Coprime Factorization Approach Research Articles

Non-linear forced vibration control for a vertical wing-plate with sustainable perturbation by using internal model control mechanism

This article studies the non-linear vibration control problem for a vertical wing-plate with sustainable perturbation by using piezoelectric actuator. For the vertical wing-plate system with hysteresis non-linearity, the operator-based robust right coprime factorisation approach is considered to ensure the stability of the non-linear system. After, for compensating the sustainable perturbation and hysteresis non-linearity to improve the non-linear vibration control performance, the non-linear internal model control scheme that includes the designed internal closed-loop model and the compensator is considered. Finally, simulation and experimental examples are given to show the effectiveness of the proposed control system.

A Design Method of Generalized Predictive Control Systems in Consideration of Noise

Generalized Predictive Control (GPC) is one of the model-based control methods. The control law is derived by minimizing performance index, which includes the squares of control input and the squares of the error between reference signal and output prediction, in order to make the derived control system be stable. Although coprime factorization approach has been used to extend the conventional control law in the previous researches, there has been a possibility that the order of the derived control law becomes high. Therefore, this paper extends GPC through newly-defined output prediction and proposes the method to redesign the control law or the disturbance response with keeping the closed-loop transfer function. Numerical example is shown to check the characteristic of the proposed method.

Operator-based robust nonlinear free vibration control of a flexible plate with unknown input nonlinearity

In this paper, a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity. With considering the effect of unknown input nonlinearity from the piezoelectric actuator, operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system. Simultaneously, for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity, operator based tracking compensator and estimation structure are given, respectively. Finally, both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.

Development of Operator Theory in the Capacity Adjustment of Job Shop Manufacturing Systems

With the development of industrial manufacture in the context of Industry 4.0, various advanced technologies have been designed, such as reconfigurable machine tools (RMT). However, the potential of the latter still needs to be developed. In this paper, the integration of RMTs was investigated in the capacity adjustment of job shop manufacturing systems, which offer high flexibility to produce a variety of products with small lot sizes. In order to assist manufacturers in dealing with demand fluctuations and ensure the work-in-process (WIP) of each workstation is on a predefined level, an operator-based robust right coprime factorization (RRCF) approach is proposed to improve the capacity adjustment process. Moreover, numerical simulation results of a four-workstation three-product job shop system are presented, where the classical proportional–integral–derivative (PID) control method is considered as a benchmark to evaluate the effectiveness of RRCF in the simulation. The simulation results present the practical stability and robustness of these two control systems for various reconfiguration and transportation delays and disturbances. This indicates that the proposed capacity control approach by integrating RMTs with RRCF is effective in dealing with bottlenecks and volatile customer demands.

Operator-Based Robust Nonlinear Control Analysis and Design for a Bio-Inspired Robot Arm with Measurement Uncertainties

In this paper, a robust nonlinear tracking control design for a bio-inspired robot arm with human-like motion mechanism is investigated, and the bio-inspired operator controller based on human multi-joint viscoelastic properties is designed by using operator-based robust right coprime factorization approach. The motion mechanism of human multi-joint arm is used, and the measurement uncertainties of human multi-joint arm viscoelasticity are considered in designing bio-inspired operator controller. Based on the proposed design scheme, the sufficient conditions for the robust stability are derived in considering the coupling effects and measurement uncertainties, and the output tracking performance is realized. The effectiveness of the proposed design scheme was confirmed by the simulation results based on experimental data, and the time-varying estimated experimental data of human multi-joint arm viscoelasticity is used in simulation.

Tracking Performance Improvement for Operator-based Nonlinear Robust Control of Wireless Power Transfer Systems with Uncertainties

A new operator-based nonlinear robust control design scheme for wireless power transfer systems with uncertainties is proposed in this paper. In the proposed control design system, to deal with the uncertainties in the wireless power transfer system, operator-based robust right coprime factorization approach is adopted to guarantee the robust stability. Moreover, the tracking performance is improved by using the proposed control design scheme. Simulations and experiments are tested to show the effectiveness of this proposed control design scheme.

Operator-Based Control System Analysis and Design for Nonlinear System with Input and Output Constraints

Smart material-based actuators and sensors have been widely used in practice owing to their various advantages. However, in the working process of these actuators and sensors, their output responses always deduce non-smooth nonlinear constraints. The constraint resulting from the actuator is called the input constraint and the constraint caused by the sensor is called the output constraint. These input and output constraints may induce inaccuracies and oscillations, severely degrading system performance. Therefore, the input and output constraints brought about by actuators and sensors should be considered in control system design. In this paper, system analysis for a nonlinear system with input and output constraints will be considered. The effect from the input constraint to the internal signal in the control system will be discussed. Moreover, the influence of the output constraint on the whole system will be studied. Further, the sufficient conditions for maintaining the stability of the system are obtained. Then, by using the robust right coprime factorization approach, an operator-based internal model like control structure is proposed for mitigating the input and output constraints. Finally, the effectiveness of the proposed design scheme will be confirmed through numerical simulation.

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.

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.

Experimental Study on Robust Nonlinear Forced Vibration Control for an L-Shaped Arm with Reduced Control Inputs

This paper presents an operator-based robust nonlinear control approach for an L-shaped arm vibration experimental system. The arm is driven by a linear pulse motor to move along a frame and controlled by a piezoelectric actuator in parallel. The aim of this paper is to allow the motor to move fast and reduce the arm vibration by controlling the motion of the motor and the piezoelectric actuator simultaneously. In detail, first, the vibration dynamics of the L-shaped arm is modeled based on the Euler–Bernoulli beam theory. The hysteresis of the piezoelectric actuator is modeled using a Prandtl–Ishlinskii hysteresis model. Second, by using operator-based robust right coprime factorization approach, the proposed control for the system is designed where the linear motor is optimally controlled to reduce the time consumption and the vibration at the vertical part of the arm. Meanwhile, with the hysteresis compensation, the piezoelectric actuator is used to further reduce the vibration at the horizontal part of the arm. Finally, the results of the experiment are demonstrated to verify the effectiveness of the proposed control scheme.

Operator-based robust nonlinear optimal vibration control for an L-shaped arm driven by linear pulse motor

An L-shaped arm driven by a linear pulse motor is considered in this paper, an operator-based robust nonlinear control approach is proposed to reduce the vibration of the arm. First, by separating the arm into two parts, its vibration dynamics is modelled based on Euler-Bernoulli beam theory. Second, by using operator-based robust right coprime factorization approach, two control schemes are designed, one for controlling the linear pulse motor move to the desired destination and reducing the vibration of the arm with optimal trajectory, another one is to control vibration of the arm by using a piezoelectric actuator, where a tracking compensator is designed to compensate the hysteresis of the piezoelectric actuator and make the arm vibration track to the reference values. Finally, simulation results are demonstrated to verify the effectiveness of the proposed control scheme.

Fault detection for LPV systems using Set-Valued Observers: A coprime factorization approach

This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions.

Robust stability of MIMO nonlinear uncertain systems using operator-based right coprime factorisation

ABSTRACTIn this paper, a class of multi-input–multi-output (MIMO) nonlinear systems with uncertainties is considered by using operator-based right coprime factorisation. First, based on proposed quotient operators, coupling effect of the MIMO nonlinear systems is discussed. Second, based on the operator-based right coprime factorisation approach, sufficient conditions for guaranteeing robust stability of the MIMO nonlinear systems with uncertainties are proposed by using a new unimodular operator. Finally, a simulation example is shown to illustrate the proposed design scheme for the MIMO nonlinear systems with uncertainties.

Perturbed nonlinear systems control using extended robust right coprime factorisation

ABSTRACTIn this paper, extended operator-based robust right coprime factorisation is investigated for dealing with a class of nonlinear systems with unknown bounded perturbations. First, a new kind of operator is introduced, by which operator-based right coprime factorisation approach is extended to consider the perturbed nonlinear systems. By regulating the exponent of the proposed operator, a broader class of nonlinear systems can be handled using the extended right coprime factorisation approach. Second, for guaranteeing robust stability of the perturbed nonlinear systems, feasible design schemes based on some sufficient conditions are discussed, which can reduce complicated calculation in control processing using a different unimodular operator. Finally, a simulation example is involved to illustrate the proposed design scheme for confirming the effectiveness of the proposed method.

Bio-inspired robust control of a robot arm-and-hand system based on human viscoelastic properties

A bio-inspired scheme based on the human multi-joint arm (HMJA) viscoelastic properties is proposed to design a robust controller for the complex robot arm-and-hand system (RAHS) using the operator-based robust right coprime factorization (RRCF) approach. The RAHS mainly consists of two components, a robot arm and a micro-hand with three fingers. The fingers are made up of miniature pneumatic curling soft (MPCS) actuators, and are located in the endpoint of the robot arm. The aim is for a human to intuitively control the robot arm to perform a task under unknown environments from a remote location. We identify the main limitations of standard interaction control schemes in obtaining the learned information pairs, then propose a new control approach that is inspired by the biological model of HMJA viscoelasticity in voluntary movements. To achieve the precise position of the robot arm and obtain the desired force using the micro-hand for coping with the external environment or task involved, we propose a two-loop feedback control architecture using the operator-based RRCF approach. The bio-inspired inner-loop controller is designed based on HMJA viscoelastic properties to control the angular position of the robot arm. The outer-loop controller is designed to control the fingers force by considering the stable inner-loop as a right factorization. The robust tracking conditions and the realization of the proposed control system are also discussed. Finally, the effectiveness of the proposed control system is also verified by simulation results based on experimental data.

Operator-Based Robust Nonlinear Control Design of a Robot Arm with Micro-Hand

[abstFig src='/00280004/14.jpg' width='300' text='Robot arm with micro-hand system' ] This work focuses on a robust nonlinear control design of a robot arm with micro-hand (RAMH) by using operator-based robust right coprime factorization (RRCF) approach. In the proposed control system, we can control the endpoint position of robot arm and obtain the desired force of micro-hand to perform a task, and a miniature pneumatic curling soft (MPCS) actuator which can generate bidirectional curling motions in different positive and negative pressures is used to develop the fingers of micro-hand. In detail, to control successively the precise position of robot arm and the desired force of three fingers according to the external environment or task involved, this paper proposes a double-loop feedback control architecture using operator-based RRCF approach. First, the inner-loop feedback control scheme is designed to control the angular position of the robot arm, the operator controllers and the tracking controller are designed, and the robust stability and tracking conditions are derived. Second, the complex stable inner-loop and micro-hand with three fingers are viewed as two right factorizations separately, a robust control scheme using operator-based RRCF approach is presented to control the fingers forces, and the robust tracking conditions are also discussed. Finally, the effectiveness of the proposed control system is verified by experimental and simulation results.

Operator-based experimental studies on nonlinear vibration control for an aircraft vertical tail with considering low-order modes

In this paper, a robust nonlinear control design using an operator-based robust right coprime factorization approach is considered for vibration control on an aircraft vertical tail with piezoelectric elements. First, a model of the aircraft vertical tail is derived to describe vibration response using the operator-based approach, where, to stabilize vibration of the tail, piezoelectric elements are used as actuators and a hysteresis nonlinear property of piezoelectric actuators is considered. Simultaneously, positions of the piezoelectric actuators that are stuck on the plate are arranged by using a finite element method. Then based on the obtained operator-based model, a robust nonlinear feedback control design is given by using robust right coprime factorization for the aircraft vertical tail with considering the effect of hysteresis nonlinearity from piezoelectric actuators. In particular, low-order modes are employed to design the control scheme even though vibration is configured by high-order modes. In other words, robustness is considered, and the desired performance of tracking is discussed. Finally, both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.

Adaptive Nonlinear Sensorless Control for an Uncertain Miniature Pneumatic Curling Rubber Actuator Using Passivity and Robust Right Coprime Factorization

In this brief, an adaptive nonlinear sensorless control for an uncertain miniature pneumatic curling rubber actuator is considered using passivity and the robust right coprime factorization approach. Specially, based on the robust right coprime factorization approach, robust stability is guaranteed and passivity is realized simultaneously. Then, the adaptive control system is designed for tracking performance. Support vector regression is proposed to estimate the output for avoiding the use of a sensor. Finally, the experimental setup is shown and the experimental results are provided to show the effectiveness of the proposed scheme.