An Optimal Control Modification to Model-Reference Adaptive Control for Fast Adaptation

This paper presents a method that can achieve fast adaptation for a class of model-reference adaptive control. It is well-known that standard model-reference adaptive control exhibits high-gain control behaviors when a large adaptive gain is used to achieve fast adaptation in order to reduce tracking error rapidly. High gain control creates high-frequency oscillations that can excite unmodeled dynamics and can lead to instability. The fast adaptation approach is based on the minimization of the squares of the tracking error, which is formulated as an optimal control problem. The necessary condition of optimality is used to derive an adaptive law using the gradient method. This adaptive law is shown to result in uniform boundedness of the tracking error by means of the Lyapunov s direct method. Furthermore, this adaptive law allows a large adaptive gain to be used without causing undesired high-gain control effects. The method is shown to be more robust than standard model-reference adaptive control. Simulations demonstrate the effectiveness of the proposed method

Adaptive Flight Control Design with Optimal Control Modification on an F-18 Aircraft Model

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to as the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly; however, a large adaptive gain can lead to high-frequency oscillations which can adversely affect the robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient robustness. A damping term (v) is added in the modification to increase damping as needed. Simulations were conducted on a damaged F-18 aircraft (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) with both the standard baseline dynamic inversion controller and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model

Optimal Control Modification Adaptive Law for Time-Scale Separated Systems

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method

Comparative Analysis of MIT Rule and Lyapunov Rule in Model Reference Adaptive Control Scheme

Adaptive control involves modifying the control law used by the controller to cope with the fact that the parameters of the system being controlled change drastically due to change in environmental conditions or change in system itself. This technique is based on the fundamental characteristic of adaptation of living organism. The adaptive control process is one that continuously and automatically measures the dynamic behavior of plant, compares it with the desired output and uses the difference to vary adjustable system parameters or to generate an actuating signal in such a way so that optimal performance can be maintained regardless of system changes. This paper deals with application of model reference adaptive control scheme and the system performance is compared with Lyapunov rule and MIT rule. The plant which is taken for the controlling purpose is the first order system for simplicity. The comparison is done for different values of adaptation gain between MIT rule and Lyapunov rule. Simulation is done in MATLAB and simulink and the results are compared for varying adaptation mechanism due to variation in adaptation gain

Optimal Control Modification for Time-Scale Separated Systems

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method

Estimation-based synthesis of H∞-optimal adaptive FIR filtersfor filtered-LMS problems

This paper presents a systematic synthesis procedure for H∞-optimal adaptive FIR filters in the context of an active noise cancellation (ANC) problem. An estimation interpretation of the adaptive control problem is introduced first. Based on this interpretation, an H∞ estimation problem is formulated, and its finite horizon prediction (filtering) solution is discussed. The solution minimizes the maximum energy gain from the disturbances to the predicted (filtered) estimation error and serves as the adaptation criterion for the weight vector in the adaptive FIR filter. We refer to this adaptation scheme as estimation-based adaptive filtering (EBAF). We show that the steady-state gain vector in the EBAF algorithm approaches that of the classical (normalized) filtered-X LMS algorithm. The error terms, however, are shown to be different. Thus, these classical algorithms can be considered to be approximations of our algorithm. We examine the performance of the proposed EBAF algorithm (both experimentally and in simulation) in an active noise cancellation problem of a one-dimensional (1-D) acoustic duct for both narrowband and broadband cases. Comparisons to the results from a conventional filtered-LMS (FxLMS) algorithm show faster convergence without compromising steady-state performance and/or robustness of the algorithm to feedback contamination of the reference signal

Modeling and Lyapunov-designed based on adaptive gain sliding mode control for wind turbines

In this paper, modeling and the Lyapunov-designed control approach are studied for the Wind Energy Conversion Systems (WECS). The objective of this study is to ensure the maximum energy production of a WECS while reducing the mechanical stress on the shafts (turbine and generator). Furthermore, the proposed control strategy aims to optimize the wind energy captured by the wind turbine operating under rating wind speed, using an Adaptive Gain Sliding Mode Control (AG-SMC). The adaptation for the sliding gain and the torque estimation are carried out using the sliding surface as an improved solution that handles the conventional sliding mode control. Furthermore, the resultant WECS control policy is relatively simple, meaning the online computational cost and time are considerably reduced. Time-domain simulation studies are performed to discuss the effectiveness of the proposed control strateg

Fault tolerant control of a quadrotor using L-1 adaptive control

Purpose – The growing use of small unmanned rotorcraft in civilian applications means that safe operation is increasingly important. The purpose of this paper is to investigate the fault tolerant properties to faults in the actuators of an L1 adaptive controller for a quadrotor vehicle. Design/methodology/approach – L1 adaptive control provides fast adaptation along with decoupling between adaptation and robustness. This makes the approach a suitable candidate for fault tolerant control of quadrotor and other multirotor vehicles. In the paper, the design of an L1 adaptive controller is presented. The controller is compared to a fixed-gain LQR controller. Findings – The L1 adaptive controller is shown to have improved performance when subject to actuator faults, and a higher range of actuator fault tolerance. Research limitations/implications – The control scheme is tested in simulation of a simple model that ignores aerodynamic and gyroscopic effects. Hence for further work, testing with a more complete model is recommended followed by implementation on an actual platform and flight test. The effect of sensor noise should also be considered along with investigation into the influence of wind disturbances and tolerance to sensor failures. Furthermore, quadrotors cannot tolerate total failure of a rotor without loss of control of one of the degrees of freedom, this aspect requires further investigation. Practical implications – Applying the L1 adaptive controller to a hexrotor or octorotor would increase the reliability of such vehicles without recourse to methods that require fault detection schemes and control reallocation as well as providing tolerance to a total loss of a rotor. Social implications – In order for quadrotors and other similar unmanned air vehicles to undertake many proposed roles, a high level of safety is required. Hence the controllers should be fault tolerant. Originality/value – Fault tolerance to partial actuator/effector faults is demonstrated using an L1 adaptive controller

Continuous higher order sliding mode control with adaptation of air breathing hypersonic missile

This is the peer reviewed version of the following article: Yu, P., Shtessel, Y., and Edwards, C. (2016) Continuous higher order sliding mode control with adaptation of air breathing hypersonic missile. International Journal of Adaptive Control and Signal Processing, which has been published in final form at 10.1002/acs.2664. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving: http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms}Hypersonic missile control in the terminal phase is addressed using continuous higher order sliding mode (AHOSM) control with adaptation. The AHOSM self-tuning controller is proposed and studied. The double-layer adaptive algorithm is based on equivalent control concepts and ensures non-overestimation of the control gain to help mitigates control chattering. The proposed continuous AHOSM control is validated via simulations of a hypersonic missile in the terminal phase. The robustness and high accuracy output tracking in the presence of matched and unmatched external disturbances and missile model uncertainties is demonstrate