Non-square MIMO Research Articles

Robust Adaptive Iterative Learning Control for a Generic Class of Uncertain Non-Square MIMO Systems

Robust Adaptive Iterative Learning Control for a Generic Class of Uncertain Non-Square MIMO Systems

A Novel Output-Feedback Controller for Non-Square MIMO Nonautonomous Nonlinear Systems With Unstructured Uncertainties Using Higher-Order Switching Differentiator

A Novel Output-Feedback Controller for Non-Square MIMO Nonautonomous Nonlinear Systems With Unstructured Uncertainties Using Higher-Order Switching Differentiator

A new geometric approach to the calculation of transmission zeros in the signal processing theory

In the paper, a new method concerning the estimation of transmission zeros is introduced. Following the notion related to the Smith–McMillan-like technique allowing us to determine the crucial zeros, a new solution covering the geometric approach is effectively presented and confirmed in the manuscript. Indeed, the existing non-intuitive method providing non-unique computational effort even for the well-conditioned environmental matrices can successfully be replaced without loss of generality. Therefore, in order to overcome the indicated difficulties, the rank-nullity theorem is adapted to determine the transmissions zeros, for which the matrix depending on variable coefficients loses its rank. The benefits of the new scheme in modeling of non-square MIMO signal processing systems are clearly visible. It should be emphasized that currently only the Smith–McMillan factorization allows us to calculate the transmission zeros. However, in the proposed method, it can be done faster, more intuitively and effectively.

Time domain modeling and control of complex non-linear chemical processes using relay feedback test

This study analyzes with the technology of auto tuning using relay feedback test for non-square MIMO system through process modeling, identification, input-output pairing and control strategies. However, the control configuration selection based on conventional steady-state Relative Gain Array (RGA) matrix sometimes degrades the loop performance and it needs attention. This study also deals with the real challenges in time domain modeling and appropriate pairing of loops for non-linear chemical processes. The choice of input-output pairing for square system has been extended to non-linear chemical processes. This ensures the system’s stability by selecting an appropriate manipulated-controlled variable pairing in non-linear chemical processes and the same is also tested for benchmark of non-linear chemical processes. In this study, two types of non-square systems are considered: one is systems with excess input than output variables and the other is systems with excess output than input variables. Some benchmark non-linear chemical processes, such as processes with mild nonlinearity, moderate to high nonlinearity and highly nonlinearity, are also taken for this study. Three standard benchmark processes are used in analysis of nonlinear chemical processes, namely: (1) Continuous Stirred Tank Reactor (CSTR) process; (2) hydrogen-ion- concentration (pH) process and (3) distillation column and this procedure is illustrated via simulation of 3-by-2 and 2-by-3 non-linear chemical processes.

A Loewner Interpolation Method for Power System Identification and Order Reduction

An accurate framework for power system identification and model order reduction based on the Loewner matrix method is proposed. In this approach, frequency responses corresponding to non-symmetrical non-square MIMO transfer functions are introduced as tangential data in the Loewner interpolation process. Such responses can be either computed efficiently when explicit large sparse models are available or measured when only black-box models are at disposal. Numerical results are discussed for a couple of well-reported multi-machine test systems. The accuracy of the produced models and comparison against other state-of-the-art techniques are then discussed.

Perfect Control for Right-Invertible Grünwald-Letnikov Plants–an Innovative Approach to Practical Implementation

Abstract A new perfect control algorithm dedicated to fractional-order right-invertible systems, i.e. plants with a greater number of input than output variables, is presented in this paper. It is shown that such a control strategy can be particularly applied with regard to practical tasks. Henceforth, the Grünwald-Letnikov difference operator Δ α of an assumed order α can be truncated without loss of generality. For that reason, the so-called pole-free perfect control formula can be used to minimize the essential drawback of the Grünwald-Letnikov approach engaged, so as to define the intriguing issue regarding the robust perfect control for non-integer-order right-invertible LTI discrete-time state-space systems. Simulation examples show that the presented method can compete with a classical stable-pole one, for which the actual systems described by a fractional-order model often correspond with an inconvenient asymptotic perfect control solution given by the unlimited original operator Δ α . In the end, the possibility of employing of author’s nonunique right inverses dedicated to nonsquare MIMO system matrices is demonstrated, thus giving rise to the introduction of a new powerful tool for robustification of non-integer-order closed-loop perfect control plants as well.

Analytical design based hierarchical control for non-square MIMO wood-chip refining process

This paper presents an analytical design basedhierarchical control method for non-square MIMO wood-chip refining process, whose design procedure of the control scheme contains two layers. Firstly, the lower layer loop controller with PID structure is designed separately for the mutually independent lower layer device plant, and then generalized non-square process is obtained on the basis of lower layer closed-loop system and non-square MIMO refining process. Secondly, the upper layer setting controller with the centralized PID structure is designed by the multivariable decoupling control and internal model control (IMC), and an analytical designed method for the lower layer loop controller and the upper layer setting controller is developed using the maximum sensitivity (Ms) specification. Finally, Simulation results demonstrate the effectiveness of the proposed method for control and optimal operation of the non-square MIMO refining process.

Adaptive consensus tracking of non-square MIMO nonlinear systems with input saturation and input gain matrix under directed graph

This paper deals with the leader-following consensus problems of non-square multi-input/multi-output multi-agent systems in the presence of control input saturation and uncertain external disturbances. The agents have unknown high-order nonlinear dynamics and communicate together under any directed graph containing a spanning tree. A distributed adaptive method is designed to solve the problem. Moreover, a constant full-rank matrix with an adaptive gain is used instead of approximation of the unknown gain matrix by neural networks. Therefore, the proposed controller’s structure simplifies its implementation. The unknown nonlinearities are estimated by a radial basis function neural network. The ultimate boundness of the closed-loop system is guaranteed through Lyapunov stability analysis by introducing suitably driven adaptive rules. Finally, the simulation results verify the performance of the proposed control method.

L1 adaptive output feedback control for underactuated MIMO systems

This paper addresses the problem of output feedback control for underactuated (non-square) MIMO systems with unknown input gain and matched uncertainties. The L1 adaptive output feedback control architecture in this paper includes a state predictor, an error observer, adaptation laws, and a low-pass filter. It is shown that the proposed control strategy guarantees that the error signals of the closed-loop system are semi-globally bounded. Simulation results are presented to validate the theoretical claims.

Observer based robust neuro-adaptive control of non-square MIMO nonlinear systems with unknown dynamics

This paper addresses a robust adaptive control problem of non-square nonlinear systems with unmeasurable states. The systems are assumed to be multi-input/multi-output subject to dynamical uncertainties and external disturbances. The approach is studied for two cases, i.e., underactuated and over-actuated nonlinear systems. The new observer does not need to satisfy the SPR conditions. Moreover, a constant full-rank matrix with an adaptive gain is used to approximate the unknown gain matrix. Therefore, the proposed controller’s structure simplifies its implementation. The unknown nonlinearity is estimated neural networks. Stability of the closed-loop system is proved using Lyapunov analysis. The feasibility of the proposed approach is validated by simulation examples.

An optimal centralized predictive control scheme applied to a Non-Square MIMO benchmark problem

This paper aims at the implementation of advanced control technique such as Generalized Predictive Control (GPC) for non-square Multi-Input-Multi-Output (MIMO) benchmark problem. The process considered is a coupled distillation column (3 input, 2 output) studied by Levein and Morari. The design approach for tuning controller parameters in conventional methods of a non-square system is a big challenge, as it involves computational complexities. In this work, predictive algorithm with constraints on the input and output control signals are developed and compared with the PID controller by retaining its non-minimum phase characteristics. GPC uses Controlled Autoregressive and Integrated Moving-Average (CARIMA) model. Simulation studies demonstrate the superiority of the constrained GPC over GA-PID controller for a non-square multivariable process. The effectiveness of the advance control structure ensures the reduction in computational complexities and fast convergences with better tracking capabilities.

Squaring-Up Method in the Presence of Transmission Zeros

Non-square MIMO systems are becoming increasingly common, as the addition of multiple sensors is becoming prevalent. However, square systems are needed sometimes as an leverage when it comes to design and analysis, as they possess desirable properties such as invertibility and strict positive realness. This paper presents a method to square-up a class of MIMO systems with stable transmission zeros while keeping the squared system minimum phase. The proposed method is used to carry out adaptive control of this class of systems and shown to lead to satisfactory performance in a numerical study of a 747 aircraft.

Decentralized robust control-system for a non-square MIMO system, the air-path of a turbocharged Diesel engine

The targeted purpose here is the control of a nonlinear and non-square system with three inputs and two outputs in order to reduce soot and greenhouse gas pollutants. In this paper, a non-square multivariable controller for the air-path system of a turbocharged Diesel engine is proposed. The controller is designed using the CRONE (Commande Robuste d'Ordre Non Entier) Control-System-Design approach to maintain performance and robust stability for a wide set of operating points. In this research, we focused on the multi-input multi-output system identification problem, and test-bench data were processed to find a nominal linear model. The controller was then designed via an open-loop transfer function optimization. Finally, simulation results from a simulation model show the performance of the proposed control-system.

Pole-free vs. stable-pole designs of minimum variance control for nonsquare LTI MIMO systems

This paper takes advantage of nonuniqueness of the inverse problem for nonsquare transfer function matrices of multivariable systems in order to select such poles, if any, of a minimum variance control system that can either guarantee its closed-loop stability or provide (a sort of) robustness to the control system. As a result, new pole-free and stable-pole MVC designs are offered for nonsquare LTI MIMO systems, the most general of them utilizing the Smith-factorization approach and the so-called control zeros. The new designs contribute to an illustration and extension of the Davison’s theory of (nonsquare) minimum phase systems, in that the lack or presence of (appropriate) control zeros can provide a required performance to the MVC system. Simulation examples in the Matlab/Simulink environment confirm the potential of the control zeros and their impact on redefinition of the minimum phase property

A New General Class of MVC-Related Inverses of Nonsquare Polynomial Matrices Based on the Smith Factorization

In this paper, a new class of inverses of nonsquare polynomial matrices involved in the minimum variance control (MVC) problem is presented. The new right/left inverses are based on the celebrated Smith-factorization approach. The inverses can be applied in both pole-free and stable-pole designs of robust MVC, also in case when (stable) transmission zeros are present in the nonsquare LTI MIMO system. A simulation example in the Matlab environment confirms the potential of the new inverses.

PLS based dEWMA run-to-run controller for MIMO non-squared semiconductor processes

This paper focuses on the modification of the PLS (partial least squares) modeling. The new method allows incorporation of a dEWMA (double exponentially weighted moving average) control algorithm into the standard run-to-run controller design for semiconductor processes. The resulting structure of the PLS model can extract the strongest relationship between the input and the output variables. It is particularly useful for inherent noise suppression. In addition, the resulting non-square MIMO control system can be decomposed into a multi-loop control system by employing pre-compensators and post-compensators of the PLS model, which is constructed from the input and output loading matrices. Subsequently, the conventional dEWMA controller can be separately and directly applied to each SISO control loop. The performance of the proposed method is illustrated through a chemical–mechanical polishing process in the manufacturing of the semiconductor.