scholarly journals A New Robust Controller with Applications to Bioreactors

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Alejandro Rincón ◽  
Christian Camilo Erazo Ordoñez ◽  
Felipe Londoño ◽  
Gerard Olivar Tost ◽  
Fabiola Angulo
Keyword(s):  
Tracking Error ◽  
Input Saturation ◽  
Function Technique ◽  
Model Parameters ◽  
Control Input ◽  
Input Output ◽  
Parameter Uncertainties ◽  
Observer Error ◽  
Residual Set ◽  
Input Output Linearization

In this work an anaerobic digester is controlled using input-output linearization and Lyapunov-like function methods. It is assumed that model parameters are unknown, time-varying, and bounded, and upper or lower bounds are also unknown. To tackle the effect of input saturation, a state observer is designed. The tracking and observer errors are defined in terms of the noisy measured output instead of ideal output, given by the mathematical model. The design of the observer mechanism and the update laws is based on the Lyapunov-like function technique, whereas the design of the control law is based on the input-output linearization method. In this paper two important properties of the controlled system are proven. First, the observer error converges asymptotically to a residual set whose size is user-defined, and such convergence is not disrupted, neither by the input saturation nor by the parameter uncertainties. Second, when the control input is nonsaturated the tracking error converges to a residual set whose size is user-defined. The model parameter uncertainties are included to prove the convergence of errors. Finally, a numerical example to validate the developed control is presented.

scholarly journals Iterative Learning Control of a Nonlinear Aeroelastic System despite Gust Load

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Xing-zhi Xu ◽  
Ya-kui Gao ◽  
Wei-guo Zhang
Keyword(s):  
Control Strategy ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Control Surface ◽  
Stream Velocity ◽  
Control Input ◽  
Parameter Uncertainties ◽  
Composite Energy

The development of a control strategy appropriate for the suppression of aeroelastic vibration of a two-dimensional nonlinear wing section based on iterative learning control (ILC) theory is described. Structural stiffness in pitch degree of freedom is represented by nonlinear polynomials. The uncontrolled aeroelastic model exhibits limit cycle oscillations beyond a critical value of the free-stream velocity. Using a single trailing-edge control surface as the control input, a ILC law under alignment condition is developed to ensure convergence of state tracking error. A novel Barrier Lyapunov Function (BLF) is incorporated in the proposed Barrier Composite Energy Function (BCEF) approach. Numerical simulation results clearly demonstrate the effectiveness of the control strategy toward suppressing aeroelastic vibration in the presence of parameter uncertainties and triangular, sinusoidal, and graded gust loads.

scholarly journals Actuator Saturation and Control Design for Buildings Structural Systems with Improved Uncertainty Description

2013 ◽  
Vol 20 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Y.C. Ding ◽  
F.L. Weng ◽  
Z.A. Yu
Keyword(s):  
Closed Loop ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Lyapunov Theory ◽  
Loop System ◽  
Structural Systems ◽  
Control Input ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Earthquake Excitation

The problem of robustly active vibration control for a class of earthquake-excited structural systems with time-delay and saturation in the control input channel and parameter uncertainties appearing in all the mass, damping and stiffness matrices is concerned in this paper. The objective of the designing controllers is to guarantee the robust stability of the closed-loop system and attenuate the disturbance from earthquake excitation. Firstly, by using the linear combination of some matrices to deal with the system's uncertainties, a new system uncertainties description, namely rank-1 uncertainty description, is presented. Then, by introducing a linear varying parameter, the input saturation model is described as a linear parameter varying model. Furthermore, based on parameter-dependent Lyapunov theory and linear matrix inequality (LMI) technique, the LMIs-based conditions for the closed-loop system to be stable are deduced. By solving those conditions, the controller, considering the actuator saturation, input delay and parameters uncertainties, is obtained. Finally, a three-storey linear building structure under earthquake excitation is considered and simulation results are given to show the effectiveness of the proposed controllers.

scholarly journals Non-Certainty-Equivalent Adaptive Control of a Nonlinear Aeroelastic System

2010 ◽  
Vol 56 (4) ◽  
pp. 463-471 ◽  
Author(s):  
Keum Lee ◽  
Sahjendra Singh
Keyword(s):  
Adaptive Control ◽  
Control System ◽  
Certainty Equivalent ◽  
Control Surface ◽  
Limit Cycle Oscillation ◽  
Stream Velocity ◽  
Model Parameters ◽  
Control Input ◽  
Parameter Uncertainties ◽  
Aeroelastic System

Non-Certainty-Equivalent Adaptive Control of a Nonlinear Aeroelastic SystemThe development of a non-certainty-equivalent adaptive control system for the control of a nonlinear aeroelastic system is the subject of this paper. The prototypical aeroelastic wing section considered here includes structural nonlinearity and a single control surface for the purpose of control. Its dynamical model has two-degree-of-freedom and describes the plunge and pitch motion. It is assumed that the model parameters (except the sign of one of the control input coefficients) are not known. The uncontrolled aeroelastic model exhibits limit cycle oscillation beyond a critical free-stream velocity. Based on the attractive manifold, and the immersion and invariance methodologies, a non-certainty-equivalent adaptive state variable feedback control law for the trajectory tracking of the pitch angle is derived. Using the Lyapunov analysis, asymptotic convergence of the state variables to the origin is established. It is shown that the trajectory of the system converges to a manifold. The special feature of the designed control system is that the closed-loop system asymptotically recovers the performance of a deterministic controller. This cannot happen if certainty-equivalent adaptive controllers are used. Simulation results are presented which show that the control system suppresses the oscillatory responses of the system in the presence of large parameter uncertainties.

Adaptive Tracking in Mobile Robots With Input-Output Linearization

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Cesáreo Raimúndez ◽  
Alejandro F. Villaverde ◽  
Antonio Barreiro
Keyword(s):  
Neural Network ◽  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Adaptive Controller ◽  
Lyapunov Theory ◽  
Input Output ◽  
External Perturbations ◽  
Neural Network Controller ◽  
Input Output Linearization

This paper presents a neural network adaptive controller for trajectory tracking of nonholonomic mobile robots. By defining a point to follow (look-ahead control), the path-following problem is solved with input-output linearization. A computed torque plus derivative (PD) controller and a dynamic inversion neural network controller are responsible for reducing tracking error and adapting to unmodeled external perturbations. The adaptive controller is implemented through a hidden layer feed-forward neural network, with weights updated in real time. The stability of the whole system is analyzed using Lyapunov theory, and control errors are proven to be bounded. Simulation results demonstrate the good performance of the proposed controller for trajectory tracking under external perturbations.

scholarly journals Robust Discrete-Time Nonlinear Attitude Stabilization of a Quadrotor UAV Subject to Time-Varying Disturbances

2021 ◽  
Author(s):  
Fatih Adiguzel ◽  
Tarik Veli Mumcu
Keyword(s):  
Discrete Time ◽  
Disturbance Observer ◽  
Uncertain System ◽  
Time Varying ◽  
Input Output ◽  
Parameter Uncertainties ◽  
Nonlinear Disturbance Observer ◽  
Nonlinear Disturbance ◽  
Quadrotor System ◽  
Input Output Linearization

A discrete-time improved input/output linearization controller based on a nonlinear disturbance observer is considered to secure the stability of a four-rotor unmanned aerial vehicle under constant and time-varying disturbances, as well as uncertain system parameters for its attitude behaviour. Due to the nature of the quadrotor system, it contains the most extreme high level of nonlinearities, system parameter uncertainties (perturbations), and it has to cope with external disturbances that change over time. In this context, an offset-less tracking for the quadrotor system is provided with the input/output linearization controller together with a discrete-time pre-controller. In addition, the robustness of the system is increased with a discrete-time nonlinear disturbance observer for time-varying disturbances affecting the system. The main contribution of this study is to provide highly nonlinearities cancellation to guarantee the aircraft attitude stability and to propose a robust control structure in discrete-time, considering all uncertainties. Various simulation studies have been carried out to illustrate the robustness and effectiveness of the proposed controller structure.

scholarly journals Two-Valued Control for a Second-Order Plant with Additive External Disturbance

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Alejandro Rincon ◽  
Felipe Londoño ◽  
Fabiola Angulo
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Function Method ◽  
Controller Design ◽  
Tracking Error ◽  
Reference Signal ◽  
Second Order ◽  
State Feedback Control ◽  
Control Input ◽  
Residual Set

In this work a two-valued state feedback control for a plant of second order with known constant coefficients and an additive bounded disturbance is designed. In this controller the control signal can take only two possible values. The controller design is based on Lyapunov-like function method, achieving the convergence of the tracking error to a user-defined residual set. A boundedness condition for the user-defined reference signal is defined, which is necessary to allow out-put tracking. The developed scheme avoids large commutation rate of the control input. The controller design and stability analysis have important contributions with respect to closely related controllers based on the direct Lyapunov method, namely, (i) conditions to guarantee the expected convergence of the tracking error are established. These conditions are imposed on the reference signal and the extreme values of the control input. The stability analysis is developed by means of the Lyapunov-like function method and the Barbalat's Lemma and includes (ii) the bounded nature of the Lyapunov function, (iii) the monotonic convergence of the Lyapunov function to a residual set, and (iv) the asymptotic convergence of the tracking error to a residual set of user-defined size.

Two-degree-of-freedom Controller Design for Uncertain Processes Using Input/output Linearization Control Technique

2011 ◽  
Vol 11 (1) ◽  
pp. 16 ◽  
Author(s):  
Pisit Sukkarnkha ◽  
Chanin Panjapornpon
Keyword(s):  
Disturbance Rejection ◽  
Control Structure ◽  
Control Method ◽  
Random Noise ◽  
Degree Of Freedom ◽  
Control Technique ◽  
Input Output ◽  
Tracking Controller ◽  
Two Degree Of Freedom ◽  
Input Output Linearization

In this work, a new control method for uncertain processes is developed based on two-degree-of-freedom control structure. The setpoint tracking controller designed by input/output linearization technique is used to regulate the disturbance-free output and the disturbance rejection controller designed is designed by high-gain technique. The advantage of two-degree-of-freedom control structure is that setpoint tracking and load disturbance rejection controllers can be designed separately. Open-loop observer is applied to provide disturbance-free response for setpoint tracking controller. The process/disturbance-free model mismatches are fed to the disturbance rejection controller for reducing effect of disturbance. To evaluate the control performance, the proposed control method is applied through the example of a continuous stirred tank reactor with unmeasured input disturbances and random noise kinetic parametric uncertainties. The simulation results show that both types of disturbances can be effectively compensated by the proposed control method.

scholarly journals A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 82
Author(s):  
Alejandro Rincón ◽  
Gloria M. Restrepo ◽  
Fredy E. Hoyos
Keyword(s):  
Lyapunov Functions ◽  
Dead Zone ◽  
Tracking Error ◽  
Input Saturation ◽  
Chemical Reactor ◽  
Second Order ◽  
Control Law ◽  
Compact Set ◽  
State Variables ◽  
Robust Observer

In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor.

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