Model Predictive Control with Unscented Kalman Filter for Nonlinear Implicit Systems
A class of implicit systems is known as a more
generalized class of systems than a class of explicit systems. To
establish a control method for such a generalized class of systems, we
adopt model predictive control method which is a kind of optimal
feedback control with a performance index that has a moving
initial time and terminal time. However, model predictive control
method is inapplicable to systems whose all state variables are not
exactly known. In other words, model predictive control method is
inapplicable to systems with limited measurable states. In fact, it
is usual that the state variables of systems are measured through
outputs, hence, only limited parts of them can be used directly. It is
also usual that output signals are disturbed by process and sensor
noises. Hence, it is important to establish a state estimation method
for nonlinear implicit systems with taking the process noise and
sensor noise into consideration. To this purpose, we apply the model
predictive control method and unscented Kalman filter for solving
the optimization and estimation problems of nonlinear implicit
systems, respectively. The objective of this study is to establish a
model predictive control with unscented Kalman filter for nonlinear
Attitude Stabilization of Satellites Using Random Dither Quantization
Recently, the effectiveness of random dither
quantization method for linear feedback control systems has
been shown in several papers. However, the random dither
quantization method has not yet been applied to nonlinear feedback
control systems. The objective of this paper is to verify the
effectiveness of random dither quantization method for nonlinear
feedback control systems. For this purpose, we consider the attitude
stabilization problem of satellites using discrete-level actuators.
Namely, this paper provides a control method based on the random
dither quantization method for stabilizing the attitude of satellites
using discrete-level actuators.
Iterative Learning Control of Two Coupled Nonlinear Spherical Tanks
This paper presents modeling and control of a highly nonlinear system including, non-interacting two spherical tanks using iterative learning control (ILC). Consequently, the objective of the paper is to control the liquid levels in the nonlinear tanks. First, a proportional-integral-derivative (PID) controller is applied to the plant model as a suitable benchmark for comparison. Then, dynamic responses of the control system corresponding to different step inputs are investigated. It is found that the conventional PID control is not able to fulfill the design criteria such as desired time constant. Consequently, an iterative learning controller is proposed to accurately control the coupled nonlinear tanks system. The simulation results clearly demonstrate the superiority of the presented ILC approach over the conventional PID controller to cope with the nonlinearities presented in the dynamic system.
Unconventional Calculus Spreadsheet Functions
The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.
Actuator Fault Detection and Fault Tolerant Control of a Nonlinear System Using Sliding Mode Observer
In this work, we use the Fault detection and isolation and the Fault tolerant control based on sliding mode observer in order to introduce the well diagnosis of a nonlinear system. The robustness of the proposed observer for the two techniques is tested through a physical example. The results in this paper show the interaction between the Fault tolerant control and the Diagnosis procedure.
Fault Diagnosis of Nonlinear Systems Using Dynamic Neural Networks
This paper presents a novel integrated hybrid
approach for fault diagnosis (FD) of nonlinear systems. Unlike most
FD techniques, the proposed solution simultaneously accomplishes
fault detection, isolation, and identification (FDII) within a unified
diagnostic module. At the core of this solution is a bank of adaptive
neural parameter estimators (NPE) associated with a set of singleparameter
fault models. The NPEs continuously estimate unknown
fault parameters (FP) that are indicators of faults in the system. Two
NPE structures including series-parallel and parallel are developed
with their exclusive set of desirable attributes. The parallel scheme is
extremely robust to measurement noise and possesses a simpler, yet
more solid, fault isolation logic. On the contrary, the series-parallel
scheme displays short FD delays and is robust to closed-loop system
transients due to changes in control commands. Finally, a fault
tolerant observer (FTO) is designed to extend the capability of the
NPEs to systems with partial-state measurement.
Identification of Nonlinear Systems Using Radial Basis Function Neural Network
This paper uses the radial basis function neural
network (RBFNN) for system identification of nonlinear systems.
Five nonlinear systems are used to examine the activity of RBFNN in
system modeling of nonlinear systems; the five nonlinear systems are
dual tank system, single tank system, DC motor system, and two
academic models. The feed forward method is considered in this
work for modelling the non-linear dynamic models, where the KMeans
clustering algorithm used in this paper to select the centers of
radial basis function network, because it is reliable, offers fast
convergence and can handle large data sets. The least mean square
method is used to adjust the weights to the output layer, and
Euclidean distance method used to measure the width of the Gaussian
Identification of Nonlinear Systems Structured by Hammerstein-Wiener Model
Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.
Gaussian Process Model Identification Using Artificial Bee Colony Algorithm and Its Application to Modeling of Power Systems
This paper presents a nonparametric identification of
continuous-time nonlinear systems by using a Gaussian process
(GP) model. The GP prior model is trained by artificial bee colony
algorithm. The nonlinear function of the objective system is estimated
as the predictive mean function of the GP, and the confidence
measure of the estimated nonlinear function is given by the predictive
covariance of the GP. The proposed identification method is applied
to modeling of a simplified electric power system. Simulation results
are shown to demonstrate the effectiveness of the proposed method.
Backstepping Sliding Mode Controller Coupled to Adaptive Sliding Mode Observer for Interconnected Fractional Nonlinear System
Performance control law is studied for an
interconnected fractional nonlinear system. Applying a backstepping
algorithm, a backstepping sliding mode controller (BSMC) is
developed for fractional nonlinear system. To improve control law
performance, BSMC is coupled to an adaptive sliding mode observer
have a filtered error as a sliding surface. The both architecture
performance is studied throughout the inverted pendulum mounted on
a cart. Simulation result show that the BSMC coupled to an adaptive
sliding mode observer have stable control law and eligible control
amplitude than the BSMC.
Generalized Differential Quadrature Nonlinear Consolidation Analysis of Clay Layer with Time-Varied Drainage Conditions
In this article, the phenomenon of nonlinear
consolidation in saturated and homogeneous clay layer is studied.
Considering time-varied drainage model, the excess pore water
pressure in the layer depth is calculated. The Generalized Differential
Quadrature (GDQ) method is used for the modeling and numerical
analysis. For the purpose of analysis, first the domain of independent
variables (i.e., time and clay layer depth) is discretized by the
Chebyshev-Gauss-Lobatto series and then the nonlinear system of
equations obtained from the GDQ method is solved by means of the
Newton-Raphson approach. The obtained results indicate that the
Generalized Differential Quadrature method, in addition to being
simple to apply, enjoys a very high accuracy in the calculation of
excess pore water pressure.
Trajectory Estimation and Control of Vehicle using Neuro-Fuzzy Technique
Nonlinear system identification is becoming an important tool which can be used to improve control performance. This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for controlling a car. The vehicle must follow a predefined path by supervised learning. Backpropagation gradient descent method was performed to train the ANFIS system. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in controlling the non linear system.
Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems
This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.
Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI
Design of an observer based controller for a class of
fractional order systems has been done. Fractional order mathematics
is used to express the system and the proposed observer. Fractional
order Lyapunov theorem is used to derive the closed-loop asymptotic
stability. The gains of the observer and observer based controller are
derived systematically using the linear matrix inequality approach.
Finally, the simulation results demonstrate validity and effectiveness
of the proposed observer based controller.
Robust Integrated Navigation of a Low Cost System
Robust nonlinear integrated navigation of GPS and
low cost MEMS is a hot topic of research these days. A robust filter
is required to cope up with the problem of unpredictable
discontinuities and colored noises associated with low cost sensors.
H∞ filter is previously used in Extended Kalman filter and Unscented
Kalman filter frame. Unscented Kalman filter has a problem of
Cholesky matrix factorization at each step which is a very unstable
operation. To avoid this problem in this research H∞ filter is
designed in Square root Unscented filter framework and found 50%
more robust towards increased level of colored noises.
Identification of a PWA Model of a Batch Reactor for Model Predictive Control
The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.
Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization
This paper discusses a design of nonlinear observer by
a formal linearization method using an application of Chebyshev Interpolation
in order to facilitate processes for synthesizing a nonlinear
observer and to improve the precision of linearization.
A dynamic nonlinear system is linearized with respect to a linearization
function, and a measurement equation is transformed into
an augmented linear one by the formal linearization method which is
based on Chebyshev interpolation. To the linearized system, a linear
estimation theory is applied and a nonlinear observer is derived. To
show effectiveness of the observer design, numerical experiments
are illustrated and they indicate that the design shows remarkable
performances for nonlinear systems.
Adaptive Sliding Mode Observer for a Class of Systems
In this paper, the performance of two adaptive
observers applied to interconnected systems is studied. The
nonlinearity of systems can be written in a fractional form. The first
adaptive observer is an adaptive sliding mode observer for a Lipchitz
nonlinear system and the second one is an adaptive sliding mode
observer having a filtered error as a sliding surface. After comparing
their performances throughout the inverted pendulum mounted on a
car system, it was shown that the second one is more robust to
estimate the state.
Stable Robust Adaptive Controller and Observer Design for a Class of SISO Nonlinear Systems with Unknown Dead Zone
This paper presents a new stable robust adaptive controller and observer design for a class of nonlinear systems that contain i. Coupling of unmeasured states and unknown parameters ii. Unknown dead zone at the system actuator. The system is firstly cast into a modified form in which the observer and parameter estimation become feasible. Then a stable robust adaptive controller, state observer, parameter update laws are derived that would provide global adaptive system stability and desirable performance. To validate the approach, simulation was performed to a single-link mechanical system with a dynamic friction model and unknown dead zone exists at the system actuation. Then a comparison is presented with the results when there is no dead zone at the system actuation.
Design of Nonlinear Observer by Using Augmented Linear System based on Formal Linearization of Polynomial Type
The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.
Dispenser Longitudinal Movement ControlDesign Based on Auto - Disturbances –Rejection - Controller
Based on the feature of model disturbances and uncertainty being compensated dynamically in auto – disturbances-rejection-controller (ADRC), a new method using ADRC is proposed for the decoupling control of dispenser longitudinal movement in big flight envelope. Developed from nonlinear model directly, ADRC is especially suitable for dynamic model that has big disturbances. Furthermore, without changing the structure and parameters of the controller in big flight envelope, this scheme can simplify the design of flight control system. The simulation results in big flight envelope show that the system achieves high dynamic performance, steady state performance and the controller has strong robustness.
Auto Regressive Tree Modeling for Parametric Optimization in Fuzzy Logic Control System
The advantage of solving the complex nonlinear
problems by utilizing fuzzy logic methodologies is that the
experience or expert-s knowledge described as a fuzzy rule base can
be directly embedded into the systems for dealing with the problems.
The current limitation of appropriate and automated designing of
fuzzy controllers are focused in this paper. The structure discovery
and parameter adjustment of the Branched T-S fuzzy model is
addressed by a hybrid technique of type constrained sparse tree
algorithms. The simulation result for different system model is
evaluated and the identification error is observed to be minimum.
Neuro-Fuzzy Network Based On Extended Kalman Filtering for Financial Time Series
The neural network's performance can be measured by efficiency and accuracy. The major disadvantages of neural network approach are that the generalization capability of neural networks is often significantly low, and it may take a very long time to tune the weights in the net to generate an accurate model for a highly complex and nonlinear systems. This paper presents a novel Neuro-fuzzy architecture based on Extended Kalman filter. To test the performance and applicability of the proposed neuro-fuzzy model, simulation study of nonlinear complex dynamic system is carried out. The proposed method can be applied to an on-line incremental adaptive learning for the prediction of financial time series. A benchmark case studie is used to demonstrate that the proposed model is a superior neuro-fuzzy modeling technique.
Emotional Learning based Intelligent Robust Adaptive Controller for Stable Uncertain Nonlinear Systems
In this paper a new control strategy based on Brain
Emotional Learning (BEL) model has been introduced. A modified
BEL model has been proposed to increase the degree of freedom,
controlling capability, reliability and robustness, which can be
implemented in real engineering systems.
The performance of the proposed BEL controller has been
illustrated by applying it on different nonlinear uncertain systems,
showing very good adaptability and robustness, while maintaining
Stability Analysis of a Class of Nonlinear Systems Using Discrete Variable Structures and Sliding Mode Control
This paper presents the application of discrete-time
variable structure control with sliding mode based on the 'reaching
law' method for robust control of a 'simple inverted pendulum on
moving cart' - a standard nonlinear benchmark system. The
controllers designed using the above techniques are completely
insensitive to parametric uncertainty and external disturbance. The
controller design is carried out using pole placement technique to find
state feedback gain matrix , which decides the dynamic behavior
of the system during sliding mode. This is followed by feedback gain
realization using the control law which is synthesized from 'Gao-s
reaching law'. The model of a single inverted pendulum and the
discrete variable structure control controller are developed, simulated
in MATLAB-SIMULINK and results are presented. The response of
this simulation is compared with that of the discrete linear quadratic
regulator (DLQR) and the advantages of sliding mode controller over
DLQR are also presented
Neuro-Hybrid Models for Automotive System Identification
In automotive systems almost all steps concerning the
calibration of several control systems, e.g., low idle governor or
boost pressure governor, are made with the vehicle because the timeto-
production and cost requirements on the projects do not allow for
the vehicle analysis necessary to build reliable models. Here is
presented a procedure using parametric and NN (neural network)
models that enables the generation of vehicle system models based
on normal ECU engine control unit) vehicle measurements. These
models are locally valid and permit pre and follow-up calibrations so
that, only the final calibrations have to be done with the vehicle.
A Supervisory Scheme for Step-Wise Safe Switching Controllers
A supervisory scheme is proposed that implements Stepwise Safe Switching Logic. The functionality of the supervisory scheme is organized in the following eight functional units: Step- Wise Safe Switching unit, Common controllers design unit, Experimentation unit, Simulation unit, Identification unit, Trajectory cruise unit, Operating points unit and Expert system unit. The supervisory scheme orchestrates both the off-line preparative actions, as well as the on-line actions that implement the Stepwise Safe Switching Logic. The proposed scheme is a generic tool, that may be easily applied for a variety of industrial control processes and may be implemented as an automation software system, with the use of a high level programming environment, like Matlab.