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controlled invariant varieties for second order polynomial control systems

IFAC-PapersOnLine 2024年第17期58卷 368-373页

作者： Melanie Harms Eva Zerz Michael Herty

We investigate controlled invariant varieties for second order input-affine control systems with polynomial nonlinearity. For autonomous, first order systems, a variety V is said to be invariant if any trajectory starting in V remains in V for all times. We discuss how to adapt this notion in the second order case and give conditions to decide whether a variety is invariant for a second order system using symbolic computation. This results serve as a foundation to characterise controlled invariant varieties, i.e., varieties that can be rendered invariant by a polynomial state feedback.

关键词： Algebraic systems theory Applications of Algebraic and Differential Geometry in systems Theory Computations in systems Theory Feedback control systems nonlinear systems and control AMS Subject Classifications: 93B25 93B40 93C10

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Bounds on the growth rate of time-invariant switching max-min-plus-scaling discrete-event systems

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IFAC-PapersOnLine 2024年第17期58卷 404-409页

作者： Ton van den Boom Sreeshma Markkassery Bart De Schutter Delft Center for Systems and Control (DCSC) TU Delft The Netherlands

We consider the growth rate of a switching max-min-plus-scaling (S-MMPS) system in a discrete-event framework. We show that an explicit, time-invariant, monotone, and arbitrarily switching MMPS system has a bounded growth rate. Further, we propose a mixed-integer linear programming problem to calculate the estimates of the smallest upper bound and the largest lower bound of the growth rate of an S-MMPS system.

关键词： Max-plus algebra Switching max-min-plus-scaling systems Algebraic systems Theory Discrete Event systems nonlinear systems and control

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A Closed Loop Gradient Descent Algorithm applied to Rosenbrock's function

A Closed Loop Gradient Descent Algorithm applied to Rosenbro...

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Australian and New Zealand control Conference (ANZCC)

作者： Bhattacharjee, Subhransu S. Petersen, Ian R. Australian Natl Univ Canberra ACT 0200 Australia

ISBN: (纸本)9781665416504

We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an improvement on existing momentum-based gradient optimisation methods. Also using Lyapunov stability analysis, we demonstrate the performance of the continuous-time version of the algorithm. Using numerical simulations, we consider the performance of its discrete-time counterpart obtained by using the symplectic Euler method of discretisation.

关键词： Learning systems Time-varying systems nonlinear systems and control

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nonlinear Dynamic Modeling of a Robotic Endoscopy Platform on Synthetic Tissue Substrates

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JOURNAL OF DYNAMIC systems MEASUREMENT AND control-TRANSACTIONS OF THE ASME 2021年第1期143卷 011005页

作者： Formosa, Gregory A. Prendergast, J. Micah Humbert, J. Sean Rentschler, Mark E. Univ Colorado Dept Mech Engn Adv Med Technol Lab 1111 Engn Dr427 UCB Boulder CO 80309 USA Univ Colorado Dept Mech Engn Bioinspired Percept & Robot Lab 1111 Engn Dr427 UCB Boulder CO 80309 USA

A scaled robotic endoscopy platform (REP) was previously developed to efficiently test new control schemes in a simulated colon environment. This article presents the derivation and tuning of a nonlinear model of the REP operating on various substrates. The modeling technique and novel empirical friction profiling demonstrated here are useful for a wide variety of devices interacting with unconventional substrates. The model is first derived from the REP drivetrain inertial characteristics, and then the interaction with synthetic tissue is quantified by an automated traction measurement system for multiple substrates. The resulting model is then used with ground-truth VICON and sensor data to optimize uncertain parameters by minimizing pose error over a variety of tests and substrates. The results show an average error reduction of 67% over all tests and substrates, with a worst-case 10% open-loop final position error. The success of these results proves a robust dynamic model of the REP and its tissue interactions without the need to model complex and computationally expensive viscoelastic material properties or discrete/nonlinear events such as stalling. The resulting model will be used to develop model-based feedback control for estimation, disturbance rejection, and autonomy for the REP in an actuated colon simulator.

关键词： modeling of dynamic systems mechatronics robotics system identification nonlinear systems and control

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Robust Liquid Level control of Quadruple Tank System - Second Order Sliding Mode Approach 6

Robust Liquid Level Control of Quadruple Tank System - Secon...

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6th Conference on Advances in control and Optimization of Dynamical systems (ACODS)

作者： Chaudhari, Vinita Tamhane, Bhagyashri Kurode, Shailaja Coll Engn Dept Elect Engn Pune Maharashtra India

In this paper, second order sliding mode control is proposed for liquid level control in a quadruple tank system. The system has internal cross coupling in its four tank setup, and realizes in a nonlinear model. The proposed twisting algorithm (TA) based controller is complemented with an exact differentiator for estimating the derivatives of the outputs. Simulation results are provided to validate the efficacy of the proposal. (C) 2020, IFAC (International Federation of Automatic control) Hosting by Elsevier Ltd. All rights reserved.

关键词： nonlinear systems and control Robust control Process control and Instrumentation Complex systems Estimation

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Normalized Pseudo-control for Solid Divert & Attitude control System

Normalized Pseudo-Control for Solid Divert & Attitude Contro...

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5th IFAC Conference on Advances in control and Optimization of Dynamical systems (ACODS)

作者： Kumar, Avnish Sinha, Shashikala Bhattacharya, Abhijit DRDO PGAD RCI Hyderabad 500058 Telangana India

Faster trajectory correction and control mechanisms are required to correct the radar handing-over error coupled with homing guidance demands for Missile Interceptors. Solid Divert and Attitude control System (SDACS), which typically have a very low time constant, is one of the most efficient and accurate way to meet these demands. The SDACS has challenges both with respect to the Hot Gas Valve (HGV) technology as well as actuator requirements. The paper proposes a novel method to simplify the controller design and reduce actuator needs for the rotary hot gas valves based SDACS. The proposed method formalizes a linear Pseudo-control to track the lateral acceleration and attitude correction commands. The pseudo control requirements are tracked through the HGV rotations. The paper further proposes the normalization of the pseudo-control to make the controller generic making it invariant of the valve size and relative dimensions of the HGV's static & moving part. The paper also proposes a technique to reduce the number of actuators required for the full SDACS system by use of these near affine pseudo-controls. (C) 2018, IFAC (International Federation of Automatic control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Aerospace Engineering Homing trajectory control System modelling and identification nonlinear systems and control Pseudo-control Hot gas valve

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Model Predictive control of a Hybrid Energy Storage System Using Load Prediction 13

Model Predictive Control of a Hybrid Energy Storage System U...

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13th IEEE International Conference on control & Automation (ICCA)

作者： Baumann, Matthias Buchholz, Michael Dietmayer, Klaus Ulm Univ Inst Measurement Control & Microtechnol D-89081 Ulm Germany

ISBN: (纸本)9781538626795

Hybrid Energy Storage systems (HESS) enable the use of the advantages from different energy storages. In this work, the HESS comprises a battery with high energy density and a supercapacitor with high power density. To fully exploit the advantages of both modules within the HESS, a control strategy is needed. In this contribution, a computationally efficient model predictive control (MPC) strategy is presented for this task. Special focus is directed to the prediction of the power demand in a range of several seconds. This information is useful to follow a given power profile within the given limits of the energy storage system. Therefore, an energy transfer between battery and supercapacitor occurs depending on the expected power demand. Furthermore, the MPC manages nonlinear model equations, whereby the system behavior is accurately represented, while the presented control algorithm for a HESS is still real-time capable.

关键词： Optimal control Real-time systems control Applications nonlinear systems and control

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Adaptive Frequency Shaped Linear Quadratic control of Mechanical systems: Theory and Experiment

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JOURNAL OF DYNAMIC systems MEASUREMENT AND control-TRANSACTIONS OF THE ASME 2016年第9期138卷 091003-091003页

作者： Huang, An-Chyau Jhuang, Ting-Kai Natl Taiwan Univ Sci & Technol Dept Mech Engn Taipei 106 Taiwan

The traditional linear quadratic (LQ) controller can give optimal performance to a known linear system with weightings in the time domain, while the frequency shaped LQ (FSLQ) controller is able to provide optimal performance to the same class of systems with weightings in the frequency domain. When the system contains uncertainties, both of these two approaches fail. In this paper, an adaptive controller is proposed to an uncertain mechanical system such that LQ performance can be achieved with weightings in the frequency domain. The function approximation technique is applied to represent the uncertainties into a finite combination of a set of known basis functions. This allows the system to be with various nonlinearities and uncertainties without significant impact on the design procedure. The Lyapunovlike analysis is used to ensure convergence of the system output and boundedness of the internal signals. A dual stage is built to evaluate the performance of the proposed scheme experimentally.

关键词： adaptive and optimal control motion control nonlinear systems and control

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Robust levitation control for maglev systems with guaranteed bounded airgap

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ISA TRANSACTIONS 2015年 59卷 205-214页

作者： Xu, Jinquan Chen, Ye-Hwa Guo, Hong Beijing Univ Aeronaut & Astronaut Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Georgia Inst Technol George W Woodruff Sch Mech Engn Atlanta GA 30332 USA

The robust control design problem for the levitation control of a nonlinear uncertain maglev system is considered. The uncertainty is (possibly) fast time-varying. The system has magnitude limitation on the airgap between the suspended chassis and the guideway in order to prevent undesirable contact. Furthermore, the (global) matching condition is not satisfied. After a three-step state transformation, a robust control scheme for the maglev vehicle is proposed, which is able to guarantee the uniform boundedness and uniform ultimate boundedness of the system, regardless of the uncertainty. The magnitude limitation of the airgap is guaranteed, regardless of the uncertainty. (C) 2015 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Magnetic levitation Uncertain systems and robust control nonlinear systems and control

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VARIANT FACTOR TECHNIQUE FOR TRACKING control OF A CLASS OF nonlinear systems WITH INPUT SATURATION

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control AND INTELLIGENT systems 2013年第3期41卷 1-1页

作者： Peng, Kemao Chen, Ben M. Temasek Laboratories National University of Singapore Singapore Department of Electrical and Computer Engineering National University of Singapore Singapore

A variant factor (VF) technique is developed for the control design of a class of single-input and single-output affine nonlinear systems with input saturation. The main ideas of VF are to convert an affine nonlinear system into a linear time-invariant system similar to the dynamic inversion and then to use the ideas of the composite nonlinear feedback (CNF) technique to design a control law for the converted linear system with the input saturation. A VF is introduced to guarantee the resulting closed-loop system asymptotically stable in presence of the input saturation. The VF control laws retain the similar properties of the CNF control laws. With the VF control law, the system output can asymptotically track the step reference and the resulting closed-loop system can achieve better tracking performance than that with the control law 0designed with the dynamic inversion.

关键词： nonlinear systems and control dynamic inversion composite non-linear feedback input saturation tracking control

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