Computer Aided Implementation of Estimator Based Inverse Dynamics Controller for the Control of Non-Measurable State Variables of an Autonomous Hybrid System

Abstract

Abstract-A Computer aided implementation of an estimator based inverse dynamics controller (EBIDC) algorithm for the efficient control of the states, especially the non-measurable states of an autonomous hybrid system (AHS) is proposed in this paper. Case of a cylindrical three-tank hybrid system is demonstrated. The studies combining behaviors of both discrete event and continuous systems are of utmost importance nowadays and thus study of dynamics of hybrid systems and control strategies for performance improvement is very important in the present scenario. This algorithm makes use of a state estimator for estimating all the states of the system which uses a generic nonlinear model of the actual system. The efficacy of the developed EBIDC is demonstrated by conducting simulation studies using Matlab under different operating modes of the system. Both set point tracking and disturbance rejection capabilities of the proposed controller are also confirmed in this work. The robustness of EBIDC in controlling the non-measurable states is also analyzed under different uncertainties.Index Terms-Autonomous hybrid systems, derivative-free state estimator, estimator based inverse dynamics controller, unscented kalman filter (UKF) in state estimation. I. INTRODUCTIONHybrid system is a very dynamic branch of engineering which deals with the systems of continuous, discrete time and discrete event behavior. In some of the earlier works reported, theories behind hybrid automata and the discrete control of continuous plant were considered [1], [2]. Later many approaches were reported in the literature in which the systems were considered to contain both continuous and discrete behavior and control of such systems were accomplished [3]- [16]. Subsequently studies like Lyapunov technique, applied for continuous nonlinear systems were extended to hybrid systems in [4]. Linear approximations of nonlinear systems were carried out in most of such studies as in [4] and [5]. In [6], with the help of constraint logic programming with interval arithmetic, a rigorous modeling, simulation and analysis approach for hybrid systems were proposed. A collection of modeling and classification of different benchmark hybrid systems are presented in [7]. However, direct use of nonlinear models for analysis and control of hybrid systems were reported in very few works and still it is a challenging area of research.The potential of dynamic models of hybrid systems developed in state estimation along with the modeling was investigated in [10]-[14] and [16]. Recently, using Bayesian approach, a nonlinear model of hybrid system was proposed by combining multiple local linear models in [11].Using such model a novel state identification method and predictive control of the system were proposed for a class of hybrid systems.[12], [13] had recommended an ensemble Kalman filter (EnKF) based nonlinear model predictive control (NMPC) and UKF based fault tolerant control schemes for controlling the output variables of the AHS. In addition to UKF and EnKF bas...

Experimental Investigations on Performance Comparison of EKF and ANN Based Controllers with UKF Based Controller for Autonomous Hybrid Systems with Uncertainties

“…The general block diagram of the estimator along with plant and controller is provided in Fig. 2 [22]. Different notations used in this section are similar to that in [20] Dimension and description of variables used in the algorithms are given below.…”

“…Out of different state estimation schemes, UKF based scheme is the mostly suggested technique for hybrid systems as it is suitable for highly nonlinear systems [8,9,[20][21][22]. The nonlinear and derivative free nature [21] of this algorithm makes the efficient state estimation of highly complex and nonlinear systems like hybrid systems possible.…”

“…The advantages and disadvantages of these three closed loop control schemes with the estimation methods forming the elements of such closed loop control systems, are investigated in this work with experimentations. The investigation also includes detailed performance comparison of EKFC and ANNC with existing UKFC [22] when the plant is operating under various uncertainties and operating conditions such as servo/ regulatory operations, parameter uncertainties, initial condition mismatch, system faults etc.…”

“…The nonlinear model predictive control (NMPC) in [20] and fault tolerant model predictive control in [21], for hybrid systems, utilized this in its state estimation part. UKF based inverse dynamics controller was developed in [22] for controlling the non-measurable states of the hybrid systems. During the performance analysis in [22], it is found that the performance can be improved with the reduced estimation time requirement for the UKF algorithm and with the improved robustness under real time uncertainties.…”

“…UKF based inverse dynamics controller was developed in [22] for controlling the non-measurable states of the hybrid systems. During the performance analysis in [22], it is found that the performance can be improved with the reduced estimation time requirement for the UKF algorithm and with the improved robustness under real time uncertainties. Authors have proposed methods to overcome these implementation issues [23] by designing EKF based and artificial neural network (ANN) based state estimators for estimating the states.…”