Single-input Single-output Case Research Articles

Performance analysis and precoder design for IRS-assisted MIMO system with non-linear power amplifiers

In this work, a point-to-point intelligent-reflecting-surface (IRS) assisted single input single output (SISO) model is first developed and later modified to the multiple-input multiple-output (MIMO) case. For the SISO case, the transmitter or the access point (AP) is assumed to be equipped with a non-linear memory-less power amplifier (PA). A PA is assumed to be present for each data stream at the AP or base station (BS) side for the MIMO case. For both cases, three different types of PAs (A) Soft envelope limiter (SEL), (B) Solid-state power amplifier (SSPA), and (C) Travelling wave tube amplifier (TWTA) are considered. A Bussgang decomposition of the transmitted signal is then utilized for further analysis. A modified channel model is conceived for the AP-IRS-User equipment (UE) link based on the reflecting IRS elements’ radar cross-section (RCS). For the SISO system, both perfect and imperfect geometries of IRS elements with uniformly distributed element size errors are considered. An approximate closed-form expression for the upper bound on the above system’s spectral efficiency (SE) with ideal IRS elements is derived. The expression of the SE for two special cases of (A) Infinitely large IRS and (B) Ideal PA is deduced. Approximate closed-form expressions of various quality parameters for the IRS-assisted MIMO system with ideal and non-ideal PAs are also derived and verified numerically. Maximum ratio transmission (MRT) based precoder for this system is designed assuming that the information about the BS-UE link, BS-IRS-UE link, and the non-linear PA statistics is available at the BS. A closed-form expression for the SE of this system with this precoder is then derived and verified for various parametric situations.

Control of dead-time process: From the Smith predictor to general multi-input multi-output dead-time compensators

This review paper deals with the analysis, design, and tuning of dead-time compensators for stable and unstable multi-input multi-output (MIMO) processes with multiple time delays. It is well known that, even in the single-input single-output case, processes with significant dead times are difficult to control using standard feedback controllers. For MIMO systems, the study of processes with dead time is more involved, particularly when the process behavior exhibits different dead times in the different input-output relationships. Because of this, much research has been conducted in the last 50 years on this subject, with different approaches and proposals of controllers for covering a variety of objectives. Thus, this paper gives an overview of this important topic, focusing on the solutions derived from the Smith Predictor. First, a historical perspective of the different controllers proposed in the literature is presented. Then, the general solution of the problem is developed, paying particular attention to robustness and disturbance rejection properties, because of their importance and usefulness in industrial processes. All the development is done in the discrete-time case, which allows direct digital implementation. Two simulation case studies are presented to illustrate some of the ideas discussed in the paper, and an experimental case study is used to discuss aspects of practical implementation.

On the Stopping Criteria in Nonlinear Unknown Input Observability Condition

Observability of nonlinear systems with unknown inputs was recently characterized in terms of dimension of an observability codistribution, obtained from Lie derivatives of outputs with respect to an infinite set of vector fields. However, the suggested stopping criterion does not apply to all systems, and the applicability condition is difficult to check. This article provides a new stopping criterion which holds universally and is easy to check. Moreover, we show that for systems with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> states, in the single-input single-output case the algorithm for computing observability codistribution converges in no more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3n-1$</tex-math></inline-formula> steps, while in the multi-input multi-output case addition of each independent input or output channel reduces this upper bound by one.

On the link between pole-zero distance and maximum reachable damping in MIMO systems

This paper studies the possibility of extending the already proved link between the pole-zero distance and the maximum reachable damping ratio in single input single output (SISO) systems to multiple inputs multiple outputs (MIMO) ones. This extension is shown to be possible when the considered system presents specific properties: (i) it is equipped with collocated transducers with small authority, (ii) the system has a small modal density in the frequency band of interest and (iii) a low authority control law is used. It is indeed demonstrated that when these three conditions are satisfied, the analytical development of the closed-loop poles convergence is equivalent to the one observed with SISO cases, except that the anti-resonances are replaced by the transmission zeros (TZs). Consequently, it is concluded that the maximum reachable damping ratio is directly proportional to the pole-transmission zero distance for such MIMO systems. This conclusion is demonstrated with two numerical examples (a cantilever beam and a simply supported plate) and experimentally validated on a cantilever beam where all the studied systems are equipped with two collocated pairs of piezoelectric patches.

Interlacing Properties of System-Poles, System-Zeros, and Spectral-Zeros in MIMO Systems

Single-input single-output (SISO), systems with zeros interlacing poles (ZIP) have been extensively studied in the literature and have received interest widely. However, the ZIP property for multiple-input and multiple-output (MIMO), systems has not been pursued sufficiently. In this article, we pursue the ZIP property for MIMO systems and link this to strict passivity. For the class of systems that admit a symmetric state-space realization, which for the SISO case is equivalent to ZIP, we obtain sufficient conditions under which MIMO systems too have ZIP. We also present new results in the context of “spectral-zero” of a system, a notion that plays a key role in many optimal control and estimation problems. We formulate conditions under which the spectral-zeros of a MIMO system are real, and further conditions that guarantee that the system-zeros, spectral-zeros, and the system-poles are all interlaced for MIMO systems.

Subsampling bootstrap in network DEA

Data Envelopment Analysis (DEA), provides an empirical estimation of the production frontier, based on an observed sample of decision making units (DMUs). Except for the single input-single output case, the asymptotic distribution of the DEA estimator can only be approximated through bootstrapping approaches. Therefore, bootstrapping techniques have been widely applied in the DEA literature to make statistical inference for the cases when the production process has a single-stage structure. However, in many cases, the transformation of inputs into outputs has an inner structure that needs to be considered. This paper examines the applicability of the subsampling bootstrap procedure in the approximation of the asymptotic distribution of the DEA estimator when the production process has a network structure, and in the presence of undesirable factors. Evidence on the performance of subsampling bootstrap is obtained through Monte Carlo experiments for the case of two-stage series structures, where overall and stage efficiency estimates are calculated using the additive decomposition approach. Results indicate great sensitivity both to the sample and subsample size, as well as to the data generating process. Subsampling methodology is then applied to construct confidence interval estimates for the overall and stage efficiency scores of railways in 22 European countries, where the railway transport process is decomposed into two stages and the railway noise pollution problem is considered as an undesirable output.

Optimal vibration isolation and alignment over non-rigid bases with the CRO-SL ensemble

This work proposes the design of both Single-Input–Single-Output (SISO) and Multiple-Input–Multiple-Output (MIMO) isolation controllers, when the interaction between the isolator system and the base structure is considered. The problem to be addressed is based on the reduction of the vibration of every platform, and also on the alignment between the different isolators. Both techniques, SISO and MIMO, are optimally tuned by the recently-proposed Coral Reefs Optimisation with Substrate Layers (CRO-SL), a multi-method ensemble evolutionary approach. In the proposed design, the stability of both systems (the isolators and the supporting structure) is verified. Also, the importance of considering the supporting structure dynamic is shown, by comparing the results with those obtained when the base structure is assumed to be rigid and infinitely heavy. This work shows considerable and not obvious improvements when the interaction between the isolator system and the base frame is considered. Numerical examples are included to illustrate the significant differences between using SISO and MIMO cases, and to motivate the use of CRO-SL. In addition, a real application example is analysed based on experimental data. Verified practical guidelines to be followed in experimental tests are finally shown.

Reset Control of Parallel MISO Systems

The proportional–integral plus Clegg integrator (PI + CI) controller is a hybrid extension of the proportional–integral (PI) controller that is able to overcome fundamental limitations of the linear and time-invariant control systems, potentially obtaining faster responses without increasing overshooting. This work focused on the analysis and design of PI + CI controllers and reset controllers in general, for the case of parallel multiple-input single-output (MISO) systems, extending previous design methods developed for the single-input single-output (SISO) case. Several design strategies were developed: one for first-order MISO plants achieving a flat response with a finite settling time, and for second-order MISO plants obtaining a fast response with a reduced overshoot and settling time in comparison with non-hybrid strategies. Several case studies were also developed to illustrate the potential of the proposed methods.

Vibration control of a piezoelectric cantilever smart beam by ℒ 1 adaptive control system

In this paper, the modelling and design of an state feedback control system applied for vibration control of a smart piezoelectric flexible Euler–Bernoulli cantilever beam is presented. For a Single-Input Single-Output (SISO) case by retaining the first two dominant vibratory modes, the dynamics of the system is presented. Classical adaptive control law, with time-varying parameters and in presence of disturbance, is employed to suppress the vibration of the beam. Three Piezoelectric patches, two as actuators and the other as a sensor, are bonded to the structure at the support of the beam and along the length of the beam. The beam structure is modelled in the state space form using the concept of piezoelectric theory, the Euler–Bernoulli beam theory and the Finite Element technique. Also, for comparing the performance of the proposed controller, PID and LQR control systems are applied. Simulation results, first for constant parameters and then for time-varying parameters and disturbance, represent the better performance of the proposed control system in comparison to the other mentioned controllers.

Hybrid machine learning detection for orbital angular momentum over turbulent MISO wireless channel

This work proposes a machine learning detection scheme for wireless orbital angular momentum (OAM) communication systems. The new scheme works for single-input–single-output (SISO) and multiple-input–single-output (MISO) wireless communication between the transmitter and the receiver. The transmitter encodes its data in OAM modes which are constructed using Laguerre–Gaussian beam form. The transmitted beams travel through a wireless channel with weak to medium turbulence strength and they arrive at random positions on the same receiver area. The authors proposed detection scheme allows the reception of multiple overlapping beams without prior knowledge of beams centre positions. The proposed scheme uses a novel technique of receiver segmentation and space filtering along with neural network to decode the received beams. Simulations show the detection efficiency and the enhanced performance of their proposed scheme for the SISO case and the MISO case with 2, 4, and 16 beams.

Robust output consensus of homogeneous multi-agent systems with negative imaginary dynamics

This paper addresses the robust output consensus problem for multiple homogeneous negative imaginary (NI) systems subject to L2 external disturbances and model uncertainties. The principal aim of this paper is to extend and overcome limitations in previous studies which had required restrictive assumptions to be imposed and thereby derive necessary and sufficient conditions for robust output consensus of networked NI systems when such assumptions do not hold. In doing so, the recently published robust NI stability results are utilised. An advantage of the derived conditions is that they depend on the dc and infinite frequency gains of the systems as well as the network graph but not on the precise dynamics of the systems. Furthermore, it is shown that the derived conditions specialise to the earlier results in literature either by imposing the same assumptions or by imposing different ones which had not been known previously. It is also shown that the derived conditions simplify in the single-input single-output case and an intuition about these results is provided. Finally, examples are given which demonstrate the effectiveness of the proposed results over earlier results when earlier assumptions are not met.

An optimal instrumental variable approach for continuous-time multiple input-single output fractional model identification

Abstract This paper proposes an instrumental variable approach for continuous-time system identification using fractional models with multiple input single output context. This work is an extension of the simplified refined instrumental variable approach (srivcf ) developed for single input-single output fractional model identification (Malti et al. (2008a); Victor et al. (2013)) to the multiple input-single output case. Monte Carlo simulation analysis is used to demonstrate the performance of the proposed approach. A study is then provided to motivate differentiation order estimation, and more specifically, commensurate order estimation.

Frequency-domain analysis of linear systems with periodic jumps: Definition of hybrid transfer function, pole and zero

A frequency-domain analysis is carried out for a class of linear systems in the presence of periodic time-driven jumps. The result is achieved by introducing the notion of transfer function in this context, and by relying on a suitably defined transform for hybrid arcs, whose properties are comprehensively discussed. It is firstly shown that knowledge of the transfer function permits the computation in closed-form of the complete (state and output) response of the hybrid plant, which may be otherwise intractable from the computational point of view. Moreover, the hybrid transfer function resulting from series interconnection of two plants is derived and exploited to introduce and discuss, in the single-input single-output case, the concepts of zero and pole of the hybrid transfer function. Differently from the classical purely continuous or discrete time cases, only a subset of the latter is related to the stability properties of the hybrid system.

Input–output linearization of non-linear time-varying delay systems: the single-input single-output case

Abstract This paper deals with the input–output linearization of non-linear time-varying delay systems. We introduce an extension of the Lie derivative for time-varying delay systems and derive sufficient conditions for the existence of a causal and bounded non-linear feedback linearizing the input–output behaviour of the system. Sufficient conditions ensuring the internal stability after output stabilization are also presented. Finally, several examples illustrating our main results are discussed.

Robustness Analysis of MIMO Mechatronic Systems in the Frequency Domain

A new and general method of robustness analysis for linear dynamic systems containing both electrical and mechanical components is proposed in this paper. The method is based on the convex optimization theory and, therefore, it is accurate, efficient, and scales well with the number of unknown variables. The method is applied to two examples: a piezoelectric harvester (single-input single-output case) and a double mass–spring–damper system (multiple-input multiple-output (MIMO) case). In both cases, upper and lower bounds of the magnitude response are computed and compared to the Monte Carlo method. The results show that parametric variation affect strongly the performance output, uncertainty must be taken into account for a robust design, and that the proposed method is a great improvement to the existing method in the literature.

Identification of channels with single and multiple inputs and outputs under linear constraints

The channel identification problem for multiple-input multiple-output (MIMO) channels under linear constraints can be formulated as solving a linear system which involves finite-dimensional Gabor matrices and a pre-determined unstructured matrix that represents the linear constraints. While matrices of the latter type are fixed a priori by the constraints, Gabor matrices depend on the choice of their generating windows which is often chosen by the user. This is important since even if the matrix associated with the linear constraints is ill-conditioned, the full system may be solvable if the windows are designed appropriately.We prove that linear constraints consisting of a single equation always remove a single degree of freedom in the channel identification problem, in the sense that preknowledge of such constraints allows identification of MIMO channels with support size one greater than the fundamental limit. However, we give an explicit example showing that this statement does not generalize to the case of multiple constraints. In the single-input single-output (SISO) case, we provide some sufficient conditions on the linear side constraints under which the corresponding SISO channels are identifiable.

Improving the Stability Behavior of Limiting Zeros for Multivariable Systems Based on Multirate Sampling

It is well-known that existence of unstable sampling zeros is recognized as a major barrier in many control problems, and stability of sampling zeros, in general, depends on the type of hold circuit used to generate the continuous-time system input. This paper is concerned with stability of limiting zeros, as the sampling period tends to zero, of multivariable sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time plant with the relative degrees being two and three, and a sampler in cascade. In particular, the main focus of the paper is how to preserve the stability of limiting zeros when at least one of the relative degrees of a multivariable system is more than two. In this case, the asymptotic properties of the limiting zeros on the basis of normal form representation of continuous-time systems are analyzed and approximate expressions for their stability are discussed as power series expansions with respect to a sufficiently small sampling period. More importantly, unstable sampling zeros of the sampled-data models mentioned above can be avoided successfully through the contribution of this paper, whereas a zero-order hold (ZOH) or a fractional-order hold (FROH) fails to do so. It is a further extension of previous results for single-input single-output cases to multivariable systems.

Highly Accurate and Asymptotic Analysis on the SOP Over SIMO &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$\alpha$ &lt;/tex-math&gt; &lt;/inline-formula&gt;–&lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$\mu$ &lt;/tex-math&gt; &lt;/inline-formula&gt; Fading Channels

In order to fill the gap of the mathematical analysis's lack for the secrecy outage probability (SOP) over single-input multiple-output (SIMO) α-μ wiretap fading channels, this letter initially provides highly accurate and asymptotic closed-form expressions for the SOP. The novel highly accurate formulations are derived in a simple and general form in terms of the bivariate Fox's H-function, which is extensively used in the literature. In addition, the asymptotic analysis of the SOP is derived at high signal-to-noise ratio regime. The obtained expressions are numerically validated and compared with the Monte-Carlo simulation results. The derived SOP is in highly accurate match with simulation results for the SIMO case, and a perfect match with simulated results for single-input single-output (SISO) case.

Asymptotic bit error rate analysis of free space optical systems using spatial diversity

Free space optical (FSO) communication is used to provide very high speed network connection to end users, especially the last mile users thereby enabling cost-effective, fast and secure internet service to them. But the single input single output (SISO) connection is highly hampered by the atmospheric turbulence and pointing error of the link. As a solution to this problem, the spatial diversity technique can be used to improve the communication service. The bit error rate (BER) analysis for the received signal to noise ratio (SNR) is analyzed in this paper to study the performance improvement over the SISO case for the system over the generalized atmospheric turbulence channel known as the Málaga turbulence channel. A new expression for the BER in terms of the beta function is derived and the diversity gain and coding gain are obtained from the same.

Transmission Channel Characteristics of Relay Dual-Polarization MIMO System for Hypersonic Vehicles Under Plasma Sheath

The blackout problem caused by plasma sheath is a serious obstacle to the communication system of hypersonic vehicles. The uplink relay transmission method is an effective means of mitigating serious attenuation caused by plasma sheath. This paper proposes a Ka-band $2\times2$ dual-polarization multiple-input multiple-output (MIMO) scheme by adopting a left-/right-hand circular polarized antenna to increase channel capacity and signal quality. The relay dual-polarized MIMO channel model between the hypersonic vehicle and satellite is established by emphasizing the plasma sheath effect, especially the cross-polar coupling and polar correlation under plasma sheath. Useful numerical results on the relay dual-polarized MIMO ergodic channel capacity are analyzed. Thus, significant capacity gains with respect to the conventional single-input single-output case are illustrated based on this analysis. Simulation results show that the relay dual-polarized MIMO method can increase the channel ergodic capacity by 1.9–2 times under most circumstances, and the angle between the selected relay satellite and the vehicle normal direction should be minimal. This statistical channel model can be applied to the wireless communication system design and evaluation for hypersonic vehicles.