Numerical Approach to Nonlinear Control Design

1996 ◽  
Vol 118 (2) ◽  
pp. 332-337 ◽  
Author(s):  
Mile Ostojic
Keyword(s):  
Tracking Control ◽  
Recurrence Relations ◽  
Control Design ◽  
Numerical Approach ◽  
Control Algorithms ◽  
Control Laws ◽  
New Approach ◽  
Parameter Variations ◽  
Error Dynamics ◽  
Nonlinear Plants

The paper presents a new approach to designing tracking control of uncertain nonlinear plants. The approach is entirely based on numerical methods and corresponding recurrence relations. It results in recursive control laws that resolve plant nonlinearities and compensate all disturbances and parameter variations. Also, it enables a free shaping of the control error dynamics. Control algorithms based on the method of successive substitutions and the Newton’s method are studied in detail. Detailed description of an application and experimental evaluation is included.

Model Tracking Control of Hamiltonian Systems

1989 ◽  
Vol 111 (4) ◽  
pp. 656-660 ◽  
Author(s):  
H. Flashner ◽  
J. M. Skowronski
Keyword(s):  
Tracking Control ◽  
Cartesian Product ◽  
Large Angle ◽  
Control Law ◽  
Simulation Studies ◽  
Control Laws ◽  
New Approach ◽  
Finite Time Horizon ◽  
Plant Simulation ◽  
Two Degree Of Freedom

A new approach is presented for deriving control laws for dynamic systems that can be formulated by Hamilton’s canonical equations. The approach uses the complete nonlinear equations of the system without requiring linearization. It is shown that the error equations, between the system and a Hamiltonian model to be followed, can be described by Hamilton’s canonical equations. Using the concept of diagonal set in the cartesian product of the system and the model states, a control law is derived using the Liapunov stability approach. The resulting control law allows tracking within a stipulated precision, and also with a finite time horizon. To demonstrate the method, a control law is derived for a two degree of freedom manipulator, designed to follow a linear plant. Simulation studies show fast convergence of the state error for a large angle motion maneuver.

scholarly journals Robust Switched Control Design for Nonlinear Systems Using Fuzzy Models

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wallysonn Alves de Souza ◽  
Marcelo Carvalho Minhoto Teixeira ◽  
Máira Peres Alves Santim ◽  
Rodrigo Cardim ◽  
Edvaldo Assunção
Keyword(s):  
Lyapunov Function ◽  
Design Method ◽  
Time Derivative ◽  
Control Design ◽  
Linear Matrix ◽  
Control Laws ◽  
Switching Law ◽  
Fuzzy Models ◽  
Switched Control ◽  
Nonlinear Plants

The paper proposes a new switched control design method for some classes of uncertain nonlinear plants described by Takagi-Sugeno fuzzy models. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology eliminates the need to find the membership function expressions to implement the control laws. The control designs of a ball-and-beam system and of a magnetic levitator illustrate the procedure.

Backward Path Tracking of Mobile Robot with Two Trailers

2014 ◽  
Vol 716-717 ◽  
pp. 1512-1517
Author(s):  
Yu Ma ◽  
Yong Zhang ◽  
Jin Cheng ◽  
Qin Jun Zhao
Keyword(s):  
Mobile Robot ◽  
Tracking Control ◽  
Path Tracking ◽  
Control Law ◽  
Control Laws ◽  
New Approach ◽  
Smooth Control ◽  
The Social ◽  
Continuous Progress ◽  
Nonlinear Smooth

With the social development and the continuous progress of science and technology, the mobile robots can greatly improve efficiency, reduce costs, many of these applications can be attributed to the backward path tracking control problem. A controller for backward path tracking of mobile robot with two trailers is addressed in this paper. The paper presents a new approach to stabilizing the system in backward motion by controlling the orientation angles of the two trailers. Nonlinear smooth control laws for orientations of the trailers with asymptotic stability in backward motion are then proposed. The result simulated in Simulink illustrates the effectiveness of the control law and the controller.

scholarly journals A Distance-Reduction Trajectory Tracking Control Algorithm for a Rear-Steered AGV

2018 ◽  
Vol 7 (2) ◽  
pp. 81-94
Author(s):  
Anugrah K Pamosoaji
Keyword(s):  
Trajectory Tracking ◽  
Tracking Control ◽  
Control Algorithm ◽  
Control Design ◽  
Control Algorithms ◽  
Trajectory Tracking Control ◽  
Reference Distance ◽  
Position And Orientation

This paper presents a Lyapunov-based switched trajectory tracking control design for a rear-steered automated guided AGV (AGV). Given a moving reference whose position and orientation have to be tracked by the AGV, the main objective of the controller is to reduce AGV’s distance from the reference while adjusting its orientation. The distance reduction issue is important, especially in huge warehouses operating a group of AGVs, since the rate of AGV-to-reference distance reduction contributes to the possibility of AGV-to-AGV collision. A set of control algorithms is proposed to handle large AGV’s orientation. Simulations that show the performance of the proposed method is presented.

scholarly journals Formation Tracking Control and Obstacle Avoidance of Unicycle-Type Robots Guaranteeing Continuous Velocities

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4374
Author(s):  
Jose Bernardo Martinez ◽  
Hector M. Becerra ◽  
David Gomez-Gutierrez
Keyword(s):  
Obstacle Avoidance ◽  
Tracking Control ◽  
Global Coordinate System ◽  
Avoidance Task ◽  
Time Varying ◽  
Control Laws ◽  
Formation Tracking ◽  
Control Scheme ◽  
First Time ◽  
Hierarchical Scheme

In this paper, we addressed the problem of controlling the position of a group of unicycle-type robots to follow in formation a time-varying reference avoiding obstacles when needed. We propose a kinematic control scheme that, unlike existing methods, is able to simultaneously solve the both tasks involved in the problem, effectively combining control laws devoted to achieve formation tracking and obstacle avoidance. The main contributions of the paper are twofold: first, the advantages of the proposed approach are not all integrated in existing schemes, ours is fully distributed since the formulation is based on consensus including the leader as part of the formation, scalable for a large number of robots, generic to define a desired formation, and it does not require a global coordinate system or a map of the environment. Second, to the authors’ knowledge, it is the first time that a distributed formation tracking control is combined with obstacle avoidance to solve both tasks simultaneously using a hierarchical scheme, thus guaranteeing continuous robots velocities in spite of activation/deactivation of the obstacle avoidance task, and stability is proven even in the transition of tasks. The effectiveness of the approach is shown through simulations and experiments with real robots.

Robust Tracking Control for Takagi–Sugeno Fuzzy Systems With Unmeasurable Premise Variables: Application to Tank System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
H. Ghorbel ◽  
A. El Hajjaji ◽  
M. Souissi ◽  
M. Chaabane
Keyword(s):  
Tracking Control ◽  
Fuzzy Systems ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Robust Tracking Control ◽  
Fuzzy Observer ◽  
Tank System ◽  
System States ◽  
Takagi Sugeno

In this paper, a robust fuzzy observer-based tracking controller for continuous-time nonlinear systems presented by Takagi–Sugeno (TS) models with unmeasurable premise variables, is synthesized. Using the H∞ norm and Lyapunov approach, the control design for TS fuzzy systems with both unmeasurable premises and system states is developed to guarantee tracking performance of closed loop systems. Sufficient relaxed conditions for synthesis of the fuzzy observer and the fuzzy control are driven in terms of linear matrix inequalities (LMIs) constraints. The proposed method allows simplifying the design procedure and gives the observer and controller gains in only one step. Numerical simulation on a two tank system is provided to illustrate the tracking control design procedure and to confirm the efficiency of the proposed method.

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