Nonlinear Observers for Constrained Systems

2009 ◽  
Author(s):  
Giscard A. Kfoury ◽  
Nabil G. Chalhoub
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
The State ◽  
Constrained Systems ◽  
State Variables ◽  
Nonlinear Observers ◽  
Constraint Equations ◽  
Single Cylinder Engine ◽  
Robust Observers ◽  
Selection Of

Three procedures for designing robust observers to estimate the state variables of nonlinear constrained systems have been developed in this work. All observers are based on the sliding mode methodology and assume that the number of transducers matches that of the degrees of freedom of the system. The conceptual differences between the proposed observer designs are in the number and selection of the sliding surfaces along with the formulations pertaining to their nominal models. The observers have been applied to estimate the state variables of a crank-slider mechanism of a single cylinder engine. The simulation results demonstrate the capabilities of the observers in accurately estimating the state variables of the system, including the superfluous ones, in the presence of significant structured and unstructured uncertainties. In addition, the results show that the nominal constraint equations are satisfied by the estimated state variables.

A Method for Solving Large-Scale Multiloop Constrained Dynamical Systems Using Structural Decomposition

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Tao Xiong ◽  
Jianwan Ding ◽  
Yizhong Wu ◽  
Liping Chen ◽  
Wenjie Hou
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
The State ◽  
State Variables ◽  
Structural Decomposition ◽  
Multiple Degrees Of Freedom ◽  
Constraint Equations ◽  
Constrained Dynamical Systems ◽  
Algebraic Constraint

A structural decomposition method based on symbol operation for solving differential algebraic equations (DAEs) is developed. Constrained dynamical systems are represented in terms of DAEs. State-space methods are universal for solving DAEs in general forms, but for complex systems with multiple degrees-of-freedom, these methods will become difficult and time consuming because they involve detecting Jacobian singularities and reselecting the state variables. Therefore, we adopted a strategy of dividing and conquering. A large-scale system with multiple degrees-of-freedom can be divided into several subsystems based on the topology. Next, the problem of selecting all of the state variables from the whole system can be transformed into selecting one or several from each subsystem successively. At the same time, Jacobian singularities can also be easily detected in each subsystem. To decompose the original dynamical system completely, as the algebraic constraint equations are underdetermined, we proposed a principle of minimum variable reference degree to achieve the bipartite matching. Subsequently, the subsystems are determined by aggregating the strongly connected components in the algebraic constraint equations. After that determination, the free variables remain; therefore, a merging algorithm is proposed to allocate these variables into each subsystem optimally. Several examples are given to show that the proposed method is not only easy to implement but also efficient.

Robust active disturbance attenuation control of an uncertain quadrotor

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nigar Ahmed ◽  
Ajeet kumar Bhatia ◽  
Syed Awais Ali Shah
Keyword(s):  
Control Algorithm ◽  
Sliding Mode ◽  
The State ◽  
Disturbance Attenuation ◽  
State Variables ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Content Type ◽  
Highly Nonlinear ◽  
The Stability

PurposeThe aim of this research is to design a robust active disturbance attenuation control (RADAC) technique combined with an extended high gain observer (EHGO) and low pass filter (LPF).Design/methodology/approachFor designing a RADAC technique, the sliding mode control (SMC) method is used. Since the standard method of SMC exhibits a chattering phenomenon in the controller, a multilayer sliding mode surface is designed for avoiding the chattering. In addition, to attenuate the unwanted uncertainties and disturbances (UUDs), the techniques of EHGO and LPF are deployed. Besides acting as a patch for disturbance attenuation, the EHGO design estimates the state variables. To investigate the stability and effectiveness of the designed control algorithm, the stability analysis followed by the simulation study is presented.FindingsThe major findings include the design of a chattering-free RADAC controller based on the multilayer sliding mode surface. Furthermore, a criterion of integrating the LPF scheme within the EHGO scheme is also developed to attenuate matched and mismatched UUDs.Practical implicationsIn practice, the quadrotor flight is opposed by different kinds of the UUDs. And, the model of the quadrotor is a highly nonlinear underactuated model. Thus, the dynamics of the quadrotor model become more complex and uncertain due to the additional UUDs. Hence, it is necessary to design a robust disturbance attenuation technique with the ability to estimate the state variables and attenuate the UUDs and also achieve the desired control objectives.Originality/valueDesigning control methods to attenuate the disturbances while assuming that the state variables are known is a common practice. However, investigating the uncertain plants with unknown states along with the disturbances is rarely taken in consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the UUDs as well as investigate a criterion to reduce the chattering incurred in the controller due to the standard SMC algorithm.

Adaptive output-feedback robust active disturbance rejection control for uncertain quadrotor with unknown disturbances

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nigar Ahmed ◽  
Syed Awais Ali Shah
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
Sliding Mode ◽  
The State ◽  
Active Disturbance Rejection Control ◽  
State Variables ◽  
Content Type ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control ◽  
Attitude Model

PurposeIn this research paper, an adaptive output-feedback robust active disturbance rejection control (RADRC) is designed for the multiple input multiple output (MIMO) quadrotor attitude model subject to unwanted uncertainties and disturbances (UUDs).Design/methodology/approachIn order to achieve the desired control objectives in the presence of UUDs, the low pass filter (LPF) and extended high gain observer (EHGO) methods are used for the estimation of matched and mismatched UUDs, respectively. Furthermore, for solving the chattering incurred in the standard sliding mode control (SMC), a multilayer sliding mode surface is constructed. For formulating the adaptive output-feedback RADRC algorithm, the EHGO, LPF and SMC schemes are combined using the separation principle.FindingsThe findings of this research work include the design of an adaptive output-feedback RADRC with the ability to negate the UUDs as well as estimate the unknown states of the quadrotor attitude model. In addition, the chattering problem is addressed by designing a modified SMC scheme based on the multilayer sliding mode surface obtained by utilizing the estimated state variables. This sliding mode surface is also used to obtain the adaptive criteria for the switching design gain parameters involved in the SMC. Moreover, the requirement of high design gain parameters in the EHGO is solved by combining it with the LPF.Originality/valueDesigning the flight control techniques while assuming that the state variables are available is a common practice. In addition, to obtain robustness, the SMC technique is widely used. However, in practice, the state variables might not be available due to unknown parameters and uncertainties, as well as the chattering due to SMC reduces the performances of the actuators. Hence, in this paper, an adaptive output-feedback RADRC technique is designed to solve the problems of UUDs and chattering.

scholarly journals Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Jiacai Huang ◽  
Hongsheng Li ◽  
YangQuan Chen ◽  
Qinghong Xu
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
The State ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
State Variables ◽  
Nonlinear Load ◽  
Special Case

A new robust fractional-order sliding mode controller (FOSMC) is proposed for the position control of a permanent magnet synchronous motor (PMSM). The sliding mode controller (SMC), which is insensitive to uncertainties and load disturbances, is studied widely in the application of PMSM drive. In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. In fact, the conventional SMC method can be seen as a special case of the proposed FOSMC method. The performance and robustness of the proposed method are analyzed and tested for nonlinear load torque disturbances, and simulation results show that the proposed algorithm is more robust and effective than the conventional SMC method.

scholarly journals Quantum Corrections to the Dynamics of the Gravitational System

2019 ◽  
Vol 64 (12) ◽  
pp. 1143
Author(s):  
V. V. Kuzmichev ◽  
V. E. Kuzmichev
Keyword(s):  
State Vector ◽  
Degrees Of Freedom ◽  
Wave Equations ◽  
The State ◽  
Constrained Systems ◽  
Short Introduction ◽  
Gravitational Systems ◽  
New Type ◽  
The Universe ◽  
Insight Into

A short introduction into the theory of quantum gravitational systems with a finite number of degrees of freedom is given. The theory is based on the method of quantization of constrained systems. The state vector of the system satisfies a set of wave equations which describes the time evolution of the system in the space of quantum fields. The state vector in such an approach can be normalized to unity. The theory permits a generalization to negative values of the scale factor and, being applied to cosmology, leads to the new understanding of the evolution of the universe. It gives an insight into the reasons why the regime of the expansion may change from acceleration to deceleration or vice versa, revealing a new type of quantum forces acting like dark matter and dark energy in the universe.

scholarly journals Controller Design for the Rotational Dynamics of a Quadcopter

2019 ◽  
Vol 38 (2) ◽  
pp. 269-274
Author(s):  
Rabia Rashdi ◽  
Zeeshan Ali ◽  
Javed Rahman Larik ◽  
Liaquat Ali Jamro ◽  
Urooj Baig
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Euler Method ◽  
State Variables ◽  
Nonlinear Controller ◽  
Nonlinear Dynamic Model ◽  
Highly Nonlinear

Researchers have shown their interests in establishing miniature flying robots to be utilized for, both, commercial and research applications. This is due to that fact that there appears to be a huge advancement in miniature actuators and sensors which depend on the MEMS (Micro Electro-Mechanical Systems) NEMS (Nano-Electro Mechanical Systems). This research underlines a detailed mathematical model and controller design for a quadcopter. The nonlinear dynamic model of the quadcopter is derived from the Newton-Euler method and Euler Lagrange method. The motion of a quadcopter can be classified into two subsystems: a rotational subsystem (attitude and heading) and translational subsystem (altitude and x and y motion). The rotational system is fully actuated whereas translational subsystem is under actuated. However, a quadcopter is 6 DOF (Degrees of Freedom) under actuated system. The controller design of a quadcopter is difficult due to its complex and highly nonlinear mathematical model where the state variables are strongly coupled and contain under actuated property. Nonlinear controller such as SMC (Sliding Mode Controller) is used to control altitude, yaw, pitch, and roll angles.Simulation results show that the robustness of the SMC design gives a better way to design a controller with autonomous stability flight with good tracking performance and improved accuracy without any chattering effect. The system states are following the desired trajectory as expected.

scholarly journals Chattering-Free Reference Sliding Variable-Based SMC

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Katarzyna Adamiak
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Band Width ◽  
Data Systems ◽  
State Variables ◽  
Sampled Data ◽  
Control Scheme ◽  
Chattering Free ◽  
Chattering Elimination ◽  
Selection Of

The paper addresses the problem of chattering elimination in sliding mode control for sampled data dynamical systems and proposes an innovative control scheme. The key to the proposed control method is utilizing a pregenerated nonswitching type reference sliding variable profile to control the disturbed plant. As sampled data systems contain sample-and-hold devices in their input and output channels, we carry out a discrete time analysis. We consider the discretization effects on the controller in two aspects: the pace of convergence of the system and the ultimate band width. Consequently, in the reference sliding variable generator, we analyse two reaching laws, differently adapting to changes of the controller’s frequency. We prove that this approach not only minimizes the chattering phenomenon but also provides a reduction of the quasi-sliding mode band width, which in general case remains of O(T) order. Furthermore, the proposed control method incorporates a disturbance compensation algorithm, which results in the ultimate band width of O(T2) order. Finally, we also show that a certain selection of the sliding plane guarantees limitation of all the state variables’ errors to O(T2) order as well. Therefore, the proposed control algorithm significantly improves the system’s robustness.

Modeling and Predictive Control of an Unmanned Underwater Vehicle

2019 ◽  
Author(s):  
Renato Rodriguez Nunez ◽  
Damoon Soudbakhsh
Keyword(s):  
Feedback Linearization ◽  
Degrees Of Freedom ◽  
Travel Speed ◽  
The State ◽  
Operating Conditions ◽  
State Variables ◽  
Unmanned Underwater Vehicles ◽  
Six Degrees Of Freedom ◽  
State Space System ◽  
Predictive Controller

Abstract This paper presents a model and optimal controller for Unmanned Underwater Vehicles (UUVs). We present a nonlinear six degrees of freedom model of the UUV that includes hydrodynamic and hydrostatic terms. To design the controller, we simplify the model using the geometry of the UUV as well as its operating conditions such as the depth and expected travel speed. Instead of designing a controller for the state space system, we used feedback linearization technique to decouple the motions. Then, a set of controllers were designed for each motion. To incorporate the constraints on the input and the state variables, we designed a fast Model Predictive Controller (MPC) for the UUV and compared its performance with a conventional controller.

Response Variance Reduction of a Nonlinear Mechanical System via Sliding Mode Control

1998 ◽  
Vol 120 (3) ◽  
pp. 801-805 ◽  
Author(s):  
J. Q. Sun ◽  
Qing Xu
Keyword(s):  
Sliding Mode Control ◽  
Target Tracking ◽  
Mechanical System ◽  
Variance Reduction ◽  
Sliding Mode ◽  
The State ◽  
State Variables ◽  
Mode Control ◽  
Response Variance ◽  
Special Cases

An analysis of a target tracking mechanical system subject to random base excitations is presented in this paper. Sliding mode controls are proposed to minimize the random error of target tracking. Two special cases are studied. In the first case, it is assumed that all the system parameters are known and the state variables are measurable. A sliding mode control is then determined. This highly idealized example reveals the effect of sliding mode control parameters on the reduction of response variance and provides a benchmark for designing a robust controller that deals with systems with unknown parameters. The second case deals with a robust sliding mode control where some parameters of the system are assumed to fall in a known range of values. The proposed controls are proven stable in the mean square sense. The statistical aspects of the controlled system are studied by considering the first and second order moments of the state variables. The equations for these moments are derived and solved by using the method of Gaussian closure in order to investigate the variance reduction performance of the controls.

Development of a Robust Nonlinear Observer for a Single-Link Flexible Manipulator

2004 ◽  
Author(s):  
Nabil G. Chalhoub ◽  
Giscard A. Kfoury
Keyword(s):  
Sliding Mode ◽  
Initial Conditions ◽  
The State ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Flexible Manipulator ◽  
State Variables ◽  
State Equations ◽  
On Line ◽  
Simulation Results

Accurate measurements of all the state variables of a given system are often not available due to the high cost of sensors, the lack of space to mount the transducers or the hostile environment in which the sensors must be located. The purpose of this study is to design a robust sliding mode observer that is capable of accurately estimating the state variables of the system in the presence of disturbances and model uncertainties. It should be emphasized that the proposed observer design can handle state equations expressed in the general form. The performance of the nonlinear observer is assessed herein by examining its capability of predicting the rigid and flexible motions of a compliant beam that is connected to a revolute joint. The simulation results demonstrate the ability of the observer in accurately estimating the state variables of the system in the presence of structured uncertainties and under different initial conditions between the observer and the plant. Moreover, they illustrate the deterioration in the performance of the observer when subjected to unstructured uncertainties of the system. Furthermore, the nonlinear observer was successfully implemented to provide on-line estimates of the state variables for two model-based controllers. The simulation results show minimal deterioration in the closed-loop response of the system stemming from the usage of estimated rather than exact state variables in the computation of the control signals.

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