Scheduling Strategy Using Frequency Transition for a Helicopter Simulation as a Network Control System Approximation

Oscar Esquivel-Flores, Hector Benítez-Pérez, Paul Méndez-Monrroy
Posgrado en Ciencia e Ingenieria de la Computacion, U.N.A.M.
Mexico

I.I.M.A.S., D.I.S.C.A., U.N.A.M.
Apdo. Postal 20-706, Del. A. Obregon, C.P. 01000, Mexico

Posgrado en Ingenieria, U.N.A.M.
Mexico

Abstract: This paper describes a scheduling strategy for a real time distributed system based on modifying the transmission frequency of nodes in a communication network. Scheduling is critical as it impacts the system performance due to limited computing resources. This work presents a linear time invariant model based on the frequency transition of nodes in distributed system. In this model a Linear Quadratic Regulator (LQR) controller is designed to schedule the transmission frequency of nodes. The controller assigns the transmission frequency into a region with minimum and maximum bounds intended to satisfy the network’s utility. A 2DOF helicopter simulation shows the effectiveness of this scheduling strategy.

Keywords: Distributed Systems, Real-Time, Control, Frequency transmission.

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CITE THIS PAPER AS:
Oscar ESQUIVEL-FLORES, Hector BENÍTEZ-PÉREZ, Paul MÉNDEZ-MONRROY, Scheduling Strategy Using Frequency Transition for a Helicopter Simulation as a Network Control System Approximation, Studies in Informatics and Control, ISSN 1220-1766, vol. 21 (4), pp. 393-402, 2012. https://doi.org/10.24846/v21i4y201205

1. Introduction

In recent years Real Time Distributed Systems (RTDS) have become widely used in industry and in research, such as mission-critical and long-running applications; thus they need to maintain consistency or recover from errors without suspending execution. Characteristics of RTDS include the ability to complete within time restrictions, and to provide coherence, adaptability, and stability. Recent applications of RTDS with time restrictions are implementations of Networked Control Systems (NCS), which consist of several nodes which participate in the control process and sensor/actuator activities. In order to achieve the overall objectives of all tasks in a global and distributed manner, it is necessary that each node exchanges their own information properly through communication media in a real time environment [7]. In these applications, the time requirements of a NCS must be scheduled. In general there are two types of tasks in a NCS.

The first is a periodic task that is time-triggered, in which tasks have a transmission time c_i a constant period of execution p_i, and a deadline d_i. The second type of task is aperiodic. Thus, the sum of the transmission times of n nodes’ tasks, divided into their periods p_i for a fixed priority scheduler [11], is feasible if:

(1)

Due to optimum fixed priority scheduler possesses an upper bound to processor utilization [6] is necessary to consider (1) for each node involved in the distributed system. The network scheduler is critical in a NCS, since if there is no scheduling between nodes, data transmissions may occur simultaneously leading to collisions or bandwidth violations. This behaviour results in transmission with time delays, leading to failure in complying with deadlines, data loss, and subsequent decrease in system performance. A good scheduling control algorithm minimizes the decrease in system performance [1]; nevertheless, there are no global schedulers that guarantee optimal system performance [8]. Some strategies include methods for nodes to generate proper control actions in order to optimally utilize bandwidth [4,5]. In the digital control case, the performance only depends on the sampling frequency without uncertainties. In the digital control case, the performance only depends on the sampling frequency without uncertainties. For networked control frequency transmission (FT) is a significant factor. The minimum FT f_b is necessary to guarantee good system performance without decreasing the network performance. As the FT increases the system performance improves; however, the load on the network also increases until a maximum FT f_c is reached, then the system performance decreases because the network performance is overloaded.

It is very important to modify the FT to obtain better system performance within a bounded region that is particularly defined for the current system needs. This paper presents a scheduling strategy for modifying the FT of nodes in a distributed system by controlling the transmission frequency relations. We propose a linear model in which the coefficients of the state matrix are the relations between the transmission frequencies of each node. The model uses an LQR feedback controller to modify the FT in a region located between the maximum and minimum bounds to ensure system schedulability. This network system is modelled as linear since the scheduling transitions are within a context of normal and periodic responses, although this is not always a normal condition in these types of systems. This idea is reinforced through a 2DOF helicopter simulation benchmark. This case provides a good approximation of a system response in which the main results are perform under a typical fault scenario for demonstration proposes. The FTs are discrete; thus, they change the observed phenomenon over a specific time. The transition period corresponds to a systematic observation of the phenomenon, and the minimum period is that of the possible tasks related to this modification. The phenomenon represents non-linear situations with respect to sudden changes in states, failure situations, situations, or saturation in the channel or traffic, among others. However; it is possible to propose a linear model in the context of proper use of the network, thereby deferring the modelling of nonlinearity in these systems until future work. The aim of this work is to tune the frequency for task communications based on real-time constraints and scheduling. A goal is to maintain the schedulability and thus the viability of the communication. The synchronization issue is outside the scope of this paper. The rest of this paper is organized as follows. Section 2 describes a FT model and proposes the matrix coefficients of the model. Section 3 presents a particular NCS as a study case, and Section 4 describes the numerical simulations of the presented model and the performance of the LQR controller. Brief conclusions are presented at the end.

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