scholarly journals Design of Controller for Large Scale Uncertain Systems via Reduces Order Model

2020 ◽  
Vol 6 (12) ◽  
pp. 262-267
Author(s):  
Vudikala Lalitha and Dr. T Narasimhulu
Keyword(s):  
Uncertain Systems ◽  
Large Scale ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
High Order ◽  
Reduced Order Model ◽  
Order System ◽  
Order Model ◽  
Reduced Order ◽  
High Order System

In This paper, a method of designing the Controller for large scale uncertain systems. The Controller is designed via a reduced order model for a given high order system. An optimized reduced order model is derived with minimum ISE. The proposed method guarantees stability of the reduced model, if the original high order system is stable system. A PID controller is designed for the high order original systems through its low order model proposed. This paper presents an improvement to generalized least squares method of model order reduction. The improvement enhances the flexibility of the method with very little computational requirement. The reduction procedure is simple, efficient and always generates stable reduced models for the stable high order systems. The proposed method is illustrated with typical numerical examples taken from the literature and the results are compared with the other existing methods to show its superiority.

Event-triggered sliding mode control for a high-order system via reduced-order model based design

Automatica ◽  
2020 ◽  
Vol 121 ◽  
pp. 109163 ◽  
Author(s):  
Kiran Kumari ◽  
Bijnan Bandyopadhyay ◽  
Johann Reger ◽  
Abhisek K. Behera
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
High Order ◽  
Reduced Order Model ◽  
Order System ◽  
Order Model ◽  
Reduced Order ◽  
High Order System ◽  
Model Based ◽  
Event Triggered

scholarly journals Higher Order Reduction of Uncertain Systems: Affine Arithmeti

2021 ◽  
Vol 08 (1&2) ◽  
pp. 1-4
Author(s):  
H Mallesam Dora ◽  
Keyword(s):  
Uncertain Systems ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order System ◽  
Effective Algorithm ◽  
Order Model ◽  
Reduced Order ◽  
Numerical Examples ◽  
Rigorous Study ◽  
Lower Order System

In this paper the Modified Routh Approximation (MRA) and Affine Arithmetic (AA) methods are investigates for obtaining the reduced order model (ROM) of SISO, discrete & MIMO uncertain systems into lower order system. Rigorous study and analysis of physical system direct to the outcome of systems with uncertainty instead of certain coefficients. Thus, systems having uncertain but bounded parameters known as uncertain systems are under consideration in this paper. An effective algorithm to determine the reduced order model is proposed here. This proposed methodology is verified using numerical examples available from the literature.

Control of Asymmetric Systems Using Complex Modes

1991 ◽  
Author(s):  
G. W. Fan ◽  
H. D. Nelson
Keyword(s):  
Normal Modes ◽  
Original System ◽  
High Order ◽  
Reduced Order Model ◽  
Order System ◽  
Matrix Transformations ◽  
Linear Quadratic ◽  
Order Model ◽  
Reduced Order ◽  
Complex Modes

Abstract The complex modal approach is introduced for the optimal vibration control (Linear Quadratic Regulator) of high-order nonsymmetric discrete systems. An LQ regulator is designed based on a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex coordinates are derived. A 52 degree-of-freedom finite element based rotordynamic system is used for illustration. Simulation results show that an LQ regulator based on a reduced-order system obtained by using normal modes of a high-order system with asymmetric models can possibly destabilize the original system i.e., the spill-over problem (Ulsoy, 1984), however, this problem might be avoided by applying complex modes which provides a more accurate reduced-order model than obtained by normal modes. Comparison of the reduced-order models using normal modes and complex modes is presented. Frequency, time transient and steady state responses of the controlled and uncontrolled systems are also shown.

Model Order Reduction of Transmission Line Model

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Transmission Line ◽  
Large Scale ◽  
Original System ◽  
Reduced Order Model ◽  
Benchmark Problems ◽  
Transmission Line Model ◽  
Order Model ◽  
Line Model ◽  
Reduced Order ◽  
Numerical Effort

Transmission Line model are an important role in the electrical power supply. Modeling of such system remains a challenge for simulations are necessary for designing and controlling modern power systems.In order to analyze the numerical approach for a benchmark collection Comprehensive of some needful real-world examples, which can be utilized to evaluate and compare mathematical approaches for model reduction. The approach is based on retaining the dominant modes of the system and truncation comparatively the less significant once.as the reduced order model has been derived from retaining the dominate modes of the large-scale stable system, the reduction preserves the stability. The strong demerit of the many MOR methods is that, the steady state values of the reduced order model does not match with the higher order systems. This drawback has been try to eliminated through the Different MOR method using sssMOR tools. This makes it possible for a new assessment of the error system Offered that the Observability Gramian of the original system has as soon as been thought about, an H∞ and H2 error bound can be calculated with minimal numerical effort for any minimized model attributable to The reduced order model (ROM) of a large-scale dynamical system is essential to effortlessness the study of the system utilizing approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. the application of Approximation methods is offered for arising ROM of the large-scale LTI systems which consist of benchmark problems. The time response of approximated system, assessed by the proposed method, is also shown which is excellent matching of the response of original system when compared to the response of other existing approaches .

scholarly journals Event-triggered Discrete-time Sliding Mode Control for High-order Systems via Reduced-order Model Approach

2020 ◽  
Vol 53 (2) ◽  
pp. 6207-6212
Author(s):  
Kiran Kumari ◽  
Bijnan Bandyopadhyay ◽  
Johann Reger ◽  
Abhisek K. Behera
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
High Order ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Mode Control ◽  
Event Triggered ◽  
Model Approach

scholarly journals Order Reduction based on Coulomb’s and Franklin’s laws Algorithm

2021 ◽  
Author(s):  
Ram Kumar ◽  
Afzal Sikander
Keyword(s):  
Large Scale ◽  
Linear Time ◽  
Order Reduction ◽  
Absolute Error ◽  
Search Space ◽  
Engineering Problem ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Linear Time Invariant

Abstract The Coulomb and Franklin laws (CFL) algorithm is used to construct a lower order model of higher-order continuous time linear time-invariant (LTI) systems in this study. CFL is quite easy to implement in obtaining reduced order model of large scale system in control engineering problem as it employs the combined effect of Coulomb’s and Franklin’s laws to find the best values in search space. The unknown coefficients are obtained using the CFLA methodology, which minimises the integral square error (ISE) between the original and proposed ROMs. To achieve the reduced order model, five practical systems of different orders are considered. Finally, multiple performance indicators such as the ISE, integral of absolute error (IAE), and integral of time multiplied by absolute error were calculated to determine the efficacy of the proposed methodology. The simulation results were compared to previously published well-known research.

Comparison between RST and PID controllers performance of a reduced order model and the original model of a hydraulic actuator dedicated to a semi-active suspension

2016 ◽  
Vol 13 (1) ◽  
pp. 66-71 ◽  
Author(s):  
Saad Babesse ◽  
Djameleddine Ameddah ◽  
Fouad Inel
Keyword(s):  
Transfer Functions ◽  
Linear Time ◽  
Active Suspension ◽  
High Order ◽  
Reduced Order Model ◽  
Hydraulic Actuator ◽  
Order Model ◽  
Content Type ◽  
Reduced Order ◽  
Real Process

Purpose In this paper, an effective method to calculate the reduced-order model (ROM) of high-order linear time-invariant system is elaborated; this is done by evaluating time moments of the original high-order model (HOM). Design/methodology/approach The developed method has been applied to a hydraulic actuator of antiroll bar mechanism dedicated to heavy vehicle semi-active suspension. And as the actuator is a large-scale system; and that in this case, the only control applied is a classical control and with trial and error procedure (like PID), the use of an order reduction method is necessary. Hence, the actuator that has an eighth-order transfer function with uncontrollable states has been approximated by fully controllable second-order model, which is suitable for feedback controllers (RST, LQR […]). The RST control is applied to control the roll angle of the actuator and simulations are carried out to show the effectiveness of the procedure. Findings It is clear that RST shows good tracking as compared to PID. For further work, the given RST controller has a discrete character and can be easily implemented on the real process and then as a further simulation, one can use another controller such as fractional adaptive controller. Originality/value In the recent years, the technological need of modeling order, thus the complexity of the systems, directed the researchers toward the reduction of order of these systems, not only to facilitate the analysis but also to find a suitable approximation of the high-order systems while keeping the same important characteristics as closely as possible. Several methods are available but they fail to give stable transfer functions or important characteristics of the original system.

Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

2009 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Fundamental Solution ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

Sign in / Sign up

Export Citation Format

Share Document