposed approach is that precise knowledge of the model and on-line optimization are not required to derive the control law. The effectiveness and superiority of the proposed controller is demonstrated in simulation, and compared with a robust nonlinear model predictive controller (NMPC).

Design of a gain matrix for a sliding mode observer for an artificial gas lift system

An Artificial gas lift system is an existing technology in the oil sector; which utilizes the fact that a pressure differential exists in the reservoirs tubing leading to enhanced oil recovery from the reservoir. Studies were conducted to control this process as it improves the stability and performance of gas lift. The current industrial practice depends on flow measurement as a process variable, yet, it does not depend on the measurements which would be obtained several kilometers below the ground that are technically difficult to approach due to several limitations such as huge pressures. Proper knowledge of the states would leads to a better controller design for this system. In this paper, a methodology towards the design of a sliding mode observer is investigated. The purpose of the observer is to acquire the states of a nonlinear system representing the physical system of a gas lift process in oil wells. The proposed design of an observer is based only on measurements taken above the surface.

Design of non-parametric process-specific optimal tuning rules for PID control of flow loops

Abstract The problem of designing optimal process-specific rules for non-parametric tuning is undertaken in the paper. It is shown that producing non-parametric process-specific optimal tuning rules for PID controllers leads to the problem that can be characterized as optimization under uncertainty. This happens due to the fact that tuning rules, unlike tuning constants, are produced not for a particular process or plant model but for a set of models from a certain domain. The novelty of the proposed approach is that the problem of obtaining optimal tuning rules for a flow process is formulated and solved as a problem of optimization of an integral performance criterion parametrized through values that define the domain of available process models. The considered non-parametric tuning assumes the use of the modified relay feedback test (MRFT) recently proposed in the literature. It allows one to tune the PID controller satisfying the requirements to gain or phase margins that is achieved through coordinated selection of tuning rules and test parameters. This approach constitutes a holistic approach to tuning. In the present paper, optimal tuning rules coupled with MRFT, for flow loops, are proposed. Final results are presented in the form of tables containing coefficients of optimal tuning rules for the PI controller, obtained for a number of specified gain margins. The produced non-parametric tuning rules well agree with the practice of loop tuning.

Analysis of transient oscillations in Lure systems with delay, based on dynamic harmonic balance

Transient oscillations in a Lure system are studied using the dynamic harmonic balance (DHB) principle. The DHB, recently proposed in the literature, is extended in the paper to the systems that include delays. An example illustrating application of DHB to analysis is given.