Linear Repetitive Processes Research Articles

Event-triggered sliding mode control of linear repetitive processes and its application in metal rolling process

Event-triggered sliding mode control of linear repetitive processes and its application in metal rolling process

Event-Triggered Cost-Guaranteed Control for Linear Repetitive Processes Under Probabilistic Constraints

In this article, the event-triggered cost-guaranteed control problem is investigated for a class of shift-varying linear repetitive processes (LRPs) with multiplicative noises under probabilistic constraints. First, in order to relieve the communication burden and improve the communication efficiency, the event-triggered mechanism is exploited for the shift-varying LRPs over the communication network of limited bandwidth. By constructing a novel event generator function, the order of the event triggering sequence is identified on two independent directions. Then, the probabilistic constraint is enforced onto the shift-varying LRPs under the influence of the event-triggered mechanism. With the aid of the Chi-square distribution and the completing-the-square technique, a controller design algorithm is proposed to ensure that both the probabilistic constraints and the quadratic cost index are satisfied by using the actual information at the triggering instants. Sufficient conditions are derived to guarantee the existence of event-based controllers, and the controller gains are obtained at each step by solving a series of matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed controller design method.

Dynamic ILC for Linear Repetitive Processes Based on Different Relative Degrees

The current research on iterative learning control focuses on the condition where the system relative degree is equal to 1, while the condition where the system relative degree is equal to 0 or greater than 1 is not considered. Therefore, this paper studies the monotonic convergence of the corresponding dynamic iterative learning controller systematically for discrete linear repetitive processes with different relative degrees. First, a 2D discrete Roesser model of the iterative learning control system is presented by means of 2D systems theory. Then, the monotonic convergence condition of the controlled system is analyzed according to the stability theory of linear repetitive process. Furthermore, the sufficient conditions of the controller existence are given in linear matrix inequality format under different relative degrees, which guarantees the system dynamic performance. Finally, through comparison with static controllers under different relative degrees, the simulation results show that the designed schemes are effective and feasible.

Robust feedback feed-forward PD-type iterative learning control for uncertain discrete systems over finite frequency ranges

This paper proposes a robust feedback feed-forward proportional-derivative type (PD-type) iterative learning control (ILC) scheme for a class of linear discrete systems with polytopic uncertainty over finite frequency ranges. First, the ILC process is transformed into an equivalent discrete linear repetitive process. Then, with the help of the generalized Kalman–Yakubovich–Popov lemma, the issue of a robust control law design algorithm in the process model is converted into the problem of solutions to the corresponding linear matrix inequality conditions. This procedure not only meets the robust performance specifications along the trial, but also guarantees the monotonic converge of the trial-to-trial error dynamics over finite frequency ranges. Finally, the simulations for a direct current servo motor system are adopted to show the effectiveness and superiority of the proposed method. Compared with previously established works, the new algorithm is more effective in delivering higher performance and achieving better tracking effect.

Practical Application of the Dynamic Output-Only Iterative Learning Control Design To The Crane System*

Iterative learning control applies to systems that repeatedly execute the same finite duration task. The distinguishing feature of this form of control action is that all data generated on a previous execution of the task are available to compute the control action for the subsequent execution. This paper uses the linear repetitive process stability analysis and optimization techniques to design a dynamic controller that, in contrast to previous designs in the repetitive process/2D systems setting, does not require measurement of the state dynamics or observer-based estimation. Supporting experimental validation results are also given.

New relaxed stability and stabilization conditions for both discrete and differential linear repetitive processes

The paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.

Networked Iterative Learning Fault Diagnosis Algorithm for Systems with Sensor Random Packet Losses, Time-varying Delays, Limited Communication and Actuator Failure : Application to the Hydroturbine Governor System

An iterative learning fault diagnosis (ILFD) algorithm for networked control systems (NCSs) subject to random packet losses, time-varying delays, limited communication and actuator failure is proposed in this paper. Firstly, in order to evaluate the effect of fault on system between every iteration, the information of state error and information of fault tracking estimator from the preceding iteration are used to improve the fault estimation achievement in the actual iteration. The state variable, the Bernoulli process of random packet losses, network communication delay, limited communication and actuator failure are introduced to establish an extended statespace model of the system. Secondly combining Lyapunov stability theory for linear repetitive processes and linear matrix inequality (LMI) technique, new sufficient condition for the existence of an iterative learning fault diagnosis is established. Finally, the feasibility and effectiveness of the proposed design method is illustrated on a dynamic hydroturbine governing system model based on Matlab/Simulink and TrueTime toolbox

On the reduction of repetitive processes into singular and non-singular Roesser models

In this paper we present new methods for the reduction of a polynomial system matrix describing a discrete linear repetitive process, to equivalent singular and non-singular 2-D state space representations. Particularly, a zero coprime system equivalence transformation resulting in a singular Roesser state space model, preserving the core algebraic structure of the original system matrix, is proposed. As a second step utilizing the singular Roesser model introduced, we further reduce the system to a non-singular, zero coprime system equivalent Roesser model. Both models are constructed by inspection or by applying elementary matrix manipulations and have significantly smaller dimensions compared to similar reductions found in the literature.

Design and Experimental Development of Wireless Iterative Learning Fault Estimation Algorithm With Quantization and Packet Losses

In this paper, a wireless iterative learning fault estimation algorithm (WILFEA) is proposed and validated experimentally with the aim to achieve perfect tracking of a prescribed reference trajectory for systems with packet losses and quantizer measurements that operate repetitively. First, state variables, Markov chain process of random packet losses, and a logarithmic quantizer are considered to establish an extended-state-space system model. Next, based on this model, sufficient conditions for linear repetitive processes are developed with the Lyapunov-Krasovskii technique and $H_{\infty }$ approach is applied to calculate the observer gain and the learning gain. Then, WILFEA based fault estimation is constructed. Compared with the existing methods, the proposed WILFEA improves the fault estimation performance in the current iteration by consider both state error and fault estimation error. Finally, the simulation and experimental results are used for DC-Servomotor system to illustrate the effectiveness of the proposed approach using Matlab/simulink software, LabVIEW Software, ZigBee Xbee and Arduino board.

Robust PD-Type Iterative Learning Control of Discrete Linear Repetitive Processes in the Finite Frequency Domain

This paper studies a robust iterative learning control design for discrete linear repetitive processes in the finite frequency domain. Firstly, the state-space model of the iterative learning process is deduced. Then the dynamic performance condition of the control system in the finite frequency domain is derived by combining it with the stability theory of discrete linear repetitive processes. The system performances in the finite frequency domain are then transformed into the corresponding solutions of the linear matrix inequality by using the generalised KYP lemma. Finally, an integrated state feedback PD-type iterative learning control strategy is proposed. The robust control problem with norm-bounded uncertainty and convex polyhedral uncertainty are also considered in this paper. The simulation of the injection velocity in injection molding verified that the proposed methods in this paper are more effective than the P-type state feedback iterative learning control algorithm.

New relaxed stability and stabilization conditions for differential linear repetitive processes

The paper develops new results on the stability analysis of differential linear repetitive processes. These processes are a distinct class of two-dimensional systems that arise in the modelling of physical processes and also the existing systems theory for them can be used to effect in solving control problems for other classes of systems, including iterative learning control design. This paper uses a version of the Kalman-Yakubovich-Popov Lemma to develop relaxed conditions for the stability property in terms of linear matrix inequalities. The main result is reduced conservatism in applying tests for the stability property with an extension to control law design. A numerical example to illustrate the application of the new results is also given.

Fusion estimation for multi-rate linear repetitive processes under weighted try-once-discard protocol

In this paper, the fusion estimation problem is studied for a class of discrete time-varying multi-rate linear repetitive processes (LRPs) under weighted try-once-discard protocol. The LRPs are measured by multiple sensors that are allowed to have different sampling periods, and the state updating period of the LRPs is also allowed to be different from the sampling periods of the asynchronous sensors. To facilitate the estimator design, the lifting technique is applied to transform the multi-rate LRPs to single-rate ones. Moreover, due to limited communication capability, the weighted try-once-discard protocol is adopted to schedule the asynchronous sensors. A set of local estimators is designed such that the upper bounds on the local estimation error covariances are guaranteed, and such upper bounds are then minimized by appropriately designing the estimator gains. Furthermore, the estimates from the local estimators are fused by recurring to the sequential covariance intersection fusion method. Finally, a simulation example is given to demonstrate the effectiveness of the proposed fusion estimation scheme.

Equivalence of wave linear repetitive processes and the singular 2-D Roesser state-space model

This paper develops a direct method for transforming a polynomial system matrix describing a discrete wave linear repetitive process to a 2-D singular state-space Roesser model description where all relevant properties, including the zero coprimeness properties of the system matrix, are retained. It is shown that the transformation is zero coprime system equivalence. The structure of the resulting system matrix in singular form and the transformation are also established.

Repetitive Process Control of Additive Manufacturing With Application to Laser Metal Deposition

Additive manufacturing (AM) is a set of manufacturing processes that have promise in the production of complex, functional structures that cannot be fabricated with conventional manufacturing, and in the repair of high-value parts. However, a significant challenge to the adoption of AM processes to these applications is proper process control. Because AM processes exhibit dynamics in two dimensions—within a layer and from one layer to the next—unconventional tools are needed to enable the necessary process control. Here, stability analysis and control design are presented for the laser metal deposition (LMD) process, based on a previously developed 2-D modeling framework. Linear repetitive process results are extended in order to analyze the stability of this class of systems. A layer-to-layer process controller is developed using a spatial dynamic model of the process and layer-domain closed-loop poles. The stability analysis and control methodology are applied to the LMD process, which is known to exhibit layer-to-layer instability in both open-loop and in-process control depositions. Walls are experimentally fabricated using constant process parameters and the proposed control methodology. The results demonstrate that the proposed control methodology is able to track the reference height and remove the unstable ripple dynamic that naturally occurred in the open-loop deposition.

Event-Triggered Recursive Filtering for Shift-Varying Linear Repetitive Processes.

This paper addresses the recursive filtering problem for shift-varying linear repetitive processes (LRPs) with limited network resources. To reduce the resource occupancy, a novel event-triggered strategy is proposed where the concern is to broadcast those necessary measurements to update the innovation information only when certain events appear. The primary goal of this paper is to design a recursive filter rendering that, under the event-triggered communication mechanism, an upper bound (UB) on the filtering error variance is ensured and then optimized by properly determining the filter gains. As a distinct kind of 2-D systems, the LRPs are cast into a general Fornasini-Marchesini model by using the lifting technique. A new definition of the triggering-shift sequence is introduced and an event-triggered rule is then constructed for the transformed system. With the aid of mathematical induction, the filtering error variance is guaranteed to have a UB which is subsequently optimized with appropriate filter parameters via solving two series of Riccati-like difference equations. Theoretical analysis further reveals the monotonicity of the filtering performance with regard to the event-triggering threshold. Finally, an illustrative simulation is given to show the feasibility of the designed filtering scheme.

Two-Dimensional Modeling and System Identification of the Laser Metal Deposition Process

Additive manufacturing (AM) processes fabricate parts by adding material in a layer-by-layer fashion. In order to enable closed-loop process control—a major hurdle in the adoption of most AM processes—compact models suitable for control design and for describing the layer-by-layer material addition process are needed. This paper proposes a two-dimensional modeling framework whereby the deposition of the current layer is affected by both in-layer and layer-to-layer dynamics, both of which are driven by the state of the previous layer. The proposed framework can be used to describe phenomena observed in AM processes such as layer rippling and large defects in laser metal deposition (LMD) processes. Further, the proposed framework can be used to create two-dimensional dynamic models for the analysis of layer-to-layer stability and as a foundation for the design of layer-to-layer controllers for AM processes. In the application to LMD, a two-dimensional linear–nonlinear–linear (LNL) repetitive process model is proposed that contains a linear dynamic component, which describes the dynamic evolution of the process from layer to layer, cascaded with a static nonlinear component cascaded with another linear dynamic component, which describes the dynamic evolution of the process within a given layer. A methodology, which leverages the two-dimensional LNL structure, for identifying the model process parameters is presented and validated with quantitative and qualitative experimental results.

Resilient Filtering for Linear Time-Varying Repetitive Processes Under Uniform Quantizations and Round-Robin Protocols

In this paper, the resilient filtering problem is investigated for a class of linear time-varying repetitive processes with communication constraints. The communication between the sensors and the remote filter, which is subject to uniform quantizations, is carried out through a shared communication medium where only one sensor has access to the network at each transmission time. To prevent data from collisions, the Round-Robin (R-R) protocol scheduling is applied to orchestrate the transmission order of sensor nodes in a periodic manner. Moreover, stochastic perturbations on the gain parameters are taken into account in the course of the actual filter implementation. The main purpose of the addressed problem is to design a resilient filter such that, in the presence of the uniform quantization, the R-R protocol, and the filter gain perturbation, a certain upper bound is guaranteed on the filtering error variance and subsequently minimized at each time instant. By means of intensive stochastic analysis and mathematical induction, sufficient condition is provided to ensure the local minimization of certain upper bound on the filtering error variance. Furthermore, the boundedness issue is also discussed with respect to the filtering error variance. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed filter strategy.

On the stability and the stabilization of linear discrete repetitive processes

This article deals with stability and stabilization issues for linear two-dimensional (2D) discrete models. More precisely, we focus on repetitive processes and Roesser models. Within the algebraic analysis approach to linear systems theory, we first show how a given linear repetitive process can be transformed into an equivalent linear Roesser model. We then prove that the structural stability is preserved by this equivalence transformation. This enables us to design new approaches for stabilizing linear repetitive processes by means of existing methods for computing a state feedback control law stabilizing a linear 2D discrete Roesser model. We also show that we can interpret the stability along the pass of a linear repetitive process as its structural stability. This implies that one of our new approaches can be applied to stabilize along the pass a linear repetitive process which is only stable from pass to pass.

Finite-Time Stability and Control of 2D Continuous–Discrete Systems in Roesser Model

This study is conducted to investigate stability and control problems within a finite-time interval for a 2D continuous–discrete system in Roesser model. The concepts of finite-time stability (FTS) and finite-time boundedness (FTB) are naturally extended to the 2D continuous–discrete system. Recursive relations between system states are first obtained, then sufficient conditions for FTS and FTB in the system are derived, and a finite-time controller is supplied to the system. Sufficient conditions for finite-time stabilization are also provided for the linear repetitive process. Examples of metal rolling operation are presented to illustrate the proposed method.

Equivalent 2-D nonsingular Roesser models for discrete linear repetitive processes

ABSTRACTThe elementary operations algorithm is used to establish that a system matrix describing a discrete linear repetitive process can be transformed to that of a 2-D nonsingular Roesser model where all the input–output properties are preserved. Moreover, the connection between these system matrices is shown to be input–output equivalence. The exact forms of the resulting system matrix and the transformation involved are established. Some areas for possible future use/application of the developed results are also briefly discussed.