Multivariable Control of an Over-Head Crane System Based on Entire Eigen-Structure Assignment

2010 ◽  
Author(s):  
Hamed Moradi ◽  
K. Haji Hajikolaei ◽  
Firooz Bakhtiari-Nejad ◽  
Aria Alasty
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
Control Strategies ◽  
Control Signal ◽  
Space Representation ◽  
Linear Time Invariant ◽  
State Space Representation ◽  
Stabilization Control ◽  
Structure Assignment ◽  
Time Invariant

Motion and stabilization control strategies are required to improve positioning accuracy, transportation time and swing angle of an overhead crane system. In this paper, a controller is designed to enhance both efficiency and safety and to extend the system application to other engineering fields. An over-head crane is modeled as a linear time invariant (LTI) system with two degrees of freedom. Trolley position and cable angle are the controlled outputs while the force exerted on trolley and torque on the load are the control inputs of the system. After state-space representation of the problem, feedback control is designed for tracking objective. An increase in the overall speed of the system time response corresponds to an increase in the control signal and leads to additional cost. Therefore, developing a code in MATLAB, eigenvalues and eigenvectors of the system are chosen optimally until an appropriate response is achieved; while the gains of control signal remain small.

scholarly journals On Parametrizations of State Feedbacks and Static Output Feedbacks and Their Applications

2021 ◽  
Author(s):  
Yossi Peretz
Keyword(s):  
Linear Time ◽  
Linear Constraint ◽  
Pole Placement ◽  
Space Representation ◽  
Static State ◽  
Linear Time Invariant ◽  
State Space Representation ◽  
Time Invariant ◽  
Time Linear ◽  
Static Output

In this chapter, we provide an explicit free parametrization of all the stabilizing static state feedbacks for continuous-time Linear-Time-Invariant (LTI) systems, which are given in their state-space representation. The parametrization of the set of all the stabilizing static output feedbacks is next derived by imposing a linear constraint on the stabilizing static state feedbacks of a related system. The parametrizations are utilized for optimal control problems and for pole-placement and exact pole-assignment problems.

Zeno-free adaptive event-triggered control design

2018 ◽  
Vol 41 (8) ◽  
pp. 2328-2337 ◽  
Author(s):  
Hassan Adloo ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Performance Criterion ◽  
Linear Time Invariant ◽  
Event Triggering ◽  
Linear Time Invariant Systems ◽  
System States ◽  
Time Invariant ◽  
Event Triggered

This paper presents a new general framework for adaptive event-triggered control strategy to extend average inter-event interval, while maintaining the performance of the system. The proposed event-triggering mechanism is acquired from input to state stability conditions, which is defined in terms of system states as well as an adaptation parameter. Under the Lipschitz assumption, a positive lower bound on sampling durations is also established that is essential to restrain the Zeno behavior. Applying the proposed method to linear time-invariant systems, leads to sufficient conditions to guarantee asymptotic stability in the form of matrix inequalities. Moreover, it is shown that there exist more degrees of freedom to improve the performance criterion from theoretical aspects. Finally, in order to show capability of the proposed method and its better performance compared with some recent works, numerical simulations are presented.

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration

1999 ◽  
Vol 121 (3) ◽  
pp. 316-321 ◽  
Author(s):  
Jian Lin ◽  
R. G. Parker
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Linear Time ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
Factors Affecting ◽  
Linear Time Invariant ◽  
Gyroscopic Effects ◽  
Time Invariant

This work develops an analytical model of planetary gears and uses it to investigate their natural frequencies and vibration modes. The model admits three planar degrees of freedom for each of the sun, ring, carrier and planets. It includes key factors affecting planetary gear vibration such as gyroscopic effects and time-varying stiffness. For the linear, time-invariant case, examination of the associated eigenvalue problem reveals the well-defined structure of the vibration modes, where the special structure results from the cyclic symmetry of planetary gears. Vibration modes are classified into rotational, translational and planet modes. The unique characteristics of each type of mode are analytically investigated in detail. For each class of mode, reduced-order eigenvalue problems are derived.

Modal H∞-Control in the Context of a Rotor Being Subject to Unbalance Excitation and Gyroscopic Effect

2013 ◽  
Author(s):  
Rudolf Sebastian Schittenhelm ◽  
Bernd Riemann ◽  
Stephan Rinderknecht
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Linear Time ◽  
Rotational Frequency ◽  
Gyroscopic Effect ◽  
Actual System ◽  
Linear Time Invariant ◽  
Optimal Controllers ◽  
Problem Description ◽  
Time Invariant

H∞-optimal controllers are designed for a rotor being subject to unbalance excitation and gyroscopic effect. The system possesses two unbalance-induced resonances within its operating range. The presence of gyroscopic effect is challenging for linear time invariant controller design because of the associated dependence of the system dynamics on the rotational frequency of the rotor. Controllers thus have to be robust against deviation of the actual system behavior from the controller design point model. For vibration control purposes, there are two piezoelectric actuators installed in one of the two supports of the rotor. The signals of four inductive sensors measuring the displacements of the two discs of the rotor are used for controller design. In this article, H∞-optimal controllers are designed on the basis of input and output weighting as well as weighting of modal degrees of freedom and modal excitations. It is shown that superior control performance is achieved using modal weighting since a more accurate problem description of rotors excited by unbalance is incorporated in controller design. Results in this article show furthermore that it is possible to design well performing H∞-optimal controllers for a gyroscopic rotor by means of iterative controller design without taking model uncertainty directly into account via weighting of certain FRFs of the system to be controlled.

Nonlinear Analysis of Vibro-Impacts for Unloaded Gear Pairs With Various Excitations and System Parameters

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jong-yun Yoon ◽  
Iljae Lee
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
System Model ◽  
System Parameters ◽  
Linear Time Invariant ◽  
Gear Mesh ◽  
The Stability ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Gear Rattle

Torsional systems with clearance-type nonlinearities have inherent vibratory problems such as gear rattle. Such vibro-impacts generally occur on the unloaded gear pairs of a vehicle correlated with the firing excitation of an engine. This study investigates the gear rattle phenomena on unloaded gear pairs with different excitation conditions and various system parameters. First, a linear time-invariant system model with six degrees of freedom is constructed and then a numerical analysis is applied to the gear rattle motion. Smoothening factors for clutch stiffness and hysteresis are employed for the stability of numerical simulations. Second, the dynamic characteristics of vibro-impacts are studied by examining the fast Fourier transform (FFT) components of the gear mesh force in a high frequency range. The effects of various system parameters on the vibro-impacts are examined using a nonlinear system model. Finally, the vibro-impacts, in terms of “single-sided” and “double-sided” impacts, are identified in phase planes.

A Combined Method for the Investigation of Coupled Bandpass-Lowpass Nonlinear Oscillators Based on Hilbert Transform and Perturbation Analysis

2006 ◽  
Author(s):  
Nikolaos I. Xiros ◽  
Ioannis T. Georgiou
Keyword(s):  
Hilbert Transform ◽  
Perturbation Analysis ◽  
State Vector ◽  
Linear Time ◽  
External Disturbance ◽  
The State ◽  
Space Representation ◽  
Linear Time Invariant ◽  
State Space Representation ◽  
The Hilbert Transform

The nonlinear coupling dynamics between a bandpass and a lowpass subsystem is investigated by partitioning the system state vector to a lowpass and a bandpass part. The corresponding dynamic equations of the lowpass part are formed on the assumption of linearity when unforced. Its excitation includes an external disturbance vector and a nonlinear static term, standing for the coupling of the lowpass dynamics to the bandpass part of the full system. For the bandpass part, the constant matrices appearing in the conventional form of the state-space representation of linear time invariant systems are substituted by matrix functions depending upon the state vector of the lowpass subsystem. A convenient method for describing this interaction between spectrally separated subsystems, which can be established only if their coupling is nonlinear, is the Hilbert transform. The methodology proposed is applied to a typical electromechanical oscillator, where it is compared against the standard perturbation analysis results.

scholarly journals Time History Analysis of Frame Structure Systems by State-space Representation Method

2020 ◽  
Vol 10 (1) ◽  
pp. 140-147
Author(s):  
Barham H. Ali ◽  
Brwa A. Saeed ◽  
Twana A. Hussein
Keyword(s):  
Dynamic Analysis ◽  
State Space ◽  
Linear Time ◽  
Time History ◽  
Equation Of Motion ◽  
Space Representation ◽  
State Space Representation ◽  
History Analysis ◽  
Linear Differential ◽  
Time Invariant

This paper develops the state-space representation (SSR) in the field of seismic analysis of the building structures. Dynamic analysis of multi-degree-of-freedom structures involves the solution of second-order linear differential equations which they represent the equation of motion of the structure. In this paper, a SSR was formulated to replace differential equation with two coupled first-order linear differential equations. The objectives of this study are as follows: (i) To implement the SSR as a powerful tool in dynamic analysis of frame structures and (ii) to conduct a linear time history analysis for large structures subjected to ground acceleration and the seismic responses of the building were studied as well. The analysis was based on the assumption that the system is elastic linear time-invariant system and material nonlinearity is not considered. The 1940 El-Centro earthquake time history record has been used in the study. There are many effective traditional methods which can be used for carrying out linear dynamic analysis of the structures, however, this paper introduces a state-space model as an alternative approach to perform this analysis. The advantage of this method, it works properly with MATLAB software, gives explicit result for time-invariant systems, applied to multi-input and multi-output control systems, solve the equation of motion for complicated dynamic problems.

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