Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.

Simultaneous state and input estimation with application to a two-link robotic system

This paper addresses the problem of estimating simultaneously the state and input of a nonlinear system with application to a two link robotic manipulator - the Pendubot. The system nonlinearity comprises a Lipschitz function with respect to the state, and a nonlinear term which is a function of both the state and input. It is shown that under some conditions, an observer can be designed to estimate simultaneously the system’s state and input. Simulation and experimental results, obtained around the inverted equilibrium position, are presented to demonstrate the validity of the approach.

Fast finite-time consensus of a class of high-order uncertain nonlinear systems

This paper poses and solves a new problem of consensus control where the task is to make the fixed-topology multi-agent network, with each agent described by an uncertain nonlinear system in chained form, to reach consensus in a fast finite time. Our development starts with a set of new sliding mode surfaces. It is proven that, on these sliding mode surfaces, consensus can be achieved if the communication graph has the proposed directed spanning tree. Next, we introduce the multi-surface sliding mode control to drive the sliding variables to the sliding mode surfaces in a fast finite time. The control Lyapunov function for fast finite time stability, motivated by the fast terminal sliding mode control, is used to prove the reachability of the sliding mode surface. A recursive design procedure is provided, which guarantees the boundedness of the control input.

Some properties of finite-time stable stochastic nonlinear systems

In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.

Nonlinear DSTATCOM controller design for distribution network with distributed generation to enhance voltage stability

This paper presents a nonlinear controller design for a DSTATCOM connected to a distribution network with distributed generation (DG) to regulate the line voltage by providing reactive power compensation.The controller is designed based on the partial feedback linearization which transforms the nonlinear system into a reduced-order linear system and an autonomous system whose dynamics are known as internal dynamics of the system. This paper also investigates the stability of internal dynamics of a DSTATCOM as it is a basic requirement to design partial feedback linearizing controllers. The performance of the proposed controller is evaluated in terms reactive power compensation to enhance the voltage stability of distribution with DG.

Swing-up and stability control of Wheeled Acrobot (WAcrobot)

In this paper the Wheeled Acrobot (WAcrobot), a novel mechanical system consisting of an underactuated double inverted pendulum robot (Acrobot) equipped with actuated wheels, is described. This underactuated and highly nonlinear system has potential applications in mobile manipulators and leg-wheeled robots. It is also a testbed for researchers studying advanced methodologies in nonlinear control. The control system for swing-up of the WAcrobot based on collocated or non-collocated feedback linearisation to linearise the active or passive Degree Of Freedom (DOF) followed by Linear Quadratic Regulator (LQR) to stabilise the robot is discussed. The effectiveness of the proposed scheme is validated with numerical simulation. The numerical results are visualised by graphical simulation to demonstrate the correlation between the numerical results and the WAcrobot physical response.

Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.

Molecular and cellular characterisation of the zinc uptake (Znu) system of Nostoc punctiforme

Metal homoeostasis in cyanobacteria is based on uptake and export systems that are controlled by their own regulators. This study characterises the zinc uptake (Znu) system in Nostoc punctiforme. The system was found to comprise of three subunits in an ACB operon: a Zn2+-binding protein (ZnuA18), a transmembrane domain (ZnuB) and an ATPase (ZnuC). These proteins are encoded within the znu operon regulated by a zinc uptake transcription repressor (Zur). Interestingly, a second Zn2+-binding protein (ZnuA08) was also identified at a distal genomic location. Interactions between components of the ZnuACB system were investigated using knockouts of the individual genes. The znuA08-, znuA18-, znuB- and znuC- mutants displayed overall reduced znuACB transcript levels, suggesting that all system components are required for normal expression of znu genes. Zinc uptake assays in the Zn2+-binding protein mutant strains showed that the disruption of znuA18 had a greater negative effect on zinc uptake than disruption of znuA08. Complementation studies in Escherichia coli indicated that both znuA08 and znuA18 were able to restore zinc uptake in a znuA- mutant, with znuA18 permitting the highest zinc uptake rate. The N. punctiforme zur was also able to complement the E. coli zur- mutant.

An observer design procedure for a class of nonlinear time-delay systems

This paper considers a class of uncertain, nonlinear differential state delayed control systems and presents a reduced-order observer design procedure to asymptotically estimate any vector state functionals. The method proposed involves decomposition of the delayed portion of the system into two parts: a matched and mismatched part. Provided that the rank of the mismatched part is less than the number of the outputs, a reduced-order linear functional observer, with any prescribed stability margin, can be constructed by using a simple procedure. A numerical example is given to illustrate the new design procedure and its features.

Nonlinear identification of pneumatic servo-drive

Three nonlinear approaches to model the nonlinear pneumatic servo- drive are presented. The three nonlinear approaches are: (1) the multi input-single output (MISO) approach, which describes the single input-single output (SISO) nonlinear plant using a MISO linear representation which allows replacement of the nonlinear analysis by a linear one without approximation, and is studied in both time and frequency domains; (2) piecewise linearization, which systematically replaces, using artificial neural network, the nonlinear surface representing the plant in the hyper input-output space by a number of linear planes that are continuous over the boundaries between them; and (3) Adaptive Neuro-Fuzzy Inference System (ANFIS), in which the fuzzy rules are placed in a neural network structure, and which consequently utilizes neural networks learning rules to systematically tune the nonlinear fuzzy model. The superiority of these nonlinear models over the best model that can be developed using linear identification techniques is shown.

A new blind signal separation algorithm for instantaneous MIMO system

We address the problem of adaptive blind source separation (BSS) from instantaneous multi-input multi-output (MIMO) channels. In this paper, we propose a new constant modulus (CM)-based algorithm which employ nonlinear function as the de-correlation term. Moreover, it is shown by theoretical analysis that the proposed algorithm has less mean square error (MSE), i.e., better separation performance, in steady state than the cross-correlation and constant modulus algorithm (CC-CMA). Numerical simulations show the effectiveness of the proposed result.

Characterisation of Ni–Ti thin films produced by filtered arc deposition

Ti–49.5 at%Ni thin films have been formed by deposition onto Si and glass substrates using a filtered arc deposition system (FADS). The films deposited on glass were composed of nanocrystalline parent phase grains contained within an amorphous matrix. The films deposited onto silicon were crystalline, and were largely parent phase whereas a bulk alloy of the same composition would be expected to be martensite. The stabilisation of the parent phase is proposed to be a grain size effect, with the critical grain size for parent phase stabilisation being about 30 nm.

Characterisation of nickel(II) extraction by 2-hydroxy-5-nonylacetophenone oxime (LIX 84) in a micellar phase

The properties of the nickel(II)/2-hydroxy-5-nonylacetophenone oxime (HNAPO), an active ingredient in LIX 84, extraction system were characterised in a micellar system. The extinction coefficient, λ_max of HNAPO (316 nm) and the Ni²⁺ complex (387 nm) in a neutral micellar system, poly dispersed octa-ethyleneglycol mono-n-dodecyl ether (G₁₂A₈) were determined as 3100 and 3500 M⁻¹ cm⁻¹, respectively. HNAPO was found to have a neutral micellar phase and bulk aqueous phase pK_a of 11.5 and 12.5, respectively. The extraction equilibrium constant, K_ex, was determined to be 10^−8.0, and the deviation from theory observed at high pH can be accounted for by consideration of the competition for nickel(II) ions by hydroxide ions and HNAPO. A micellar phase of octa-ethyleneglycol mono-n-dodecyl ether (C₁₂E₈) was determined to be an appropriate model of the free oil/water interface from the solubilised location of HNAPO. Utilising the interfacial probe, 4-heptadecyl-7-hydroxy coumarin (HHC) allowed the determination of the electrostatic surface potential of mixed micelles of G₁₂A₈ and sodium dodecyl sulphate (SDS) or dodecyl trimethyl ammonium chloride (DTAC). The electrostatic surface potential was a linear function of the number of additional surfactant monomers within the G₁₂A₈ micelle, for the concentration range studied. For G₁₂A₈/DTAC mixed micelles, the surface potential was given by +1.1 mV per DTAC molecule per micelle, and for G₁₂A₈/SDS mixed micelles the relationship was −1.4 mV per SDS molecule per micelle.