Jump modes analysis and observer design for discrete singular systems

This paper is concerned with the reconstructability and detectability of the jump modes of discrete singular systems. The notion of jump modes can be considered as the discrete counterpart of the impulsive modes of continuous singular systems which has been extensively studied. The effect of jump modes on the existence of reduced order normal Luenberger observers for discrete singular systems is investigated. Necessary and sufficient conditions for the existence of normal Luenberger observers and the corresponding observer design procedure are obtained.     

Stabilization of linear systems in the presence of output measurement saturation

This note considers siso nonlinear systems, which have a linear controllable and observable part followed by a measurement saturation nonlinearity. A controller is presented, which feeds back only the saturating output measurements and nevertheless globally asymptotically stabilizes the system. The equilibrium is actually reached in finite time, i.e. the controller is dead beat.     

On the preservation of observability under sampling

In this paper, we investigate the problem of the preservation of observability under sampling.     

An observation algorithm for nonlinear systems with unknown inputs

This paper deals with the design of unknown input observers for nonlinear systems. An algorithm which determines if the state and the unknown input of the system can be recovered in finite time is introduced. This algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers. The proposed method is useful to relax some restrictive conditions of the existing nonlinear unknown input observer design procedures.     

Identification of block-oriented nonlinear systems using orthonormal bases

In this paper, new noniterative algorithms for the identification of (multivariable) block-oriented nonlinear models consisting of the interconnection of linear time invariant systems and static nonlinearities are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. Two different block-oriented nonlinear models are considered in this paper, viz., the Hammerstein model, and the Wiener model. For the Hammerstein model, the proposed algorithm provides consistent estimates even in the presence of colored output noise, under weak assumptions on the persistency of excitation of the inputs. For the Wiener model, consistency of the estimates can only be guaranteed in the noise free case. Key in the derivation of the results is the use of basis functions for the representation of the linear and nonlinear parts of the models. The performance of the proposed identification algorithms is illustrated through simulation examples of two benchmark problems drawn from the process control literature, viz., a binary distillation column and a pH neutralization process.     

Remarks on nonlinear adaptive observer design

A solution to the problem of state estimation for systems with unknown parameters is to use some on-line adaptation of the observer parameters. On the basis of various existing results for such adaptive observer designs, a unifying “adaptive observer form” is proposed in this paper. This form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters, as well as additional properties which further allow parameter estimation. As an example, it is shown how an adaptive observer can be designed for a class of state affine systems.     

Local controllability of nonlinear systems

The local controllability of control systems with an arbitrary number of controls is considered, first on an open set and then at a given point; necessary conditions are derived concerning the Lie algebra T′ generated by the input vector fields, and applied to gradient systems.The main results are a geometric sufficient condition for local controllability at a point, and an equivalent condition based on the computation of Lie brackets, assuming T′ to be (n − 1)-dimensional.     

Global observability of a class of nonlinear discrete time systems

It is shown that discrete time systems whose dynamics are governed by piecewise monotone maps of the interval are globally observable under a general class of observations. The results rest on the fact that the dynamics are ergodic.     

Stability properties of a class of sampled regulators with sector bounded nonlinear systems

Recently proposed methods for the design of sampled regulators for unknown linear time invariant systems are considered. It is shown that the regulators satisfy sufficient conditions which guarantee stability when the linear plant is in series with a sector bounded nonlinear, and possibly time varying, element. Furthermore, a simple modification to the methods proposed permits the design of regulators to guarantee closed loop stability when the nonlinear characteristic is in the sector (ε, M) for arbitrarily small ε > 0 and any M > 0.     

A constructive speed observer design for general Euler–Lagrange systems

Astolfi, Ortega, and Venkatraman (2010) recently proved the existence of a globally exponentially convergent speed observer for general Euler–Lagrange systems. Key to their result, is a function defined by certain integrals which cannot be solved a priori, and may not have explicit analytic solutions. In this paper, this obstacle to a constructive design is removed and equations that solve the speed observer problem are given in closed form. The design is further simplified by removing up to one third of the observer states used in Astolfi et al. (2010). With the significant reduction in complexity, the new observer is easily applied to estimate the angular velocities in a Furuta pendulum example.     

Functional integration in CAD systems

This paper examines the issue of integration in CAD systems and argues that for integration to be effective, it must address the functional aspects of a CAD system. It discusses the need for integrated systems and, within a structural engineering context, identifies several facets of integration that should be targeted. These include 2-D drafting and 3-D modelling, graphical and nongraphical design information, the CAD data structure and its user interface, as well as integration of the drafting function with other engineering applications. Means of achieving these levels of integration are briefly discussed and a prognosis for the future development of integrated systems explored. Particular attention is paid to the emergence (and potential role) of ‘product models’ which seek to encapsulate the full range of data elements required to define completely an engineering artefact.     

On spectral controllability of multi-input time-delay systems

It is proved that under certain verifiable conditions, spectral controllability of a linear system with commensurate state delays and with m inputs, m > 1, implies the existence of an n × 1 vector b contained in the image of the control matrix B such that the system with B replaced by b is spectrally controllable. Both the necessity and the sufficiency of these conditions are shown, a procedure to construct b is given, and an example is discussed.     

Local and global controllability for nonlinear systems

A technique to study local and global controllability properties for a wide class of nonlinear systems is presented. In addition to an extensive study of systems on ² we propose — as an application of our method — a new criterion for global controllability of systems with polynomial drift term, defined on ⁿ. In the case of linear systems, the criterion reduces to the classical Kalman condition.A study of local controllability at the equilibrium point of the drift term of systems defined on ² enables us not only to rederive a local controllability result derived by Hermes [4,5], but also to extend this result when no assumptions are made on the boundedness of the controls.     

Terminal sliding mode observers for a class of nonlinear systems

This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer.     

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.     

State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.     

On the stabilization of controllable and observable systems by an output feedback law

For control systems which can be locally stabilized in small time by means of a dynamic periodic time-varyingstate feedback law, we give a sufficient condition on Lie derivatives of the output for local stabilization in small time by means of a dynamic periodic time-varyingoutput feedback law. If the system is analytic our sufficient condition is also necessary.     

Data structures and DBMS for computer-aided design systems

The structures for the storage of data in CAD systems influence to a large extent the effectiveness of the system. This paper reviews the wide range of data structures and database management systems (DBMS) available for structuring CAD data. Examples of basic data types are drawn from the MODULA-2 language. The relationship between these basic data types, their composite structures and the classical data models (on which many DBMS are based) is discussed, and the limitations of existing DBMS in modelling CAD data highlighted. A set of requirements for CAD database management systems is drawn up and the emerging role of product models (which seek to encapsulate the totality of data elements required to define fully an engineering artefact) is explored.     

Global controllability of linear autonomous systems: A geometric consideration

The global controllability in finite time of a linear autonomous system with restrained controls is investigated. Necessary and sufficient conditions are obtained by an approach based on the consideration of geometric properties of the system.