Placing Multibody System to Equilibrium State by Using Multiple PID Controllers and Genetic Algorithm

2005 ◽  
Author(s):  
Mario Duras
Keyword(s):  
Genetic Algorithm ◽  
Equilibrium State ◽  
Pid Controller ◽  
Multibody System ◽  
Initial Conditions ◽  
Contact Forces ◽  
Resultant Force ◽  
Valve Train ◽  
Dynamics Simulation ◽  
Initial State

During development of MBS (Multibody System) dynamics simulation tool that evaluates contact forces between bodies, a procedure had to be developed for placing general MBS to equilibrium state. The procedure would be executed before dynamics simulation starts, to ensure stable and convergent simulation from its beginning. As very broad range of stiffnesses is coupled within the same model and additionally contact forces are evaluated, placing system to satisfactory initial state is not a simple task. Algorithm for initial conditions must place bodies to positions that would provide smallest possible (zero) resultant force on each body. After several approaches being tested, usage of PID (Proportional-Integral-Derivative) controllers showed greatest potential for solving the problem in a stable and fast manner. Such controller would be attached to each body and will move bodies to positions with smallest resultant force. To completely model PID controller, three parameters must be evaluated - gains for each controller action. For optimal combination of three parameters - conditions on force convergence and resultant force end value (zero) must be satisfied. Analysis showed that parameters for controller actions cannot be fixed and work successfully for MBSs with different number of DOF (Degrees of Freedom). Based on that, PID controller parameter range has been evaluated by Genetic Algorithm after repeated tests on systems of different types and number of DOF. Parameters choice and PID controller behavior were checked on models of engine timing drives (belt and chain drives with lashes) with several hundred DOF and simple model of Single Valve Train with just few DOF. Tests showed correct choice of PID parameters and stable iteration procedure regardless of DOF number and type of MBS. This paper focuses on determination of PID controller parameters by analyzing influence of MBS structure to procedure for reaching equilibrium state. Analysis is mainly focused on convergence and stability of the procedure.

Construction of point vortex equilibria via Brownian ratchets

2007 ◽  
Vol 463 (2082) ◽  
pp. 1525-1541 ◽  
Author(s):  
Paul K Newton ◽  
George Chamoun
Keyword(s):  
Equilibrium State ◽  
Initial Conditions ◽  
Point Vortex ◽  
Singular Values ◽  
Basis Set ◽  
Frobenius Norm ◽  
Initial State ◽  
Optimal Basis ◽  
Equilibrium Configurations ◽  
Value Decomposition

A theory capable of producing equilibrium configurations of point vortices in the plane, along with a numerical scheme to compute them, is described. The theory is formulated as a problem in linear algebra where one must find solutions to the matrix equation , where A is the (1/2) N ( N −1)× N non-normal configuration matrix obtained by requiring that all intervortical distances remain fixed, and are the N -vortex strengths. For existence of an equilibrium, A must have a non-trivial nullspace. We consider the singular values of A ; when this has one or more zero singular values, the nullspace of A is non-empty and an equilibrium exists for some choice of Γ . New equilibrium configurations are found numerically by randomly depositing N points in the plane, which generically gives rise to a configuration matrix A with empty nullspace. Using the sum of squares of the k smallest singular values of A as a ‘ratchet’, we ‘thermally fluctuate’ the configuration, allowing each point to execute a random walk in the plane, retaining only those configurations which reduce this quantity at the next step. The configuration is thus driven to one with nullspace ( A )= k >0. These converged states are not necessarily nearby their initial configurations, typically they are asymmetric, and often we can drive the same initial state to several different equilibria. A reverse-ratchet method is also described, which can produce initial conditions that would evolve to a specified equilibrium state. Once a converged final state is achieved, the full singular value decomposition of A is used to calculate an optimal basis set for the nullspace of A and thus all allowable Γ . The distribution of the singular values gives important information on the size of each equilibrium state (as measured by Frobenius norm), their distance from each other (spacing and density) and how far a randomly chosen system of N points in the plane is from the nearest equilibrium configuration with a specified rank, as well as its Shannon entropy.

scholarly journals Handling Initial Conditions in Vector Fitting for Real Time Modeling of Power System Dynamics

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2471
Author(s):  
Tommaso Bradde ◽  
Samuel Chevalier ◽  
Marco De Stefano ◽  
Stefano Grivet-Talocia ◽  
Luca Daniel
Keyword(s):  
Dynamical Systems ◽  
Power System ◽  
System Dynamics ◽  
Real Time ◽  
Initial Conditions ◽  
Test System ◽  
Initial State ◽  
Power System Dynamics ◽  
Vector Fitting ◽  
Time Modeling

This paper develops a predictive modeling algorithm, denoted as Real-Time Vector Fitting (RTVF), which is capable of approximating the real-time linearized dynamics of multi-input multi-output (MIMO) dynamical systems via rational transfer function matrices. Based on a generalization of the well-known Time-Domain Vector Fitting (TDVF) algorithm, RTVF is suitable for online modeling of dynamical systems which experience both initial-state decay contributions in the measured output signals and concurrently active input signals. These adaptations were specifically contrived to meet the needs currently present in the electrical power systems community, where real-time modeling of low frequency power system dynamics is becoming an increasingly coveted tool by power system operators. After introducing and validating the RTVF scheme on synthetic test cases, this paper presents a series of numerical tests on high-order closed-loop generator systems in the IEEE 39-bus test system.

scholarly journals Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor

Actuators ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 148
Author(s):  
Sarah Makarem ◽  
Bülent Delibas ◽  
Burhanettin Koc
Keyword(s):  
Genetic Algorithm ◽  
Pid Controller ◽  
Good Alternative ◽  
Data Driven ◽  
Grid Search ◽  
Single Source ◽  
Dual Frequency ◽  
Dual Source ◽  
Stage System ◽  
Piezoelectric Ultrasonic Motor

Ultrasonic motors employ resonance to amplify the vibrations of piezoelectric actuator, offering precise positioning and relatively long travel distances and making them ideal for robotic, optical, metrology and medical applications. As operating in resonance and force transfer through friction lead to nonlinear characteristics like creep and hysteresis, it is difficult to apply model-based control, so data-driven control offers a good alternative. Data-driven techniques are used here for iterative feedback tuning of a proportional integral derivative (PID) controller parameters and comparing between different motor driving techniques, single source and dual source dual frequency (DSDF). The controller and stage system used are both produced by the company Physik Instrumente GmbH, where a PID controller is tuned with the help of four search methods: grid search, Luus–Jaakola method, genetic algorithm, and a new hybrid method developed that combines elements of grid search and Luus–Jaakola method. The latter method was found to be quick to converge and produced consistent result, similar to the Luus–Jaakola method. Genetic Algorithm was much slower and produced sub optimal results. The grid search has also proven the DSDF driving method to be robust, less parameter dependent, and produces far less integral position error than the single source driving method.

Motion Planning of a Nonholonomic Multibody System Using Genetic Algorithm

2003 ◽  
Author(s):  
Xin-Sheng Ge ◽  
Li-Qun Chen
Keyword(s):  
Genetic Algorithm ◽  
Motion Planning ◽  
Nonholonomic System ◽  
Multibody System ◽  
Planning Problem ◽  
Control Approach ◽  
Velocity Constraints ◽  
Nonholonomic Motion Planning ◽  
Optimal Control Approach ◽  
Motion Planning Problem

The motion planning problem of a nonholonomic multibody system is investigated. Nonholonomicity arises in many mechanical systems subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the control problem of system can be converted to the motion planning problem for a driftless control system. In this paper, we propose an optimal control approach for nonholonomic motion planning. The genetic algorithm is used to optimize the performance of motion planning to connect the initial and final configurations and to generate a feasible trajectory for a nonholonomic system. The feasible trajectory and its control inputs are searched through a genetic algorithm. The effectiveness of the genetic algorithm is demonstrated by numerical simulation.

PSO-Based Tunning of PID Controller for Speed Control of DC Motor

2014 ◽  
Vol 7 (3) ◽  
pp. 65-79
Author(s):  
Ibrahem S. Fatah
Keyword(s):  
Genetic Algorithm ◽  
Particle Swarm Optimization ◽  
Pid Controller ◽  
Dc Motor ◽  
Proportional Integral Derivative ◽  
Stable Convergence ◽  
Swarm Optimization ◽  
Tuning Parameters ◽  
Pid Controller Tuning ◽  
Rising Time

In this paper, a Proportional-Integral-Derivative (PID) controller of DC motor is designed by using particle swarm optimization (PSO) strategy for formative optimal PID controller tuning parameters. The proposed approach has superior feature, including easy implementation, stable convergence characteristics and very good computational performances efficiency. The DC Motor Scheduling PID-PSO controller is modeled in MATLAB environment. Comparing with conventional PID controller using Genetic Algorithm, the planned method is more proficient in improving the speed loop response stability, the steady state error is reduced, the rising time is perfected and the change of the required input do not affect the performances of driving motor with no overtaking.

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