A Direct Adaptive Control Method With Desired Compensation For Robotic Manipulators

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model. Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinite-dimensional Hilbert space. The result will not require the use of the standard Barbalat's lemma which requires certain signals to be uniformly continuous. This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model. In particular, we examine conditions for a set of ideal trajectories to exist for the tracking problem. Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.

Stable direct adaptive neural controller of nonlinear systems based on single auto-tuning neuron

In this paper, we introduce a direct fractional order adaptive control design based on model reference adaptive control (MRAC) structure for a class of commensurate fractional order linear systems with an arbitrary relative degree, and whose parameters are unknown. By generalising the application of standard direct MRAC strategy to plants described by fractional order models, we develop a fractional adaptive control scheme (FOMRAC) based on the output feedback. We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory. The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem. Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

The force tracking error is dependent on both the position tracking error and the estimated parameter error so that, in constrained adaptive robot control, the convergence of the estimated parameter error becomes more important than in unconstrained adaptive robot control. However, in the direct adaptive controller, the parameter adaptation is driven only by the tracking error in the joint motion, while in the indirect adaptive controller, the parameter estimation is driven only by the prediction error in the joint torque. Based on this observation a new combined direct and indirect adaptive controller driven by both the tracking error and the prediction error is developed for constrained robots with inertia parameter uncertainty. Stability of the combined adaptive controllers is established in the Lyapunov sense. The combined control improves both position and force tracking performance compared with direct adaptive control. The computer simulations are presented to demonstrate the proposed schemes.

This paper presents the development of direct adaptive control laws to enable an autonomous unmanned aerial vehicle (UAV) to track reference trajectories in the presence of external disturbances. A maneuver database of reference trajectories is computed offline from a linear UAV dynamic model using an optimization routine. Each maneuver in the database is therefore represented as a state trajectory, as well as the control input sequence that generates that trajectory. The trajectory tracking control laws are designed to enable a UAV to follow reference trajectories from this maneuver database. A disturbance accommodating control law is first developed and applied for the tracking of reference trajectories while the UAV is subjected to a persistent external disturbance. This control design requires a state-space disturbance generator model and the derivation of ideal trajectories from a reference model, which requires the solution of a set of matching conditions. A direct adaptive controller is then developed to enable the UAV to track reference trajectories while subject to modeling error and external disturbances. The adaptive controller also requires a disturbance model and the existence of ideal trajectories, but it does not require the explicit solution of the matching conditions. Simulation results for the disturbance accommodating controller and the adaptive controller are presented using a linear six-degree-of-freedom dynamic model that is representative of typical UAV dynamics. The results show that, although both controllers track reference trajectories and provide disturbance rejection, the adaptive controller is better suited for handling modeling errors or uncertainties.

Fire-rule-based direct adaptive type-2 fuzzy H∞ tracking control

Various advanced control strategies are applied to a direct-drive SCARA robot and studied in computer simulations. Besides computed torque control and direct adaptive control, heuristic optimal control, a new path control scheme for robotic manipulators, is included in the comparison study. PD control, the traditional robot control method, is used for generating a comparing baseline. While all schemes are applied for the same tracking task, the effect of modelling errors and measurement noise is considered in robot performance evaluation. Simulation results show that (1) without model errors, all advanced control schemes can achieve higher tracking accuracy than PD control; (2) with a random measurement error of 1%, computed torque and direct adaptive control methods are inferior to PD control; (3) heuristic control proves to be the most robust control scheme in case of mixed model and measurement errors.

A controller to rotate a rigid body between two successive orientations is designed. Particular features are the fact that it is based on the quaternion approach, known to provide singularity-free attitude description, and it is adaptive in the sense that it does not need specific knowledge of the inertia matrix. Global stability of the overall controller is proved analytically and tested in computer simulations. © 1994 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system

The modified positive position feedback (MPPF) controller, an active vibration control method that uses collocated piezoelectric actuator actuators and sensors, is developed using an adaptive controller. The adaptive mechanism consists of two main parts: (1) frequency adaptation and (2) adaptive controller. Frequency adaptation only tracks the frequency of vibrations using fast Fourier transforms. The obtained frequency is then fed to MPPF compensators and the adaptive controller. This provides a unique feature for MPPF by extending its domain of capabilities from controlling tonal vibrations to broadband disturbances. The adaptive controller mechanism consists of a reference model that is of the same order as the MPPF system and its compensators. The adaptive law provides the additional control force that is needed for controlling frequency changes caused by broadband vibrations. The experimental results show that the frequency adaptation method that is derived has worked quite well. The results also indicate that the MPPF can provide significant vibration reduction on a cantilever beam that is used throughout the experiments.

This paper shows that stable direct adaptive control of an LTI plant is possible using knowledge of only the plant order. The approach is based on periodic control, which relocates system zeros. No prior knowledge of the plant high-frequency gain or relative degree is used, and persistent excitation is not required. More importantly, no assumption or knowledge is required as to whether the plant is minimum or nonminimum phase. >

Intelligent switching adaptive control for uncertain nonlinear dynamical systems

This paper proposes a new scheme for direct neural adaptive control that works efficiently employing only one neural network, used for simultaneously identifying and controlling the plant. The idea behind this structure of adaptive control is to compensate the control input obtained by a conventional feedback controller. The neural network training process is carried out by using two different techniques: backpropagation and extended Kalman filter algorithm. Additionally, the convergence of the identification error is investigated by Lyapunov's second method. The performance of the proposed scheme is evaluated via simulations and a real time application.

A parameterization for a linear system is presented to design a direct model reference adaptive pole placement controller. This parameterized model is one of the structured nonminimal models. The exponentially weighted least-squares algorithm is employed to estimate the control parameters. The direct adaptive controller has the exponential weighting properties by the proposed method of selecting the characteristic polynomials of the sensitivity function filters in connection with the reference model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The problem of direct model reference adaptive control for multi input multi output (MIMO) uncertain plants with unknown high frequency gain matrix (HFGM) is addressed in the paper. Two schemes of adaptive control algorithms using augmented error estimators and relaxed assumption concerning HFGM are proposed. It is assumed that the minimum of modulus of HFGM determinant is known. The first scheme involves the resettable approximation of the inversion of HFGM estimate in control law. The second scheme is based on modification of conventional augmented error estimator by introduction of a switched projection mechanism. The proposed theoretical ideas are wrapped up by simulation examples.