Speed‐up and performance evaluation of piecewise‐linear DC analysis

The good convergence properties of piecewise‐linear (PWL) DC analysis have been thoroughly discussed in many papers. This paper, in turn, concentrates on the speed of PWL DC analysis, where the boundary crossing of linear regions plays a crucial role. Fast methods are presented for performing the following boundary‐crossing computations: LU‐decomposition update, matrix‐equation solution, boundary‐crossing direction, and damping‐factor determination. Special attention is given to those PWL DC analysis methods that perform PWL modelling of the non‐linear components on the fly; an adaptive method is proposed for controlling the accuracy of PWL modelling and speeding up simulation. The computational efficiency of the accelerated PWL DC analysis is discussed and compared with that of conventional, Newton–Raphson iteration‐based, DC analysis. Finally, the performance evaluation is completed with realistic simulation examples: it is demonstrated that the speed of the accelerated PWL DC analysis is comparable with that of the conventional DC analysis. Copyright © 2006 John Wiley & Sons, Ltd.     

A novel empirical study of the two‐dimensional non‐linear drain‐current behaviour in sub‐micrometre MOS transistors

This paper presents a simple, quasi‐static, non‐linear (saturated mode) NMOS drain‐current model for Volterra‐series analysis. The model is based on a linear transconductance, a linear drain‐source conductance and a purely non‐linear drain‐source current generator. The drain‐current dependency on both drain‐source and gate‐source voltages is included. Model parameters are then extracted from direct numerical differentiation of DC I/V measurements performed on a 160 × 0.25 µm NMOS device. This paper presents the Volterra analysis of this model, including algebraic expressions for intercept points and output spectrum. The model has been verified by comparing measured two‐tone iIP₂ and iIP₃ with the corresponding model predictions over a wide range of bias points. The correspondence between the modelled and measured response is good. Copyright © 2005 John Wiley & Sons, Ltd.     

A combined approach for the identification of continuous non‐linear systems

The identification of a non‐linear continuous output‐only system from a time series is considered for the case that the functional form of the model is not known beforehand. To estimate both functions and parameters, a combination of non‐parametric modelling based on non‐linear regression and parametric modelling based on a multiple shooting algorithm is proposed. This strategy to determine non‐linear differential equations is exemplified on experimental data from a chaotic circuit where an accurate reconstruction of the observed attractor is obtained. Copyright © 2003 John Wiley & Sons, Ltd.     

An efficient piecewise‐linear DC analysis method for general non‐linear circuits

The convergence problems of conventional DC analysis can be partly avoided by using piecewise‐linear analysis. This paper proposes a piecewise‐linear DC analysis method that can efficiently handle arbitrary couplings between non‐linear circuit elements. Piecewise‐linear modelling of the non‐linear circuit elements is automatically performed during simulation, using simplicial subdivisions. The number of linear regions, and thereby iterations, is considerably reduced by combining the common parts of separate simplicial subdivisions. Due to these reasons and since the method is formulated with the commonly used modified nodal approach, it has been possible to implement the method in the general‐purpose circuit simulator APLAC. The correct operation of the method is demonstrated with three examples. Copyright © 1999 John Wiley & Sons, Ltd.     

A measurement‐based approach with accuracy evaluation and its applications to circuit analysis and synthesis

In this paper, we evaluate a useful general model for linear direct current (DC) networks, containing design parameters, multiple inputs and outputs. The outputs are rational multivariate functions of the parameters and linear functions of the inputs. For an unknown linear system, the unknown coefficients of these functions can be determined by taking a suitable number of measurements and solving a set of linear equations constructed from selected measurement data. The rational functions are useful to support the design such that outputs can be constrained to a desired interval. An interesting result was the particular case where the parameter varied is located at the output terminal. This is an alternative way to estimate the Thévenin equivalent of a circuit. Real data are in general noisy with accuracy dependent on the tolerance of components and on the measurement device used. We present a detailed analysis of the application of the measurement‐based approach under real experiments. Initially, a resistive DC circuit case is presented, and the results are verified by simulation and experimental laboratory data. Finally, practical circuits, such as a conditioning signal stage with an operational amplifier, and a boost DC–DC converter are considered. Copyright © 2017 John Wiley & Sons, Ltd.     

Global adaptive output feedback controllers with application to non‐linear friction compensation

In this paper, we consider a class of non‐linear systems in which a set of constant parameters is unknown and some state variables are not available for measurement. For such systems we provide a constructive procedure for the solution of the global adaptive tracking problem with dynamic partial state feedback. We illustrate an application of the control strategy to the adaptive non‐linear friction compensation of a DC motor servomechanism. We improve previous results in tow directions: we allow for a subset of the unmeasurable states to enter in a system non‐linearly; we consider systems which are linearly parametrized with respect to a set of unknown constant parameters. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive output tracking for a class of non‐linear time‐delay systems

In this paper the output tracking control problem for a class of non‐linear time delay systems with some unknown constant parameters is addressed. Such a problem is solved in the case that the non‐linear time‐delay system has full delay relative degree and stable internal dynamics. It is supposed moreover that the output and its time derivatives until n?1, where n is the length of the state vector (euclidean part), do not depend explicitly on the unknown parameters. This work is the first step towards the application of the methodologies of adaptive control for non‐linear delayless systems, based on tools of differential geometry, to non‐linear time‐delay systems too. Copyright © 2004 John Wiley & Sons, Ltd.     

Self‐adjoint S‐parameter sensitivities for lossless homogeneous TLM problems

We present a novel efficient algorithm for the estimation of S‐parameter sensitivities in homogeneous and lossless transmission line modelling (TLM) problems. Our approach estimates S‐parameter adjoint‐based sensitivities without actually carrying out any adjoint simulation. By applying a transformation to the original TLM simulation we establish an isomorphism between the original and the adjoint problem. The unique properties of the TLM node in a lossless and homogeneous problem are also exploited in establishing the isomorphism. For an electromagnetic structure with N_p ports, only the N_p original simulations utilized in evaluating the S‐parameters are required to estimate their sensitivities as well. Our novel approach is illustrated through estimating S‐parameter sensitivities with respect to waveguide discontinuities. Good match is obtained between our sensitivity estimates and those calculated using finite differences at the response level. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficient estimation of adjoint‐variable S‐parameter sensitivities with time domain TLM

We present a novel algorithm for efficient estimation of S‐parameter sensitivities with the time‐domain transmission line modelling (TLM) method. The original electromagnetic structure is simulated using TLM to obtain the S‐parameters in the desired frequency band. For each port, an adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the S‐parameters in the desired frequency band are estimated using only the original and adjoint simulations. For a structure with N_p ports and n designable parameters, our approach requires only N_p additional simulations regardless of n. This can be easily contrasted with the 2nN_p additional simulations required by the central difference approximation. Our algorithm is illustrated through the estimation of S‐parameter sensitivities with respect to the dimensions of waveguide discontinuities. Very good match is obtained between our sensitivity estimates and those obtained using central difference approximation. Copyright © 2005 John Wiley & Sons, Ltd.     

On the transposition of Gm–C filters to DC stabilized log‐domain filters

High‐order log‐domain filters could be designed by transposing the already known linear‐domain G_m–C filter topologies to the corresponding topologies in the log‐domain. This is achieved by using a non‐linear transconductor configuration, where the output current is exponentially related to its input and output voltages. A drawback of the non‐linear transconductor configuration already introduced in the literature is that a number of the transposed log‐domain filter topologies suffer from DC instability, while in some others a DC offset current appears at their output. In order to eliminate the aforementioned problems a modified non‐linear transconductor configuration for transposing G_m–C filter topologies to log‐domain filter topologies is introduced in this paper. The achieved improvements are demonstrated through a number of log‐domain filter configurations derived using the already introduced and the proposed transposition schemes. Copyright © 2006 John Wiley & Sons, Ltd.     

Convergence analysis of the RLS identification algorithm with exponential forgetting in stationary ARX‐structures

The recursive least‐squares (RLS) identification algorithm is often extended with exponential forgetting as a tool for parameter estimation in time‐varying stochastic systems. The statistical properties of the parameter estimates obtained from such an extended RLS‐algorithm depend in a non‐linear way on the time‐varying characteristics and on the forgetting factor. In this paper, the RLS‐estimator with exponential forgetting is applied to time‐invariant Gaussian autoregressions with second‐order stationary external inputs, i.e.to Gaussian ARX‐processes. Approximate expressions for the asymptotic bias and covariance of the parameter estimates when the forgetting factor tends to one and time to infinity are given, showing that the bias is non‐zero and that the covariance function decays exponentially with a rate that is given by the forgetting factor. The orders of magnitude of the errors in the asymptotic expressions are also derived. Copyright © 1999 John Wiley & Sons, Ltd.     

MIMO multi‐periodic repetitive control system: universal adaptive control schemes

This paper presents a simple adaptive multi‐periodic repetitive control scheme when the MIMO LTI plant is not necessarily positive real (PR), however it is strictly minimum‐phase, the spectrum of high‐frequency gain matrix CB is symmetric and lies in the open right/left half complex plane(sign/spectrum definite). The non‐identifier‐based direct adaptive control technique, which does not need plant parameter information, is used to construct adaptive schemes and the system stability is analysed by Lyapunov second method. The extension to plant under certain non‐linear perturbations and an exponential stability scheme are also discussed. Finally, an adaptive proportional plus multi‐periodic repetitive control scheme is proposed. The theoretical findings are supported with simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

A new model reference adaptive control for linear time‐varying systems

Recent results on the adaptive control of linear time‐varying systems have considered mostly the case in which the range or rate of parameter variations is small. In this paper, a new state feed‐back model reference adaptive control is developed for systems with bounded arbitrary parameter variations. The important feature of the proposed adaptive control is an uncertainty estimation algorithm, which guarantees almost zero tracking error. Note that the conventional parameter estimation algorithm in the adaptive control guarantees only bounded tracking error. Copyright © 2000 John Wiley & Sons, Ltd.     

An efficient algorithm for finding all DC solutions of piecewise‐linear circuits

An efficient algorithm is proposed for finding all DC solutions of transistor circuits where characteristics of transistors are represented by piecewise‐linear (PWL) convex monotone functions. This algorithm is based on a simple test (termed the linear programming, LP, test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem by surrounding component PWL functions by rectangles. Then the dual simplex method is applied, by which the number of pivotings per region becomes very small. In this letter, we propose a new LP test using the dual simplex method and triangles. The proposed test is not only efficient but also more powerful than the conventional test using the simplex method or rectangles. Copyright © 2008 John Wiley & Sons, Ltd.     

An indirect adaptive pole‐placement control for MIMO discrete‐time stochastic systems

In this paper, an indirect adaptive pole‐placement control scheme for multi‐input multi‐output (MIMO) discrete‐time stochastic systems is developed. This control scheme combines a recursive least squares (RLS) estimation algorithm with pole‐placement control design to produce a control law with self‐tuning capability. A parametric model with a priori prediction outputs is adopted for modelling the controlled system. Then, a RLS estimation algorithm which applies the a posteriori prediction errors is employed to identify the parameters of the model. It is shown that the implementation of the estimation algorithm including a time‐varying inverse logarithm step size mechanism has an almost sure convergence. Further, an equivalent stochastic closed‐loop system is used here for constructing near supermartingales, allowing that the proposed control scheme facilitates the establishment of the adaptive pole‐placement control and prevents the closed‐loop control system from occurring unstable pole‐zero cancellation. An analysis is provided that this control scheme guarantees parameter estimation convergence and system stability in the mean squares sense almost surely. Simulation studies are also presented to validate the theoretical findings. Copyright © 2005 John Wiley & Sons, Ltd.     

Direct adaptive control for non‐linear uncertain systems with exogenous disturbances

A direct adaptive non‐linear control framework for multivariable non‐linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non‐linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov‐based and guarantees partial asymptotic stability of the closed‐loop system; that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant. In the case of bounded energy L₂ disturbances the proposed approach guarantees a non‐expansivity constraint on the closed‐loop input–output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Finite‐model adaptive control using an LS‐like algorithm

Adaptive control problem of a class of discrete‐time nonlinear uncertain systems, of which the internal uncertainty can be characterized by a finite set of functions, is formulated and studied by using an least squares (LS)‐like algorithm to design the feedback control law. For the finite‐model adaptive control problem, this algorithm is proposed as an extension of counterpart of traditional LS algorithm. Stability in sense of pth mean for the closed‐loop system is proved under a so‐called linear growth assumption, which is shown to be necessary in general by a counter‐example constructed in this paper. The main results have been also applied to parametric cases, which demonstrate how to bridge the non‐parametric case and parametric case. Copyright © 2006 John Wiley & Sons, Ltd.     

Piecewise linear second moment statistical simulation of ICs affected by non‐linear statistical effects

This paper presents a methodology for statistical simulation of non‐linear integrated circuits affected by device mismatch. This simulation technique is aimed at helping designers maximize yield, since it can be orders of magnitude faster than other readily available methods, e.g. Monte Carlo. Statistical analysis is performed by modeling the electrical effects of tolerances by means of stochastic current or voltage sources, which depend on both device geometry and position across the die. They alter the behavior of both linear and non‐linear components according to stochastic device models, which reflect the statistical properties of circuit devices up to the second order (i.e. covariance functions). DC, AC, and transient analyses are performed by means of the stochastic modified nodal analysis, using a piecewise linear stochastic technique with respect to the stochastic sources, around a few automatically selected points. Several experimental results on significant circuits, encompassing both the analog and the digital domains, prove the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

In this paper, we are interested in the problem of adaptive control of non‐linearly parametrized systems. We investigate the viability of defining a stabilizing parameter update law for the case when the plant model is convex on the uncertain parameters. We show that, when the only prior knowledge is convexity, there does not exist an adaptation law—derivable from the standard separable Lyapunov function technique of Parks—applicable for all the state space. Therefore, we propose a semi‐adaptive state feedback controller where adaptation takes place only in the region of the state space where convexity can be used to reduce parameter uncertainty. In the remaining part of the state space we freeze the adaptation and switch to a robust controller. This scheme ensures semi‐global stability for convexly parametrized non‐linear systems with matched uncertainty. The proposed controller is then applied to the problem of temperature regulation of continuous stirred exothermic chemical reactors where reaction heat is convex in the uncertain parameters. Copyright © 2001 John Wiley & Sons, Ltd.