Coprime Factorization Research Articles

Optimal modified performance of MIMO networked control systems with multi-parameter constraints

The optimal modified performance of the multi-input multi-output (MIMO) networked control systems (NCSs) with encoding–decoding, channel noise in the forward channel and packet dropouts, quantization in the feedback channel is investigated in this paper. A new and efficient tracking performance index for the NCSs is presented which prevents variations in the tracking error where there is no integrator in the plant. The optimal modified performance is obtained by the method of coprime factorization and partial fraction. The results demonstrate that the optimal modified performance is related to the locations of the non-minimum phase (NMP) zeros, unstable poles of the given plant as well as their directions. In addition, the modified factor, packet dropouts probability, channel noise and encoding–decoding are also closely related to optimal modified performance of the NCSs. Finally, we present some particular examples to illustrate the theoretical results.

A fault detection scheme for ship propulsion systems using randomized algorithm techniques

This paper studies the fault detection problem in ship propulsion systems based on randomized algorithms. The nominal propulsion system model, model with uncertainties and model with additive and multiplicative faults are first addressed in the form of normalized left coprime factorization (LCF), respectively. The K-gap metric is then introduced to measure how far the system deviates from the nominal operation. To reduce the conservatism in the norm-based threshold, a threshold setting law and the estimation of fault detection rate (FDR) are formulated on the probabilistic assumption of uncertain and faulty parameters. The simulation results on the ship propulsion system show that the randomized technique is an efficient solution to deal with the fault detection issues.

A design method of strong stability self‐tuning controller based on on‐demand type feedback control

AbstractThis paper proposes a design method of strong stability self‐tuning controller based on on‐demand type feedback control. For safety in industrial applications, although it is important to consider on‐demand type feedback control system, the previous papers about on‐demand type feedback control did not consider the influence of noise and fixed the design parameter to constant value. Therefore, this paper extends the design parameter of on‐demand type feedback control as stable rational function through the design method of strong stability system using coprime factorization. Moreover the self‐tuning controller of the proposed method is given and the control result with noise is shown by numerical example.

Modelling and Operator-Based Nonlinear Control for a Miniature Pneumatic Bending Rubber Actuator Considering Bellows

Recently, many kinds of soft actuators composed of flexible materials, such as silicon rubber, have been studied in the mechatronics field with increasing attention on the artificial muscle in welfare, medical care and biotechnology. Particularly, pneumatic-driven soft actuator moves flexibly and works safely because of not electrical but pneumatic input, so that the actuator could perform effectively in the medical operations. A miniature pneumatic bending rubber actuator is a tiny pneumatic-driven soft actuator which has some chambers connected to only one tube providing compressed air and the chamber has bellows. This actuator can bend circularly in two directions and grab delicate objects such as fish eggs, by inputting pressure into its chambers. The actuator, however, has nonlinear property derived from elastomer in input-output relation. The actuator, therefore, sacrifices some degree of control performance instead of obtaining the passive flexibility to delicate objects. To solve the above problem, previous studies have shown, by the experiments, that the effectiveness of designing the nonlinear feedback control system using robust right coprime factorization based on the operator theory for control of the output angle of the actuator. However, the mathematical model used for designing the system caused modelling error because the bellows were not considered in deriving the model. The mathematical model should fit experimental value as well as possible for system design and there has been no example modelling of the micro hand having bellows. In this research, a new model of the micro hand considering its bellows with elastomer property is proposed. Moreover, a control system using the robust right coprime factorization based on the operator theory is designed for the new model. Finally, the effectiveness is shown in the experiment.

Generalized Nested Array: Optimization for Degrees of Freedom and Mutual Coupling

In this letter, we propose a generalized nested array (GNA) with two flexible co-prime factors for enlarging the inter-element spacing of two concatenated uniform linear subarrays. It is shown that both the prototype nested array and generalized co-prime array can be interpreted as special cases. The closed-form expressions for the range of consecutive lags and the number of unique lags are derived for any given factors. After optimization, GNA has the same number of degrees of freedom as (super) nested array but with reduced mutual coupling. Numerical simulations prove the superiority of proposed configuration using compressed sensing algorithm.

Robust stabilization of discrete generalized systems

The robust stabilization problem for generalized discrete-time systems described by polynomial or improper transfer function matrices, subject to perturbations acting on the normalized coprime factors, is solved. The maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate Riccati equations.

Coprime factors reduction of distributed nonstationary LPV systems

ABSTRACTThis paper is on the coprime factors reduction of distributed systems formed by discrete-time, heterogeneous, nonstationary linear parameter-varying subsystems. The subsystems are represented in a linear fractional transformation framework and interconnected over arbitrary directed graphs, and the communication between the subsystems is subjected to a delay of one time-step. Two methods for constructing a contractive coprime factorisation for the full-order system are proposed. This factorisation forms an augmented system which is reducible by the structure-preserving balanced truncation method. A reduced-order contractive coprime factorisation is obtained from which the reduced-order system can be formed. A robustness theorem is also provided to interpret the error bound from coprime factors reduction in terms of robust stability of the closed-loop system. A numerical example is considered at the end of the paper.

De Bruijn Sequences, Adjacency Graphs, and Cyclotomy

We study the problem of constructing De Bruijn sequences by joining cycles of linear feedback shift registers (LFSRs) with reducible characteristic polynomials. The main difficulty for joining cycles is to find the location of conjugate pairs between cycles, and the distribution of conjugate pairs in cycles is defined to be adjacency graphs. Let <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l(x)$ </tex-math></inline-formula> be a characteristic polynomial, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l(x)=l_{1}(x)l_{2}(x)\cdots l_{r}(x)$ </tex-math></inline-formula> be a decomposition of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l(x)$ </tex-math></inline-formula> into pairwise co-prime factors. First, we show a connection between the adjacency graph of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {FSR}(l(x))$ </tex-math></inline-formula> and the association graphs of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {FSR}(l_{i}(x))$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\leq i\leq r$ </tex-math></inline-formula> . By this connection, the problem of determining the adjacency graph of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {FSR}(l(x))$ </tex-math></inline-formula> is decomposed to the problem of determining the association graphs of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {FSR}(l_{i}(x))$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\leq i\leq r$ </tex-math></inline-formula> , which is much easier to handle. Then, we study the association graphs of LFSRs with irreducible characteristic polynomials and give a relationship between these association graphs and the cyclotomic numbers over finite fields. At last, as an application of these results, we explicitly determine the adjacency graphs of some LFSRs and show that our results cover the previous ones.

Effects of lag redundancy on array beam patterns and redundancy patterns for extended co-prime arrays

Lag redundancy describes the number of times a given spatial lag is measured by an array. For sparse arrays, the reduction of lag redundancies is generally desirable for lowering cost and processing overhead. However, as lag redundancies determine the natural weighting function of an array’s spectral estimates, the pattern of redundancies dictates the natural beam pattern of a given array. We consider the impact of array sparsity on sidelobe level and array gain in both weighted and unweighted conventional beamforming. This analysis is then applied to co-prime arrays, for which redundancy patterns can be determined based solely on the choice of array length and co-prime factors. It is also shown that the spatial positions of lag redundancies are semi-regular, a desirable feature for sampling some complex environments.

Operator-based robust nonlinear control for SISO and MIMO nonlinear systems with PI hysteresis

In this paper, operator based robust nonlinear control for single-input single-output U+0028 SISO U+0029 and multi-input multi-output U+0028 MIMO U+0029 nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii U+0028 PI U+0029 hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively. In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized. Finally, the effectiveness of the proposed method is confirmed by numerical simulations.

Experimental study on operator-based robust nonlinear vibration control for an L-shaped arm with unknown load

A linear-motor-driven L-shaped arm experimental system is studied in this article. The arm with unknown load is driven by the motor and actuated by a piezoelectric actuator at the same time. This study aims to control the motor motion and the actuator’s behavior simultaneously, resulting in less arm vibration. First, the arm vibration relating to the load and the linear motor is modeled by considering it as an Euler–Bernoulli beam. Then, the control design for the arm and motor is proposed using the operator-based nonlinear control approach involving an on-line discrete wavelet transform. The operator-based right coprime factorization is used to ensure the system stable and robust. The discrete wavelet transform is utilized to remove the influences of some undesired disturbances and improve the operator-based control performance. In addition, the load mass is estimated using fast Fourier transform based on the discrete wavelet transform decomposed vibration signal. Finally, experiments are conducted comparing with the previous study, and the results show that the proposed control is effective to reduce the arm vibration in less time.

Operator‐based robust non‐linear vibration control for an L‐shaped arm with unknown load by using on‐line wavelet transform

An L-shaped arm with unknown load driven by a linear pulse motor is studied in this work. To control the motor motion and the arm vibration, an operator-based non-linear control is designed using an on-line discrete wavelet transform (DWT). First, the dynamics of the L-shaped arm vibration is modelled by considering the arm as a two-dimensional Euler–Bernoulli beam. The relationship between the load and the arm vibration is given. Second, by using the on-line DWT in the operator-based non-linear control, the proposed control for the system is designed. The wavelet transform is used to estimate the load and remove the influence of some undesired uncertainties. The operator-based right coprime factorisation method is used to guarantee the robust stability of the motor-arm system. The piezoelectric actuator is utilised to further reduce the arm vibration. The hysteresis of the piezoelectric actuator is compensated by using a Prandtl–Ishlinskii hysteresis model. Finally, simulation results are demonstrated to validate the proposed control.

Operator-based robust nonlinear control of an uncertain wireless power transfer system using sliding mode technology

In this paper, a mathematical modelling of a wireless power transfer system with a buck circuit is presented. Based on this modelling, an operator-based robust nonlinear control design scheme using sliding mode technology is proposed to consider the uncertain coupling coefficient, which results from an inaccurate distance between the transmit coil and receive coil in the wireless power transfer system. The proposed control design scheme has two advantages. First, in order to tackle the uncertain coupling coefficient, operator-based right coprime factorization is applied to guarantee robust stability of the nonlinear system. Sliding mode technology is also adopted to guarantee the tracking performance of the nonlinear system. Finally, simulations and experiments of the wireless power transfer system are tested using the proposed control design scheme. Results of both the simulations and experiments show the effectiveness of the proposed control design scheme.

Controller Reduction via Structurally Balanced Truncation using Coprime Factorization

Controller Reduction via Structurally Balanced Truncation using Coprime Factorization

Simultaneous Robust, Decoupled Output Feedback Control for Multivariate Industrial Systems

This paper proposes a simultaneous robust decoupled output feedback control approach for multivariate industrial processes with parameter uncertainties. Based on the desired control performance indicators, the expected transfer function of the closed-loop multivariate system is configured as a nonsingular diagonal matrix. Using coprime factorization theory, the weighting functions are selected and the parameterization matrix and controller are designed and calculated to achieve simultaneous robust decoupled control that takes into consideration parameter uncertainties. The performance and effectiveness of the proposed approach is demonstrated using a case study based on the crown-thickness control system of the hot strip mill processes.

Anti-windup compensator design using Riccati inequality based approach

This paper presents a full-order dynamic anti-windup compensation design scheme for stable LTI systems using a Riccati inequality based approach. The scheme utilizes the Weston-Postlethwaite’s generalized anti-windup configuration and applies right coprime factorization of the plant transfer function matrix to obtain a linear conditioning scheme. The proposed anti-windup scheme ensures the internal stability of the closed-loop control system in presence of actuator saturation and also reduces the performance degradation caused by the saturation phenomena. The Riccati inequality based approach offers a simple and straightforward anti-windup compensator design method which is independent of the design of nominal controller. The effectiveness of the proposed technique is demonstrated through a MIMO example.

On Feedback Stabilization of Neutral Time Delay Systems with Infinitely Many Unstable Poles

It is shown that strictly proper neutral time delay systems having at least one asymptotic pole chain converging to a vertical line Re(s) = σ > 0 cannot be stabilized by a proper controller. A special coprime factorization can be obtained for such systems with infinitely many unstable poles, provided they are bi-proper (i.e. proper, but not strictly proper). From this factorization, stabilizing feedback controllers are obtained. Necessarily, all stabilizing controllers for this type of plants are also bi-proper.

Operator-Based Robust Nonlinear Control Design and Analysis of a Semiconductor Refrigeration Device

In this paper, an operator-based robust perfect control for nonlinear semiconductor refrigeration device with uncertainties and perturbation is considered. For the research about the properties of the semiconductor refrigeration, an aluminum plate with Peltier device is very representative. Therefore, the perfect tracking control performance of semiconductor refrigeration can be investigated by using this aluminum plate with Peltier device. Moreover, the operator based robust right coprime factorization (RRCF) approach is convenient in analysis and designing control system of nonlinear plant with uncertainties and perturbation. Based on the above reasons, an operator-based robust tracking control design for nonlinear semiconductor refrigeration device with uncertainties and perturbation is investigated by using an operator-based robust right coprime factorization approach, where the operator-based disturbance and state observers based on nominal plant properties are designed to compensate the effect of uncertainties and perturbation. A realizable operator controller is designed to improve the control performance and to realize the perfect tracking. The sufficient condition of robust stability for the designed system is derived. The robust stability condition ensured that the output tracking performance is realized. Finally, the effectiveness of the proposed design scheme was illustrated by the simulation and experimental results.

Robust Control of Nonlinear System with Input and Output Nonlinear Constraints

With the development of modern technology, actuators and sensors composed of smart materials, such as piezoceramic and magnetostrictive materials, have been widely used in practice owing to their various advantages. However, in the working process of a smart material based actuator and sensor, non-smooth nonlinear constraints in their output responses may induce inaccuracies and oscillations, which severely degrade system performance. Therefore, input and output nonlinear constraints brought about by actuators and sensors should be considered. Generally, the output nonlinear constraint, namely, non-smooth effects from sensors, has been ignored. Therefore, in this paper, a robust control for a system with an output constraint as well as with both input and output constraints will be considered. Firstly, the generalized Prandtl-Ishlinskii (PI) hysteresis model is used for describing the input and output nonlinearities owing to its excellent characteristics, the model has proved suitable in theoretical operator based settings. Further, a robust control for a nonlinear system with an output nonlinear constraint is considered by using operator based robust right coprime factorization approach. Here, operator based robust stability is considered, and the control system structure including feedforward and feedback controllers is presented with a derivation of sufficient conditions for stable controller operation. Based on the proposed conditions, the influence from an output nonlinear constraint is rejected, the systems are robustly stable, and output tracking performance can be realized. Moreover, robust stability and output tracking performance for a nonlinear system with both input and output nonlinear constraints are also analyzed.

DESIGN OF ROBUST H∞ POWER SYSTEM STABILIZER USING NORMALIZED COPRIME FACTORIZATION

This paper proposes a new design procedure of robust power system stabilizers (PSS) using H∞ control via normalized coprime factorization (NCF) approach. The design procedure of the proposed PSS is systematically described. Moreover, the selection method of the weighting function in H∞ control design is explained in a simple manner. The performance and robustness of the proposed PSS are investigated in comparison with the conventional PSS by examining the case of a single machine connected to an infinite bus (SMIB) system. The simulation results are illustrated to ensure the effectiveness of the proposed PSS.