A Control Design Method for Underactuated Mechanical Systems Using High-Frequency Inputs

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Sevak Tahmasian ◽  
Craig A. Woolsey
Keyword(s):  
Trajectory Tracking ◽  
High Frequency ◽  
Design Method ◽  
Tracking Error ◽  
Mechanical Systems ◽  
Control Design ◽  
Micro Air Vehicles ◽  
System Structure ◽  
Reference Trajectory ◽  
Underactuated Mechanical Systems

This paper presents a control design technique which enables approximate reference trajectory tracking for a class of underactuated mechanical systems. The control law comprises two terms. The first involves feedback of the trajectory tracking error in the actuated coordinates. Building on the concept of vibrational control, the second term imposes high-frequency periodic inputs that are modulated by the tracking error in the unactuated coordinates. Under appropriate conditions on the system structure and the commanded trajectory, and with sufficient separation between the time scales of the vibrational forcing and the commanded trajectory, the approach provides convergence in both the actuated and unactuated coordinates. The procedure is first described for a two degree-of-freedom (DOF) system with one input. Generalizing to higher-dimensional, underactuated systems, the approach is then applied to a 4DOF system with two inputs. A final example involves control of a rigid plate that is flapping in a uniform flow, a 3DOF system with one input. More general applications include biomimetic locomotion systems, such as underwater vehicles with articulating fins and flapping wing micro-air vehicles.

Many-Objective Optimal Design of Sliding Mode Controls

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Yousef Sardahi ◽  
Jian-Qiao Sun
Keyword(s):  
Optimal Design ◽  
Pareto Front ◽  
Sliding Mode ◽  
Design Method ◽  
Tracking Error ◽  
Control Design ◽  
Processing Algorithm ◽  
Order System ◽  
Post Processing ◽  
Control Effort

This paper presents a many-objective optimal (MOO) control design of an adaptive and robust sliding mode control (SMC). A second-order system is used as an example to demonstrate the design method. The robustness of the closed-loop system in terms of stability and disturbance rejection are explicitly considered in the optimal design, in addition to the typical time-domain performance specifications such as the rise time, tracking error, and control effort. The genetic algorithm is used to solve for the many-objective optimization problem (MOOP). The optimal solutions known as the Pareto set and the corresponding objective functions known as the Pareto front are presented. To assist the decision-maker to choose from the solution set, we present a post-processing algorithm that operates on the Pareto front. Numerical simulations show that the proposed many-objective optimal control design and the post-processing algorithm are promising.

scholarly journals Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
J. Humberto Pérez-Cruz ◽  
José de Jesús Rubio ◽  
Rodrigo Encinas ◽  
Ricardo Balcazar
Keyword(s):  
Neural Network ◽  
Trajectory Tracking ◽  
Feedback Linearization ◽  
Neural Control ◽  
Tracking Error ◽  
Uncertain System ◽  
Reference Trajectory ◽  
System A ◽  
Multiple Input ◽  
Feedback Linearization Control

The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.

Adaptive fault tolerant control for trajectory tracking of a quadrotor helicopter

2017 ◽  
Vol 40 (12) ◽  
pp. 3560-3569 ◽  
Author(s):  
Min Li ◽  
Zongyu Zuo ◽  
Hao Liu ◽  
Cunjia Liu ◽  
Bing Zhu
Keyword(s):  
Trajectory Tracking ◽  
Fault Tolerant ◽  
Tracking Error ◽  
Adaptive Controller ◽  
Reference Trajectory ◽  
Quadrotor Helicopter ◽  
Attitude Error ◽  
Inertial Parameters ◽  
Error Dynamics ◽  
Fast Adaptation

In this paper, an adaptive fault tolerant controller based on [Formula: see text] control is developed and applied to the trajectory tracking for a quadrotor helicopter. Both multiplicative and additive actuator faults are considered. The proposed design is based on nonlinear feed-forward compensations and a typical nonlinear quadrotor model with uncertain inertial parameters and external disturbances. The [Formula: see text] adaptive control design is slightly modified to adapt with the position and the attitude error dynamics. The proposed adaptive controller yields uniformly verifiable bounds on the transient and the steady-state tracking error for any designated bounded reference trajectory. In the presence of fast adaptation, the adaptive controller compensates for actuator fault and disturbances in a particular frequency range. Finally, simulation results are included to validate the effectiveness of the proposed design.

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