B. Xian

A continuous asymptotic tracking control strategy for uncertain nonlinear systems

In this note, we present a new continuous control mechanism that compensates for uncertainty in a class of high-order, multiple-input-multiple-output nonlinear systems. The control strategy is based on limited assumptions on the structure of the system nonlinearities. A new Lyapunov-based stability argument is employed to prove semiglobal asymptotic tracking.

A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems

In this paper, we develop a new discontinuous output feedback tracking controller for a class of uncertain, nonlinear, multi-input/multi-output, mechanical systems whose dynamics are first-order differentiable. A novel filter design and Lyapunov-type stability analysis are used to prove semi-global asymptotic tracking. As a by-product of the proposed framework, we also present the design of a new simple, discontinuous velocity observer that ensures global asymptotic velocity observation.

A Lyapunov-based piezoelectric controller for flexible Cartesian robot manipulators

A Lyapunov-based control strategy is proposed for the regulation of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam with a translational base support. The beam (arm) cross-sectional area is assumed to be uniform and Euler-Bernoulli beam theory assumptions are considered. Moreover, two types of damping mechanisms; namely viscous and structural dampings, are considered for the arm material properties. The arm base motion is controlled utilizing a linear actuator, while a piezoelectric (PZT) patch actuator is bonded on the surface of the flexible beam for suppressing residual beam vibrations. The equations of motion for the system are obtained using Hamiltons principle, which are based on the original infinite dimensional distributed system. Utilizing the Lyapunov method, the control force acting on the linear actuator and control voltage for the PZT actuator are designed such that the base is regulated to a desired set-point and the exponential stability of the system is attained. Depending on the composition of the controller, some favorable features appear such as elimination of control spillovers, controller convergence at finite time, suppression of residual oscillations and simplicity of the control implementation. The feasibility of the controller is validated through both numerical simulations and experimental testing.

Task-space tracking control of robot manipulators via quaternion feedback

In this paper, we consider the problem of task-space tracking control of robot manipulators. Based on a quaternion representation of the end-effector orientation, we design a class of task-space controllers that ensure asymptotic end-effector position and orientation tracking. To facilitate the control design, we first develop model-based and adaptive full-state feedback controllers. We then present a model-based output feedback controller that eliminates link velocity measurements via a model-based observer. The application of the proposed control strategy to redundant robots is also discussed. Simulation results based on a six-link manipulator system are presented for the output feedback controller.

Tracking control for robot manipulators with kinematic and dynamic uncertainty

The control objective in many robot manipulator applications is to command the end-effector motion to achieve a desired response. To achieve this objective a mapping is required to relate the joint/link control inputs to the desired Cartesian position and orientation. If there are uncertainties or singularities in the mapping, then degraded performance or unpredictable responses by the manipulator are possible. To address these issues, an adaptive tracking controller is developed in this paper for robot manipulators with uncertainty in the kinematic and dynamic models. The controller is developed based on the unit quaternion representation so that singularities associated with three parameter representations are avoided.

Output Feedback Tracking Control of an Underactuated Quad-Rotor UAV

This paper proposes a new controller for an underactuated quad-rotor family of small-scale unmanned aerial vehicles (UAVs) using output feedback (OFB). Specifically, an observer is designed to estimate the velocities and an output feedback controller is designed for a nonlinear UAV system in which only position and angles are measurable. The design is performed via a Lyapunov type analysis. A semi- global uniformly ultimate bounded (SGUUB) tracking result is achieved. Simulation results are shown to demonstrate the proposed approach.

Extremum-seeking nonlinear controllers for a human exercise machine

In this paper, a next generation exercise machine controller is developed for a single degree of freedom (DOF) system to maximize the users power output and ensure passivity with the user. In an effort to optimize the users power expenditure, a desired velocity trajectory is developed that seeks the unknown user-dependent optimal velocity setpoint. Two extremum-seeking algorithms are presented (e.g., Kristic and Deng, and Tuekosky et al.) that seek the optimal velocity setpoint while ensuring the trajectory is sufficiently differentiable. To track the reference trajectory and to ensure passivity, two controllers are developed. The first controller is developed based on the assumption that the users torque input can be measured. A second controller is designed that estimates the users torque input. Both controllers are proven to ensure that the exercise machine remains passive with respect to the users power output. The controllers are proven to yield semiglobal tracking through Lyapunov-based analyses. Proof-of-concept experimental results are provided that illustrate the performance of the torque estimation controller.

Robust tracking control of an underactuated quadrotor aerial-robot based on a parametric uncertain model

In this paper, the tracking control of a underactuated quadrotor aerial vehicle is presented where position and yaw trajectory tracking is achieved using feedback control system. The control design is complicated by considering parametric uncertainty in the dynamic modeling of the quadrotor aerial-robot. Robust control schemes are then designed using a Lyapunov-based approach to compensate for the unknown parameters in each dynamic subsystem model. Lyapunov-type stability analysis suggests a global uniform ultimately bounded (GUUB) tracking result.

Output Feedback Control for a Class of Uncertain MIMO Nonlinear Systems With Non-Symmetric Input Gain Matrix

In this paper, a new continuous output feedback control mechanism is developed for output tracking for a class of high-order multi-input nonlinear systems with an input gain matrix that is positive definite but non-symmetric. The controller yields semiglobal uniformly ultimately bounded (SGUUB) tracking while compensating for unstructured uncertainty in both the drift vector and the input matrix. First, a fullstate feedback controller is designed based on limited assumptions on the structure of the system nonlinearities and the controller is proven to yield SGUUB tracking through a Lyapunov-based analysis. Then, an output feedback control design based on a high gain observer is proposed. A comprehensive stability analysis of the closed-loop system under output feedback is carried out and a recovery of the state feedback SGUUB result is demonstrated for the output feedback control system. Neural network estimation method is employed in both state and output feedback control design to feedforward compensate for the nonlinear system uncertainty.

Extremum seeking nonlinear controllers for a human exercise machine

In this paper, a next generation exercise machine controller is developed for a single degree of freedom (DOF) system to maximize the users power output and ensure passivity with the user. In an effort to optimize the users power expenditure, a desired velocity trajectory is developed that seeks the unknown user-dependent optimal velocity setpoint. Two extremum-seeking algorithms are presented (e.g., Kristic and Deng, and Tuekosky et al.) that seek the optimal velocity setpoint while ensuring the trajectory is sufficiently differentiable. To track the reference trajectory and to ensure passivity, two controllers are developed. The first controller is developed based on the assumption that the users torque input can be measured. A second controller is designed that estimates the users torque input. Both controllers are proven to ensure that the exercise machine remains passive with respect to the users power output. The controllers are proven to yield semiglobal tracking through Lyapunov-based analyses. Proof-of-concept experimental results are provided that illustrate the performance of the torque estimation controller.