Formation control of longitudinal vehicular platoons under generic network topology with heterogeneous time delays

2018 ◽  
Vol 25 (3) ◽  
pp. 655-665 ◽  
Author(s):  
Hossein Chehardoli ◽  
Ali Ghasemi
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Formation Control ◽  
Vehicular Networks ◽  
Closed Loop ◽  
Linear Time ◽  
Characteristic Root ◽  
Multiple Delays ◽  
Loop Dynamics ◽  
The Stability

The problem of third-order consensus of homogeneous vehicular platoons in the presence of communication and parasitic delays is investigated. The communication topology of vehicular networks is assumed to be directed and generic. Therefore, a number of eigenvalues of the network’s matrix are complex, entangling the stability analysis of the closed-loop dynamics. By considering both communication and parasitic delays, a new linear centralized consensus protocol is designed for each vehicle. It will be shown that the closed-loop dynamics of vehicular networks with generic topology is in the form of linear systems with multiple delays. By presenting a new approach, the resultant linear time delay system is decoupled to individual third- and sixth-order dynamical equations. By performing the stability analysis of the new equations, it will be proven that the control parameters are independent of the network’s topology. Therefore, the control design and stability analysis will be significantly simplified compared with previous studies. To find the stable regions of time delay, the cluster treatment characteristic root method is employed. Simulation results are provided to show the effectiveness of the proposed approach.

Active Vibration Suppression With Time Delayed Feedback

2003 ◽  
Vol 125 (3) ◽  
pp. 384-388 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Vibration Suppression ◽  
Linear Time ◽  
Direct Method ◽  
System Stability ◽  
Delayed Systems ◽  
Active Vibration Suppression ◽  
Active Vibration ◽  
The Stability

Various active vibration suppression techniques, which use feedback control, are implemented on the structures. In real application, time delay can not be avoided especially in the feedback line of the actively controlled systems. The effects of the delay have to be thoroughly understood from the perspective of system stability and the performance of the controlled system. Often used control laws are developed without taking the delay into account. They fulfill the design requirements when free of delay. As unavoidable delay appears, however, the performance of the control changes. This work addresses the stability analysis of such dynamics as the control law remains unchanged but carries the effect of feedback time-delay, which can be varied. For this stability analysis along the delay axis, we follow up a recent methodology of the authors, the Direct Method (DM), which offers a unique and unprecedented treatment of a general class of linear time invariant time delayed systems (LTI-TDS). We discuss the underlying features and the highlights of the method briefly. Over an example vibration suppression setting we declare the stability intervals of the dynamics in time delay space using the DM. Having assessed the stability, we then look at the frequency response characteristics of the system as performance indications.

Efficient Computation of Stability Charts for Linear Time Delay Systems

2005 ◽  
Author(s):  
Dimitri Breda ◽  
Stefano Maset ◽  
Rossana Vermiglio
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Computational Cost ◽  
Characteristic Root ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Efficient Computation ◽  
Square Grid ◽  
Stability Chart ◽  
The Stability

A new efficient algorithm for the computation of the stability chart of linear time delay systems is proposed and tested on several examples. The stability chart is obtained by investigating the 2d-parameter space by a first coarse square grid which is then adaptively refined by triangulation to match the desired tolerance. This leads to a considerable reduction in computational cost with respect to investigate a uniform fine square grid. Stability of each point is determined by approximating the rightmost characteristic root real part via a numerical scheme recently developed by the authors and based on pseudospectral differencing methods. A Matlab code is included in appendix.

scholarly journals Practical Computational Approach for the Stability Analysis of Fuzzy Model-Based Predictive Control of Substrate and Biomass in Activated Sludge Processes

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 531
Author(s):  
Pedro M. Vallejo LLamas ◽  
Pastora Vega
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Activated Sludge ◽  
Predictive Control ◽  
Closed Loop ◽  
Complex Dynamics ◽  
Linear Time ◽  
Fuzzy Model ◽  
The Stability ◽  
The Mathematical Model

This paper presents a procedure for the closed-loop stability analysis of a certain variant of the strategy called Fuzzy Model-Based Predictive Control (FMBPC), with a model of the Takagi-Sugeno type, applied to the wastewater treatment process known as the Activated Sludge Process (ASP), with the aim of simultaneously controlling the substrate concentration in the effluent (one of the main variables that should be limited according to environmental legislations) and the biomass concentration in the reactor. This case study was chosen both for its environmental relevance and for special process characteristics that are of great interest in the field of nonlinear control, such as strong nonlinearity, multivariable nature, and its complex dynamics, a consequence of its biological nature. The stability analysis, both of fuzzy systems (FS) and the very diverse existing strategies of nonlinear predictive control (NLMPC), is in general a mathematically laborious task and difficult to generalize, especially for processes with complex dynamics. To try to minimize these difficulties, in this article, the focus was placed on the mathematical simplification of the problem, both with regard to the mathematical model of the process and the stability analysis procedures. Regarding the mathematical model, a state-space model of discrete linear time-varying (DLTV), equivalent to the starting fuzzy model (previously identified), was chosen as the base model. Furthermore, in a later step, the DLTV model was approximated to a local model of type discrete linear time-invariant (DLTI). As regards the stability analysis itself, a computational method was developed that greatly simplified this difficult task (in a local environment of an operating point), compared to other existing methods in the literature. The use of the proposed method provides useful conclusions for the closed-loop stability analysis of the considered FMBPC strategy, applied to an ASP process; at the same time, the possibility that the method may be useful in a more general way, for similar fuzzy and predictive strategies, and for other complex processes, was observed.

Degenerate Cases in Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Linear Time ◽  
Direct Method ◽  
Degenerate System ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
The Stability ◽  
Time Invariant ◽  
Degenerate Cases

A practical stability analysis, the Direct Method, for linear time invariant, time delayed systems (LTI-TDS) is revisited in this work considering the degenerate system dynamics. The principal strengths and enabling novelties of the method are reviewed along with its structured steps involved for assessing the stability. Uncommon in the literature, the Direct Method can handle large dimensional systems (e.g. larger than 2) very comfortably, it returns an explicit formula for the exact stability posture of the system for a given time delay, as such it reveals the possible detached stability pockets throughout the time delay axis. Both retarded and neutral classes of LTI-TDS are considered in this work. The main contribution here is to demonstrate the ability of the Direct Method in tackling degenerate cases. Along with the analytical arguments, example case studies are provided for a group of degeneracies. It is shown that the new method is capable of resolving them without any difficulty.

Degenerate Cases in Using the Direct Method

2003 ◽  
Vol 125 (2) ◽  
pp. 194-201 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Linear Time ◽  
Direct Method ◽  
Degenerate System ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
The Stability ◽  
Time Invariant ◽  
Degenerate Cases

A recent stability analysis, the Direct Method, for linear time invariant, time delayed systems (LTI-TDS) is revisited in this work considering the degenerate system dynamics. The principal strengths and enabling novelties of the method are reviewed along with its structured steps involved for assessing the stability. Uncommon in the literature, the Direct Method can handle large dimensional systems (e.g., larger than two) very comfortably. It returns an explicit formula for the exact stability posture of the system for a given time delay, as such it reveals the possible detached stability pockets throughout the time delay axis. Both retarded and neutral classes of LTI-TDS are considered in this work. The main contribution here is to demonstrate the ability of the Direct Method in tackling degenerate cases. Along with the analytical arguments, example case studies are provided for a group of degeneracies. It is shown that the new method is capable of resolving them without any difficulty.

Kernel and Offspring Concepts for the Stability Robustness of Multiple Time Delayed Systems (MTDS)

2006 ◽  
Vol 129 (3) ◽  
pp. 245-251 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
Characteristic Root ◽  
Invariance Property ◽  
Multiple Time ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Robustness ◽  
The Stability

A novel treatment for the stability of linear time invariant (LTI) systems with rationally independent multiple time delays is presented in this paper. The independence of delays makes the problem much more challenging compared to systems with commensurate time delays (where the delays have rational relations). We uncover some wonderful features for such systems. For instance, all the imaginary characteristic roots of these systems can be found exhaustively along a set of surfaces in the domain of the delays. They are called the “kernel” surfaces (curves for two-delay cases), and it is proven that the number of the kernel surfaces is manageably small and bounded. All possible time delay combinations, which yield an imaginary characteristic root, lie either on this kernel or its infinitely many “offspring” surfaces. Another hidden feature is that the root tendencies along these surfaces exhibit an invariance property. From these outstanding characteristics an efficient, exact, and exhaustive methodology results for the stability assessment. As an added uniqueness of this method, the systems under consideration do not have to be stable for zero delays. Several example case studies are presented, which are prohibitively difficult, if not impossible to solve using any other peer methodology known to the authors.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Sign in / Sign up

Export Citation Format

Share Document