Observability, Reconstructibility and Observer Design for Linear Mechanical Systems Unobservable in Absence of Impacts†

2003 ◽  
Vol 125 (4) ◽  
pp. 549-562 ◽  
Author(s):  
Francesco Martinelli ◽  
Laura Menini ◽  
Antonio Tornambe`
Keyword(s):  
Structural Properties ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
The State ◽  
Observer Design ◽  
State Variables ◽  
Multiple Degrees Of Freedom ◽  
Position Variable

This paper deals with a class of mechanical systems, constituted by two composite bodies which interact with each other only during collisions: since only one position variable of only one body is measured, the whole system would not be observable without impacts. Each body is possibly constituted by several masses connected by linear springs, so that the internal deformations can be taken into account (the so-called multiple-degrees-of-freedom impacts). For two relevant and different cases, the structural properties of observability and reconstructibility are studied, and observers are proposed in order to estimate all the state variables, including those that would be unobservable in absence of impacts.

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.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

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.

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.

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.

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.

Geometric description of time-dependent finite-dimensional mechanical systems

2020 ◽  
Vol 25 (11) ◽  
pp. 2050-2075
Author(s):  
Simon R. Eugster ◽  
Giuseppe Capobianco ◽  
Tom Winandy
Keyword(s):  
State Space ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Mechanical Systems ◽  
Second Order ◽  
The State ◽  
Time Dependent ◽  
Finite Dimensional ◽  
Affine Bundle ◽  
Time Position

Using the non-standard geometric structure proposed by Loos, we present a coordinate-free formulation of the theory for time-dependent finite-dimensional mechanical systems with n degrees of freedom. The state space containing the system’s information on time, position and velocity is defined as a (2 n+1)-dimensional affine bundle over an ( n+1)-dimensional generalized space-time. The main goal is to present a geometric postulate that characterizes a second-order vector field whose integral curves describe the motions of a time-dependent finite-dimensional mechanical system. The core objects of the postulate are differential two-forms on the state space, called action forms, which are in a bijective relation with second-order vector fields. The requirements for a differential two-form to be an action form allow for a coordinate-free definition of non-potential forces, which may depend on time, position and velocity. Finally, we show that not only Lagrange’s equations but also Hamilton’s equations follow directly as mere coordinate representations of the same coordinate-free postulate.

scholarly journals Robust Regulation and Tracking Control of a Class of Uncertain 2DOF Underactuated Mechanical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
David I. Rosas Almeida ◽  
Carlos Gamez ◽  
Raul Rascón
Keyword(s):  
Control System ◽  
Control Strategy ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
State Variables ◽  
Underactuated Mechanical Systems ◽  
Robust Controller ◽  
Unknown Disturbances ◽  
Robust Regulation ◽  
Regulation And Tracking

A strategy to design and implement a robust controller for a class of underactuated mechanical systems, with two degrees of freedom, which solves the problems of regulation and trajectory tracking, is proposed. This control strategy considers the partial measurement of the state vector and the presence of parametric uncertainties in the plant; these conditions are common in the implementation of a control system. The strategy is based on the use of robust finite time convergence observers to estimate the unmeasured state variables, unknown disturbances, and other signals needed for the control system implementation. The performance of the control strategy is illustrated numerically and experimentally.

A fresh approach to the design of observers for time-delay systems

2016 ◽  
Vol 40 (2) ◽  
pp. 477-503 ◽  
Author(s):  
Dinh Cong Huong
Keyword(s):  
Time Delay ◽  
State Vector ◽  
State Observer ◽  
The State ◽  
Observer Design ◽  
Delay Systems ◽  
Time Delay Systems ◽  
State Variables ◽  
State Transformation ◽  
Original State

This paper presents a fresh approach to the design of state observers for a class of time-delay systems with one time delay in the state and output vectors. By proposing a new coordinate state transformation, the system is first transformed into the new coordinates where all the delay terms associated with the state variables are injected into the system’s output and input. Thus, in the new coordinate system, a Luenberger-type state observer can be easily designed. Then, a backward state transformation problem is studied which allows us to reconstruct the original state vector of the system. Conditions for the existence of the state transformations and an algorithm for computing them are provided in this paper. We show that our approach works for a wider class of time-delay systems in the sense that when some existing state observer design methods fail to reconstruct the state vector, the proposed new change of coordinates and the observer scheme in this paper can still reconstruct the original state vector. Numerical examples and simulation results are given to illustrative the effectiveness of the proposed design approach.

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