System Dynamic Constraints Research Articles

On the convergence rate of Fletcher‐Reeves nonlinear conjugate gradient methods satisfying strong Wolfe conditions: Application to parameter identification in problems governed by general dynamics

Over the last decades, many efforts have been made toward the understanding of the convergence rate of the gradient‐based method for both constrained and unconstrained optimization. The cases of the strongly convex and weakly convex payoff function have been extensively studied and are nowadays fully understood. Despite the impressive advances made in the convex optimization context, the nonlinear non‐convex optimization problems are still not fully exploited. In this paper, we are concerned with the nonlinear, non‐convex optimization problem under system dynamic constraints. We apply our analysis to parameter identification of systems governed by general nonlinear differential equations. The considered inverse problem is presented using optimal control tools. We tackle the optimization through the use of Fletcher‐Reeves nonlinear conjugate gradient method satisfying strong Wolfe conditions with inexact line search. We rigorously establish a convergence analysis of the method and report a new linear convergence rate which forms the main contribution of this work. The theoretical result reported in our analysis requires that the second derivative of the payoff functional be continuous and bounded. Numerical evidence on a selection of popular nonlinear models is presented as a direct application of parameter identification to support the theoretical findings.

Optimal operations for hydrogen-based energy storage systems in wind farms via model predictive control

Efficient energy production and consumption are fundamental points for reducing carbon emissions that influence climate change. Alternative resources, such as renewable energy sources (RESs), used in electricity grids, could reduce the environmental impact. Since RESs are inherently unreliable, during the last decades the scientific community addressed research efforts to their integration with the main grid by means of properly designed energy storage systems (ESSs). In order to highlight the best performance from these hybrid systems, proper design and operations are essential. The purpose of this paper is to present a so-called model predictive controller (MPC) for the optimal operations of grid-connected wind farms with hydrogen-based ESSs and local loads. Such MPC has been designed to take into account the operating and economical costs of the ESS, the local load demand and the participation to the electricity market, and further it enforces the fulfillment of the physical and the system's dynamics constraints. The dynamics of the hydrogen-based ESS have been modeled by means of the mixed-logic dynamic (MLD) framework in order to capture different behaviors according to the possible operating modes. The purpose is to provide a controller able to cope both with all the main physical and operating constraints of a hydrogen-based storage system, including the switching among different modes such as ON, OFF, STAND-BY and, at the same time, reduce the management costs and increase the equipment lifesaving. The case study for this paper is a plant under development in the north Norway. Numerical analysis on the related plant data shows the effectiveness of the proposed strategy, which manages the plant and commits the equipment so as to preserve the given constraints and save them from unnecessary commutation cycles.

Surrogate based trajectory planning method for an unmanned electric shovel

Trajectory planning is a crucial precondition for mechatronic systems to achieve precise and energy-saving working activities. However, conventional trajectory planning methods are restrained by curve types, which may not obtain the optimal trajectory adequately and explicitly. To address these challenges, a surrogate based trajectory planning (STP) method is developed in this study. Firstly, the time dependent variables of the optimal control problem are discretized using appropriate design of experiment (DoE) method. All the obtained training points for establishing the trajectory/speed surrogate model serve as the design variables. Thus, updating of the training points set is equal to updating the full-time trajectory/speed curve at every optimization iteration. By setting indispensable system dynamic constraints, the optimizer can gradually find the optimal trajectory. The proposed STP method is illustrated using an unmanned electric shovel (ES) example, which builds on the excavating trajectory planning problem by incorporating the excavating efficiency and energy consumption as the objectives. Numerical results show that the STP method can achieve a better excavating performance than other conventional trajectory planning methods. Besides, the high flexibility of STP is also demonstrated across different working conditions, including variable pile angles and complex pile surfaces.

Research on CNC simulation system with instruction interpretations possessed of wireless communication

This paper proposes a novel fourth-order S-shape acc/dec control algorithm by use of the parameter restriction that applied in CNC simulation system possessed of wireless communication. Firstly, the acc/dec control strategy of equivalent trapezoid is studied. Then, the real kinematics parameters of fourth-order S-shape curve are analyzed under the condition of speed---acceleration constraint, displacement---acceleration and displacement---speed based on the proposed control strategy. Based on the system dynamics constraints and considering the seven control stages of the algorithm, the forth-order S-shape curve acc/dec control algorithm with time optimization is proposed through pre-processing. The effectiveness and reliability of the algorithm are verified through a calculation instance. Finally, the proposed algorithm is successfully realized on the newly developed CNC simulation system with instruction interpretation possessed of wireless communication. The research results will provide the theoretical basis for the simulation system and further promote the development of the virtual manufacturing system.

Robust Motion Control of a Linear Motor Positioner Using Fast Nonsingular Terminal Sliding Mode

A robust motion control system is essential for the linear motor (LM)-based direct drive to provide high speed and high-precision performance. This paper studies a systematic control design method using fast nonsingular terminal sliding mode (FNTSM) for an LM positioner. Compared with the conventional nonsingular terminal sliding mode control, the FNTSM control can guarantee a faster convergence rate of the tracking error in the presence of system uncertainties including payload variations, friction, external disturbances, and measurement noises. Moreover, its control input is inherently continuous, which accordingly avoids the undesired control chattering problem. We further discuss the selection criteria of the controller parameters for the LM to deal with the system dynamic constraints and performance tradeoffs. Finally, we present a robust model-free velocity estimator based on the only available position measurements with quantization noises such that the estimated velocity can be used for feedback signal to the FNTSM controller. Experimental results demonstrate the practical implementation of the FNTSM controller and verify its robustness of more accurate tracking and faster disturbance rejection compared with a conventional NTSM controller and a linear H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller.

Application challenges of large-scale wire robots in agricultural plants

Abstract The paper presents an efficient approach for the modelling of wire robots kinematic and dynamics considering the effects of structural elasticity. Using the simulation and animation system several potential applications in agriculture have been simulated and analysed. The paper discusses possible robot configurations, system dynamic constraints and limits, as well as reachable performance for typical large-span wire robot applications in agriculture.

Basis Task Approach to Iterative Learning Control With Applications to Micro-Robotic Deposition

Two basic requirements in iterative learning control (ILC), among others, are trial-to-trial trajectory invariance and system dynamics invariance. The ILC algorithm must be reinitiated if either the trajectory or system dynamics vary in-between trials. Here, we introduce a framework that flexibly applies ILC such that trajectory and system dynamics constraints are alleviated. The framework exploits the characteristic that many manufacturing operations are comprised of a set of repeated tasks, termed basis tasks here. Instead of applying ILC to the complete operation trajectory, the correct input signal to accurately perform each constitutive basis task is identified by ILC in a training routine. After basis task training, the corresponding input signals, termed basis signals, are applied in a coordinated manner based on instructions from task-oriented machine languages, such as the pervasive G-Code. This framework allows the reference trajectory to be arbitrarily chosen, provided it is comprised of the defined basis tasks. Key definitions, assumptions, and a general application with performance bounds are detailed. An example application on a micro-robotic deposition (μRD) rapid prototyping system displays the utility of the framework in fabricating two distinct structures without reinitiating the ILC algorithm in-between manufacturing operations.

Vehicle Constraints Enhancement for Supporting INS Navigation in Urban Environments

The complementary nature of INS and GPS can be used advantageously in navigation system design as long as GPS measurements are available. However, circumstances of complete GPS denial may occur in urban environments or in signal blockage scenarios. In such cases, the INS navigation solution drifts over time due to its inherent bias. To circumvent the INS drift, it is usually fused with external sensors. Nonetheless, use of external sensors increases the overall system cost. To reduce the need for external sensors, incorporation of vehicle constraints into the estimation process has been recently proposed. In order to improve the effect of these constraints, we propose implementing vehicle constraints both into the system and measurement models thereby enhancing the estimator performance. The paper demonstrates the contribution of the proposed approach via several field experiments. In all experiments, introducing system dynamics constraints reduced the navigation errors, compared to using only measurement constraints.

Algorithm of Trajectory Overlay Planning for Step- and Scan-move in Scanner Lithography

An algorithm of trajectory overlay planning is investigated for step-move and scan-move of step-scan lithography.Based on system dynamic constraints,several criteria of trajectory overlay planning are constructed to ensure motion parameters planned within its preset values respectively.All available instances of trajectory overlay planning are discussed,and relevant equations are further derived.As a result,the algorithm of trajectory overlay planning for step-move and scan-move is presented.The correctness and effectiveness of the algorithm are demonstrated by simulation calculation and practical results.High productivity and high motion accuracy are obtained by applying the presented method.This algorithm has been applied in the motion control system of 100 nm step-scan lithography successfully.

Sensitivity Analysis in the Optimal Design of Synchronous Machine Regulators

The usual procedure for the optimal design of linear regulators for synchronous machines is to minimize a chosen quadratic cost function subject to the system dynamics constraints. However, the optimal control synthesized in such a straightforward fashion is unsatisfactory, since it is dependent on the particular choice of system control parameters made by the investigators. Furthermore, in practice, there may be a departure of these parameters from their nominal values. In an attempt to resolve these difficulties, the paper presents a method of synthesizing optimal control in such a way as to minimize a certain cost function, while choosing the system controllable parameters in the region of near-zero sensitivity. Considering a three-machine system as an illustrative example, this method is used as a basis for the selection of voltage regulator gains. It is shown that choosing the gains in the region of low sensitivity of the optimal cost function enhances the system transient response. The method is simple and is capable of handling multi-parameter sensitivity analysis in the framework of optimal control.