Robust predictive extended state observer for a class of nonlinear systems with time-varying input delay

ABSTRACT

This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.     

Nonlinear dynamic behaviors and control based on simulation of high-purity heat integrated air separation column

In this paper, the dynamic behaviors on the basis of simulation for high-purity heat integrated air separation column (HIASC) are studied. A nonlinear generic model control (GMC) scheme is proposed based on the nonlinear behavior analyses of a HIASC process, and an adaptive generic model control (AGMC) scheme is further presented to correct the model parameters online. Related internal model control (IMC) scheme and multi-loop PID (M-PID) scheme are also developed as the comparative base. The comparative researches are carried out among these linear and nonlinear control schemes in detail. The simulation research results show that the proposed AGMC schemes present advantages in both servo control and regulatory control for the high-purity HIASC.     

Adaptive robust boundary control of shaft vibrations under perturbations with unknown upper bounds

This paper presents robust and adaptive boundary control designs to stabilize the two‐dimensional vibration of hybrid shaft model. The hybrid shaft is mathematically represented by a set of partial differential equations, governing the shaft vibrations, coupled to ordinary differential equations, describing rigid body spinning and dynamic boundary conditions. The control objective is to stabilize the transverse vibrations of the perturbed shaft while regulating the spinning rate. To achieve this, the paper first establishes robust boundary control laws that fulfil the control objective in the presence of modeling uncertainties and external disturbances operating over the shaft domain and boundary. Lyapunov‐based analyses show that the proposed robust control exponentially stabilizes the shaft with vanishing distributive perturbations, while assuring ultimately bounded vibrations in the case of nonvanishing perturbations. Then, adaptive control philosophy is utilized to achieve redesigned robust controllers that only use online adaptation of control gains without acquiring the knowledge of bounds on perturbations, as well as dynamic parameters. An advantage of this design is avoiding an overconservative robust control law, which may induce poor stability and chattering in tackling system perturbations with unknown upper bounds. Simulations through finite element method illustrate the results. Copyright © 2014 John Wiley & Sons, Ltd.     

Leader-following consensus of fractional-order multi-agent systems via adaptive control

This article focuses on the consensus problem of leader-following fractional-order multi-agent systems (MASs) with general linear and Lipschitz nonlinear dynamics. First, the distributed adaptive protocols for linear and nonlinear fractional-order MASs are constructed, respectively. We allow the control coupling gains to be time varying for each agent. Moreover, the adaptive modification schemes for the control gain are designed, which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence. Second, based on fractional-order Lyapunov stability theorem and Barbalat's lemma, two novel sufficient conditions in terms of linear matrix inequalities are provided to ensure that the leader-following consensus can be obtained in the case for any undirected connected communication graph. Furthermore, we show that the proposed algorithm also works for consensus of agents with intrinsic Lipschitz nonlinear dynamics. As a result, the proposed framework requires no global information and thus can be implemented in a fully distributed manner. Finally, the numerical simulations are given to demonstrate the effectiveness of obtained the theoretical results.     

Simultaneous synthesis of a heat exchanger network with multiple utilities using utility substages

Heat exchanger network synthesis (HENS) has progressed by using mathematical programming-based simultaneous methodology. Although various considerations such as non-isothermal mixing and bypass streams are applied to consider real world alternatives in modeling phase, many challenges are faced because of its properties within non-convex mixed-integer nonlinear programming (MINLP). We propose a modified superstructure, which contains a utility substage for use in considering multiple utilities in a simultaneous MINLP model. To improve model size and convergence, fixed utility locations according to temperature and series connections between utilities are suggested. The numbers of constraints, discrete, and continuous variables show that overall model size decreases compared with previous research. Thus, it is possible to expand the feasible search area for reaching the nearest global solution. The model's effectiveness and applications are exemplified by several literature problems, where it is used to deduce a network superior to that of any other reported methodology.     

Adaptive actuator failure compensation design for unknown chaotic multi‐input systems

In this paper, an adaptive control approach is designed for compensating the faults in the actuators of chaotic systems and maintaining the acceptable system stability. We propose a state‐feedback model reference adaptive control scheme for unknown chaotic multi‐input systems. Only the dimensions of the chaotic systems are required to be known. Based on Lyapunov stability theory, new adaptive control laws are synthesized to accommodate actuator failures and system nonlinearities. An illustrative example is studied. The simulation results show the effectiveness of the design method. Copyright © 2014 John Wiley & Sons, Ltd.     

A stiffness parameter and truncation error criterion for adaptive path following in structural mechanics

We explore a truncation error criterion to steer adaptive step length refinement and coarsening in incremental-iterative path following procedures, applied to problems in large-deformation structural mechanics. Elaborating on ideas proposed by Bergan and collaborators in the 1970s, we first describe an easily computable scalar stiffness parameter whose sign and rate of change provide reliable information on the local behavior and complexity of the equilibrium path. We then derive a simple scaling law that adaptively adjusts the length of the next step based on the rate of change of the stiffness parameter at previous points on the path. We show that this scaling is equivalent to keeping a local truncation error constant in each step. We demonstrate with numerical examples that our adaptive method follows a path with a significantly reduced number of points compared to an analysis with uniform step length of the same fidelity level. A comparison with Abaqus illustrates that the truncation error criterion effectively concentrates points around the smallest-scale features of the path, which is generally not possible with automatic incrementation solely based on local convergence properties.     

A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

The effectiveness of adaptive versus non-adaptive learning with digital educational games

For the training of academic skills, digital educational games with integrated adaptivity are promising. Adaptive games are considered superior to non-adaptive games, because they constantly assess children's performance, and accordingly adapt the difficulty of the tasks corresponding to the children's individual level. However, empirical evidence with regard to the effectivity of adaptive compared to non-adaptive games is limited. A study was conducted with 191 children from the third year of Kinder garten who were enrolled in one of three conditions, that is, playing an adaptive version of the reading game (RG), a non-adaptive version of the RG or training with pen-and-paper exercises. In all three conditions, children trained emergent reading (phonological awareness and letter knowledge) once a week for 30 min over a period of 5 weeks. Children's performance on cognitive (phonological awareness, letter knowledge, reading fluency) and non-cognitive (motivation, self-concept) factors was assessed. Results revealed a significant improvement in phonological awareness and letter knowledge in all conditions. However, no differences between the conditions were observed with respect to children's improvement on phonological awareness and letter knowledge or on their post-test scores for reading fluency. With regard to motivation and self-concept, again, no differences in these non-cognitive factors were observed across conditions.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.