Robust Piecewise-Linear State Observers for Flexible Link Mechanisms

2006 ◽  
Author(s):  
Roberto Caracciolo ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Nonlinear Model ◽  
Closed Loop ◽  
Linear Models ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Loop System ◽  
State Variables ◽  
Flexible Link ◽  
Closed Loop System ◽  
State Observers

This paper tackles the problem of designing state observers for flexible link mechanisms: an investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the pole perturbation caused by spillover, and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally-linearized one is expressed in terms of unstructured uncertainty and stability is assessed by H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.

Robust Piecewise-Linear State Observers for Flexible Link Mechanisms

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Roberto Caracciolo ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Nonlinear Model ◽  
Closed Loop ◽  
Linear Models ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Loop System ◽  
State Variables ◽  
Flexible Link ◽  
Closed Loop System ◽  
State Observers

This paper tackles the problem of designing state observers for flexible link mechanisms: An investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general and novel approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the perturbation of the poles caused by spillover and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally linearized one is expressed in terms of unstructured uncertainty and stability is assessed through H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.

Sliding Controller Design for Aero-Engines With the Rate Limitation of Actuators

2017 ◽  
Author(s):  
Shubo Yang ◽  
Xi Wang
Keyword(s):  
Closed Loop ◽  
Actuator Saturation ◽  
Sliding Mode ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Tracking Error ◽  
Loop System ◽  
Sliding Surface ◽  
Closed Loop System ◽  
Aero Engines

With the relevant theories fully developed, sliding mode control (SMC), a kind of nonlinear control strategy having particularly strong robustness and disturbance rejection properties, has been applied in a considerable number of fields, such as robotic manipulator control, power generation control in wind turbines, robust stepper motor control, etc. For aero engines, remarkable progress of adopting SMC has been made. For instance, Richter has published his research of limit management in aircraft engine controls which suggests that replacing the linear regulators with sliding controllers can overcome the obstacle of traditional min-max approach. It is revealed from publication that researchers who design sliding controller for aero engines have made every effort to focus on the sliding surface and control law of SMC while they seldom paid attention to the constraints in actuators, such as saturation and rate limitation. In practical engineering, the performance of the ideal controller is infeasible under the situation that unavoidable constraints exist. Although the actuator saturation can be avoided by introducing a velocity form controller, rate limitation can still degenerate the control performance severely. In this paper, therefore, the design of a sliding controller for aero engines with rate limitation is discussed. A speed tracking problem is described based on the engine model simplified from a nonlinear system to a piecewise linear system at selected equilibrium points. A sliding surface is defined as the generalized tracking error, and a SMC law is designed with Lyapunov analysis of the closed loop system. Simulation results verify the stability of the closed-loop system, and show that the proposed sliding controller is capable of regulating a turbofan engine for large thrust commands in a stable fashion with proper tracking performance, which can mitigate the negative effect of actuator rate limitation.

Immersion- and invariance-based adaptive missile control using filtered signals

2012 ◽  
Vol 226 (6) ◽  
pp. 646-663 ◽  
Author(s):  
K W Lee ◽  
S N Singh
Keyword(s):  
Control System ◽  
Closed Loop ◽  
Angle Of Attack ◽  
Loop System ◽  
Certainty Equivalent ◽  
Analytical Relation ◽  
Parametric Uncertainties ◽  
State Variables ◽  
Closed Loop System ◽  
Immersion And Invariance

The article presents a new non-certainty-equivalent adaptive (NCEA) longitudinal autopilot for the control of a missile based on the immersion and invariance theory. The interest here is to control the angle of attack of the missile in the presence of large parametric uncertainties. For the derivation of the control law, a backstepping design procedure is used. At each step of the design, certain filtered signals are generated for the synthesis of a stabilizing control signal and a parameter estimator. Using Lyapunov stability analysis, it is shown that in the closed-loop system, trajectory control of the angle of attack is accomplished, and the trajectories of the system are attracted to certain manifold in the space of state variables and parameter errors. For stability in the closed-loop system, an explicit analytical relation involving the controller gains is obtained. It may be pointed out that recently an adaptive autopilot based on the immersion and inversion theory has been designed, but it has stringent requirements because for its synthesis, the derivatives of the Mach number and angle of attack must be known, and a large number of parameters must be updated. The derived control system of this article is synthesized using only the state variables, and its identifier is of lower order. A traditional certainty-equivalent adaptive autopilot is also presented for comparison. Simulation results are obtained which show that the designed NCEA control system can accomplish angle of attack control despite large parametric uncertainties; and it can give better tracking performance than the traditional controller.

scholarly journals Design of Dynamic Nonlinear Control Techniques for Flexible-Link Manipulators

2008 ◽  
Vol 144 ◽  
pp. 250-256
Author(s):  
V. Gavriloiu ◽  
V. Yurkevich ◽  
K. Khorasani
Keyword(s):  
Closed Loop ◽  
Control Strategies ◽  
Output Feedback Control ◽  
Loop System ◽  
Phase Behaviour ◽  
Flexible Link ◽  
Closed Loop System ◽  
Flexible System ◽  
Advantages And Disadvantages ◽  
Control Objective

In this paper, we develop robust dynamical controllers for addressing the problems of tracking and regulation of flexible-link manipulators. The design of dynamical controllers is based on construction of a two-time scale dynamical motion of the closed-loop system. The main control objective is to achieve stability of the closed-loop system while ensuring boundedness of all the control signals as well as sufficiently small tip-position tracking requirement. In order to achieve a minimum phase behaviour for utilizing output feedback control strategy, a new redefined output is proposed. Instead of using the joint angles as outputs in the rigid-link case, a new output is chosen for the flexible-link case which will provide and guarantee stability of the closed-loop flexible system. Simulations results are provided for flexible-link manipulators using the proposed control strategies. A comparative analysis is also included to demonstrate and illustrate the advantages and disadvantages of the considered control methodologies.

Gain Scheduling Control of Gas Turbine Engines: Stability by Computing a Single Quadratic Lyapunov Function

2013 ◽  
Author(s):  
Mehrdad Pakmehr ◽  
Nathan Fitzgerald ◽  
Eric M. Feron ◽  
Jeff S. Shamma ◽  
Alireza Behbahani
Keyword(s):  
Lyapunov Function ◽  
Gas Turbine ◽  
Closed Loop ◽  
Equilibrium Points ◽  
Gain Scheduling ◽  
Gas Turbine Engine ◽  
Loop System ◽  
Closed Loop System ◽  
Quadratic Lyapunov Function ◽  
Turbine Engine

We develop and describe a stable gain scheduling controller for a gas turbine engine that drives a variable pitch propeller. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and non-equilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. Simulation results show the developed gain scheduling controller is capable of regulating a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

scholarly journals Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

2020 ◽  
Vol 45 (1) ◽  
pp. 49-64
Author(s):  
Alvaro Prado ◽  
Marco Herrera ◽  
Oswaldo Menéndez
Keyword(s):  
Predictive Control ◽  
Nonlinear Model ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Angular Position ◽  
Loop System ◽  
Invariant Sets ◽  
Closed Loop System ◽  
Pendulum System ◽  
Inverted Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

scholarly journals Oscillations in First-Order, Continuous-Time Systems via Time-Delay Feedback

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Abimael Salcedo ◽  
Joaquin Alvarez
Keyword(s):  
Continuous Time ◽  
Closed Loop ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Loop System ◽  
Closed Loop System ◽  
First Order ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Order Continuous

A technique to generate (periodic or nonperiodic) oscillations systematically in first-order, continuous-time systems via a nonlinear function of the state, delayed by a certain time d, is proposed. This technique consists in choosing a nonlinear function of the delayed state with some passivity properties, tuning a gain to ensure that all the equilibrium points of the closed-loop system be unstable, and then imposing conditions on the closed-loop system to be semipassive. We include several typical examples to illustrate the effectiveness of the proposed technique, with which we can generate a great variety of chaotic attractors. We also include a physical example built with a simple electronic circuit that, after applying the proposed technique, displays a similar behavior to the logistic map.

Safety and Performance of the Omnipod®Hybrid Closed-Loop System in Adolescents with Type 1 Diabetes over Five Days Under Free-Living Conditions

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 1376-P
Author(s):  
GREGORY P. FORLENZA ◽  
BRUCE BUCKINGHAM ◽  
JENNIFER SHERR ◽  
THOMAS A. PEYSER ◽  
JOON BOK LEE ◽  
...  
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Living Conditions ◽  
Loop System ◽  
Closed Loop System ◽  
Free Living ◽  
And Performance ◽  
Free Living Conditions
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