Single-input Single-output Linear Systems Research Articles

An effective controller design strategy for higher order systems

The recent methods that guarantee the stability of the reduced-order models are Mihailov stability, improved Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization. Further, these methods could overcome the limitations such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. This research emphasizes the design of the proposed compensating algorithm by using an additional open loop zero for the stable reduced-order models of large-scale single-input single-output linear time-invariant continuous time systems. The results of the proposed algorithm are compared with the existing compensating methods and the design is validated and illustrated numerically.

Prescribed-Time Tracking Control of MIMO Nonlinear Systems With Nonvanishing Uncertainties

It is highly desirable yet challenging to achieve zero-error tracking within a given short time period for uncertain multi-input multi-output (MIMO) nonlinear systems. Previous results are primarily state-regulation oriented and are valid only for single-input single-output (SISO) linear systems or nonlinear systems in normal-form. This note presents a tracking control solution for high-order MIMO nonlinear systems in strict-feedback-like form. The proposed control is able to achieve precise tracking within the prescribed time irrespective of initial conditions in the presence of mismatched uncertainties and non-vanishing disturbances.

Inferring Power System Dynamics From Synchrophasor Data Using Gaussian Processes

Synchrophasor data provide unprecedented opportunities for inferring power system dynamics, such as estimating voltage angles, frequencies, and accelerations along with power injection at all buses. Aligned to this goal, this work puts forth a novel framework for learning dynamics after small-signal disturbances by leveraging Gaussian processes (GPs). We extend results on learning of a linear time-invariant system using GPs to the multi-input multi-output setup. This is accomplished by decomposing power system dynamics into a set of single-input single-output linear systems with narrow frequency pass bands. The proposed learning technique captures time derivatives in continuous time, accommodates data streams sampled at different rates, and can cope with missing data and heterogeneous levels of accuracy. While Kalman filter-based approaches require knowing all system inputs, the proposed framework handles readings of system inputs, outputs, their derivatives, and combinations thereof collected from an arbitrary subset of buses. Relying on minimal system information, it further provides uncertainty quantification in addition to point estimates of system dynamics. Numerical tests verify that this technique can infer dynamics at non-metered buses, impute and predict synchrophasors, and locate faults under linear and non-linear system models under ambient and fault disturbances.

On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays

The property of external positivity of dynamic systems is commonly defined as the non-negativity of the output for all time under zero initial conditions and any given non-negative input for all time. This paper investigates the extension of that property for a structured class of initial conditions of a single-input single-output (SISO) linear dynamic system which can include, in general, certain negative initial conditions. The above class of initial conditions is characterized analytically based on the structure of the transfer function. The basic study is performed in the delay-free case, but extensions are then given for systems subject to a finite number of internal and external, in general incommensurate, point delays and for the closed-loop dynamic systems which incorporate a feedback compensator. The formulation relies on calculating the output based on the impulse responses by considering the relation of the mentioned sets of structured initial conditions with the zero-state response which allows to keep the non-negativity of the zero-input response and that of the total response provided the non-negativity for all time of the zero-state response.

Position Control Based on Add-on-Type Iterative Learning Control with Nonlinear Controller for Permanent-Magnet Stepper Motors

In this paper, a current-error-based iterative learning controller (ILC) with a nonlinear controller is proposed to improve the position-tracking performance in permanent-magnet (PM) stepper motors. Our proposed method comprises a current-error-based ILC for mechanical dynamics and a nonlinear controller for current dynamics. A nonlinear controller using a variable structure is designed to obtain the field-oriented control. This nonlinear controller can cause the PM stepper motor become a single-input single-output linear system after finite time. The add-on-type ILC with proportional–integral control is designed to improve the position-tracking performance as the systems repeatedly perform the same operation. To increase the rate of error convergence, the current-error-based ILC is designed using the plant inversion method. The condition that the error converges to zero is mathematically derived. Thus, the proposed method can reduce the position-tracking error as the systems repeatedly perform the same operation. Furthermore, the proposed method can be easily plugged into the pre-designed controller. The performance of our proposed method was evaluated via simulations. In simulations, it is observed that the proposed method reduces the position-tracking error compared to the previous methods.

Frequency-Domain Data-Driven Controller Synthesis for Unstable LPV Systems

Abstract Synthesizing controllers directly from frequency-domain measurement data is a powerful tool in the linear time-invariant framework. Ever-increasing performance requirements necessitate extending these approaches to account for plant variations. The aim of this paper is to develop frequency-domain analysis and synthesis conditions for local internal stability and H∞-performance of single-input single-output linear parameter-varying systems. The developed synthesis procedure only requires frequency-domain measurement data of the system and does not need a parametric model of the plant. The capabilities of the synthesis procedure are demonstrated on an unstable nonlinear system.

AFD-based ILC designs in frequency domain for linear discrete-time systems

The existing frequency-domain-based iterative learning control (ILC) methods are highly dependent on the mathematical models of the controlled systems. For linear discrete-time single-input single-output (SISO) systems with unknown mathematical models, this paper tries to present fully data-driven ILC designs in frequency domain. With the help of support vector machine (SVM), the input-output data of the linear discrete-time SISO system at the first repetition is utilised to constitute an adaptive Fourier decomposition (AFD) model. Then, based on the AFD model, a P-type ILC law and an extended D-type ILC law with data-driven determining techniques for learning gains are presented. It is noted that comparing with the conventional D-type ILC law, the newly proposed extended D-type ILC law exhibits superior tracking characteristic due to involving the frequency information during the ILC process. A numerical example is utilised to illustrate the effectiveness of the proposed ILC algorithms with the data-driven determining techniques for learning gains.

Discrete‐time adaptive control of uncertain sampled‐data systems with uncertain input delay: a reduction

This study proposes a discrete-time adaptive control approach for uncertain single-input single-output linear time-invariant sampled-data systems with uncertain, constant input time delay that has a known upper-bound, without explicitly estimating the time delay. To cope with the unknown time delay, a reduction approach similar to that proposed by Artstein in 1982 is used, which results in a delay-free system that simplifies the control law design. In addition, the proposed control approach is capable of coping with bounded exogenous disturbances. A rigorous stability analysis shows that the proposed control approach drives the system output to a bound around the reference signal asymptotically, in the presence of an exogenous disturbance. Moreover, simulation results are shown to verify the approach.

Reduced-order controllers for multi-agent consensus using output regulation viewpoint

Design of reduced-order distributed controllers for solving the output feedback state consensus problem in a homogeneous multi-agent network is the topic of this paper. The dynamics of each agent in this network is governed by a marginally unstable single-input single-output linear system and each agent can access the relative output of its neighboring agents. Recognizing, possibly for the first time, the similarities between the feedback structures appearing in a well-known low-gain controller design approach for solving the consensus problem and the low-gain approach to the output regulation of stable linear plants, we propose a novel controller design technique for solving the consensus problem. Our technique is frequency-domain based, unlike most of the techniques in the literature which are state–space based. Combining our technique with a recent result on the existence of stable pth-order transfer functions with a desired phase at p given frequencies, we design controllers whose order is significantly lower than the order of the controllers proposed in the consensus literature. The techniques developed in this work can be applied equally to design reduced-order controllers for solving the aforementioned consensus problem in the presence of known, uniform and arbitrarily large communication and input delays in the network.

Recursive Identification of Errors-in-Variables Systems Based on the Correlation Analysis

This paper considers a single-input single-output linear dynamic system, whose input and output are corrupted by Gaussian white measurement noises with zero means and unknown variances; the parameter estimation of such a system is a typical errors-in-variables (EIV) system identification problem. This paper proposes the correlation function-based two-step identification methods for the EIV systems. In order to obtain the unbiased parameter estimates of the EIV system, we derive the correlation function equation by using the correlation analysis method and adopt the least squares method and the instrumental variable method to recursively compute the parameter estimates of the model, resulting in the unbiased parameter estimates of the EIV systems. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

Performance limitations for discrete-time systems in the presence of multi-sinusoidal disturbance

Performance limitations for single-input single-output (SISO) linear discrete-time systems perturbed by multi-sinusoidal disturbance with additive Gaussian white noise are considered. A steady-state variance of the residual error input of the plant is used to measure the performance. Under the assumption that the disturbance frequency and plant model are known, the performance limitations are derived. Such limitations independent of the constant disturbance are then extended to the case of biased multi-sinusoidal disturbance.

An Identification Method for Single-Input Single-Output Linear Systems with Colored Output Noise Using Eigenvector Method

An Identification Method for Single-Input Single-Output Linear Systems with Colored Output Noise Using Eigenvector Method

On strongly unimodal third-order SISO linear systems with applications to pharmacokinetics

This paper addresses the problem of characterizing external positivity (equivalently, non-negative impulse response) of third-order single-input, single-output (SISO) linear systems. We show how an exact, geometric solution to this problem follows by first identifying an equivalence between the impulse response of an externally positive system on the one hand, and the probability density function of a non-negative random variable on the other, then drawing on the characterization of matrix exponential distributions, defined as probability distributions for which the Laplace transform is a rational function. The results are then extended to the characterization of strongly unimodal systems, defined as systems in which input signals with a time-derivative that has at most one sign variation (namely, are pulse-like) are mapped to output signals with the same property. The results are applied to a third-order compartmental system arising in pharmacokinetics, in which the properties of non-negativity of the impulse response and the preservation of unimodality from drug adminstration (input) to compartmental drug concentration (output) are of clinical relevance.

Removing SPR-Like Conditions in Adaptive Feedforward Control of Uncertain Systems

This paper considers the problem of designing adaptive feedforward control (AFC) systems for uncertain single-input single-output linear systems perturbed by multisinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation is known for AFC to be applicable, which is referred to in this paper as a strictly positive real (SPR)-like condition. Notable features of the solution are that persistence of excitation is not required, and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented.

Geometrical design of fractional PDμ controllers for linear time-invariant fractional-order systems with time delay

This article presents a simple procedure that allows a practical design of fractional –[Formula: see text] controllers for single-input single-output linear time-invariant fractional-order systems subject to a constant time delay. The methodology is based on a geometric approach, which provides practical guidelines to design stabilizing and non-fragile PDμ controllers. The simplicity of the proposed approach is illustrated by considering several numerical examples encountered in the control literature. Moreover, with the aim of showing the performance of the PDμ over a classical PD controller, both controllers were implemented at the end of the article in an experimental test-bench consisting a teleoperated robotic system.

An Identification Method for Single-Input Single-Output Linear Systems with White Noise Gain Function

An Identification Method for Single-Input Single-Output Linear Systems with White Noise Gain Function

A Multiple-Input Multiple-Output Cepstrum

This letter extends the concept of scalar cepstrum coefficients from single-input single-output linear time invariant dynamical systems to multiple-input multiple-output (MIMO) models, making use of the Smith–McMillan form of the transfer function. These coefficients are interpreted in terms of poles and transmission zeros of the underlying dynamical system. We present a method to compute the MIMO cepstrum based on input/output signal data for systems with square transfer function matrices (i.e., systems with as many inputs as outputs). This allows us to do a model-free analysis. Two examples to illustrate these results are included: a simple MIMO system with three inputs and three outputs, of which the poles and zeros are known exactly, that allows us to directly verify the equivalences derived in this letter, and a case study on realistic data. This case study analysis data coming from a (model of) a non-isothermal continuous stirred tank reactor, which experiences linear fouling. We analyze normal and faulty operating behavior, both with and without a controller present. We show that the cepstrum detects faulty behavior, even when hidden by controller compensation. The code for the numerical analysis is available online.

Robust PID Controller Design for Both Delay-Free and Time-Delay Systems

Robust PID controller design methods are proposed for linear single-input single-output systems. Non-parametric models represented by a finite number of frequency responses are used for them. Sufficient conditions for closed-loop stability are derived based on the Nyquist stability criterion and the sufficient conditions are reduced to convex constraints. Together with the convex constraints and closed-loop model matching problems the robust PID controller design problems are formulated as convex optimization problems. A important feature of the proposed design methods is that they can be applied to delay-free and time-delay systems in the same manner. Moreover, the proposed methods are extended to two-degree-of-freedom PID controller design methods.

Data-Driven Impulse Response Regularization via Deep Learning

We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical finite-dimensional model structures. Inspired by this development and the success of deep learning we propose a new flexible data-driven model. Our experiments indicate that the new model is capable of exploiting even more of the hidden patterns that are present in the input-output data as compared to the non-parametric models.

On model order priors for Bayesian identification of SISO linear systems

ABSTRACTA method for the identification of single input single output linear systems is presented. The method employs a Bayesian approach to compute the posterior distribution of the model parameters given the data-set. Since this distribution is often unavailable in closed form, a Metropolis Hastings algorithm is implemented to draw samples from it. To implement the sampler, the inclusion of prior information regarding the model order of the identified system is discussed. As one of the main contributions of this work, a prior over the Hankel singular values of the model is imposed. Numerical examples illustrate the method.