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This paper presents a new adaptive control approach using Chebyshev orthogonal polynomials as basis functions in a least-squares functional approximation. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. Flight control simulations demonstrate the effectiveness of the proposed adaptive control approach.
Decentralized adaptive control is considered for systems consisting of multiple interconnected subsystems. It is assumed that each subsystem s parameters are uncertain and the interconnection parameters are not known. In addition, mismatch can exist between each subsystem and its reference model. A strictly decentralized adaptive control scheme is developed, wherein each subsystem has access only to its own state but has the knowledge of all reference model states. The mismatch is estimated online for each subsystem and the mismatch estimates are used to adaptively modify the corresponding reference models. The adaptive control scheme is extended to the case with actuator failures in addition to mismatch.
A modern mechanization of a classical adaptive control concept is presented with an application to launch vehicle attitude control systems. Due to a rigorous flight certification environment, many adaptive control concepts are infeasible when applied to high-risk aerospace systems; methods of stability analysis are either intractable for high complexity models or cannot be reconciled in light of classical requirements. Furthermore, many adaptive techniques appearing in the literature are not suitable for application to conditionally stable systems with complex flexible-body dynamics, as is often the case with launch vehicles. The present technique is a multiplicative forward loop gain adaptive law similar to that used for the NASA X-15 flight research vehicle. In digital implementation with several novel features, it is well-suited to application on aerodynamically unstable launch vehicles with thrust vector control via augmentation of the baseline attitude/attitude-rate feedback control scheme. The approach is compatible with standard design features of autopilots for launch vehicles, including phase stabilization of lateral bending and slosh via linear filters. In addition, the method of assessing flight control stability via classical gain and phase margins is not affected under reasonable assumptions. The algorithm s ability to recover from certain unstable operating regimes can in fact be understood in terms of frequency-domain criteria. Finally, simulation results are presented that confirm the ability of the algorithm to improve performance and robustness in realistic failure scenarios.
A real time adaptive controller was designed and tested successfully on a fourth order laboratory dynamic system which features very low structural damping and a noncolocated actuator sensor pair. The controller, implemented in a digital minicomputer, consists of a state estimator, a set of state feedback gains, and a frequency locked loop (FLL) for real time parameter identification. The FLL can detect the closed loop natural frequency of the system being controlled, calculate the mismatch between a plant parameter and its counterpart in the state estimator, and correct the estimator parameter in real time. The adaptation algorithm can correct the controller error and stabilize the system for more than 50% variation in the plant natural frequency, compared with a 10% stability margin in frequency variation for a fixed gain controller having the same performance at the nominal plant condition. After it has locked to the correct plant frequency, the adaptive controller works as well as the fixed gain controller does when there is no parameter mismatch. The very rapid convergence of this adaptive system is demonstrated experimentally, and can also be proven with simple root locus methods.
Distributed Parameter Systems (DPS), such as systems described by partial differential equations, require infinite-dimensional state space descriptions to correctly model their dynamical behavior. However, any adaptive control algorithm must be finite-dimensional in order to be implemented via on-line digital computers. Finite-dimensional adaptive control of linear DPS requires stability analysis of nonlinear, time-varying, infinite-dimensional systems. The structure of nonadaptive finite-dimensional control of linear DPS is summarized as it relates to the existence of limiting systems for adaptive control. Two candidate schemes for finite-dimensional adaptive control of DPS are described and critical issues in infinite-dimensional stability analysis are discussed, in particular, the invariance principle, center manifold theory, and relationships between input-output and internal stability.
This paper is devoted to robust, Predictor-based Model Reference Adaptive Control (PMRAC) design. The proposed adaptive system is compared with the now-classical Model Reference Adaptive Control (MRAC) architecture. Simulation examples are presented. Numerical evidence indicates that the proposed PMRAC tracking architecture has better than MRAC transient characteristics. In this paper, we presented a state-predictor based direct adaptive tracking design methodology for multi-input dynamical systems, with partially known dynamics. Efficiency of the design was demonstrated using short period dynamics of an aircraft. Formal proof of the reported PMRAC benefits constitute future research and will be reported elsewhere.
This paper presents the design of a joint-space adaptive control scheme for controlling the slave arm motion of a dual-arm telerobot system developed at Goddard Space Flight Center (GSFC) to study telerobotic operations in space. Each slave arm of the dual-arm system is a kinematically redundant manipulator with seven degrees of freedom (DOF). Using the concept of model reference adaptive control (MRAC) and Liupunov direct method, we derive an adaptation algorithm that adjusts the PD controller gains of the control scheme. The development of the adaptive control scheme assumes that the slave arm motion is non-compliant and slowly varying. The implementation of the derived control scheme does not require the computation of manipulator dynamics which makes the control scheme sufficiently fast for real-time applications. Computer simulation study performed for the 7-DOF slave arm shows that the developed control scheme can efficiently adapt to sudden change in payload while tracking various test trajectories such as ramp or sinusoids with negligible position errors.
A decentralized model reference adaptive control (DMRAC) method is developed for large flexible structures (LFS). The development follows that of a centralized model reference adaptive control for LFS that have been shown to be feasible. The proposed method is illustrated using a simply supported beam with collocated actuators and sensors. Results show that the DMRAC can achieve either output regulation or output tracking with adequate convergence, provided the reference model inputs and their time derivatives are integrable, bounded, and approach zero as t approaches infinity.
The National Aeronautics and Space Administration s Dryden Flight Research Center completed flight testing of adaptive controls research on a full-scale F-18 testbed. The validation of adaptive controls has the potential to enhance safety in the presence of adverse conditions such as structural damage or control surface failures. This paper describes the research interface architecture, risk mitigations, flight test approach and lessons learned of adaptive controls research.
This paper is the final report for my Spring 2019 internship at the Kennedy Space Center in Cape Canaveral, Florida. The official title of my internship is 'Launch Vehicle Control Study internship,' and I spent the spring working in GMRO- Granular Mechanics and Regolith Operations. There are two components to my project involving developing an adaptive control law for a PID controller. The first component involves performing a deep study and analysis of adaptive control laws, with the goal of developing stability proofs about the control law and the gain and phase margins. The second component involves analyzing the data received after implementing the adaptive control law. Unfortunately, as of the time of writing this paper, the data is not considered ‘clean' enough to analyze. Therefore, in this paper I will give an overview of adaptive control law stability proofs and will write about the data analysis separately. Section II includes several general definitions, and the later sections have additional definitions at the end of each section.A PID (proportional integral derivative) controller is a common control algorithm which isimplemented in NASA’s rocket launch system. The idea behind the PID controller is to calculatethe error (current position – desired position) and drive it to zero by using proportional, integral,and derivative influences on the controller. For example, when a sailor steers a ship which isheading towards location 𝑥 but would like to turn the ship to reach location 𝑥∗, he/she wouldinitially turn the wheel significantly, and as the ship proceeds towards 𝑥∗ the sailor would slowlyshift the wheel back to its original position, and thereby drive the error, 𝑥∗ − 𝑥, to zero.
National Aeronautics and Space Administration (NASA) researchers have conducted a series of flight experiments designed to study the effects of varying levels of adaptive controller complexity on the performance and handling qualities of an aircraft under various simulated failure or damage conditions. A baseline, nonlinear dynamic inversion controller was augmented with three variations of a model reference adaptive control design. The simplest design consisted of a single adaptive parameter in each of the pitch and roll axes computed using a basic gradient-based update law. A second design was built upon the first by increasing the complexity of the update law. The third and most complex design added an additional adaptive parameter to each axis. Flight tests were conducted using NASA s Full-scale Advanced Systems Testbed, a highly modified F-18 aircraft that contains a research flight control system capable of housing advanced flight controls experiments. Each controller was evaluated against a suite of simulated failures and damage ranging from destabilization of the pitch and roll axes to significant coupling between the axes. Two pilots evaluated the three adaptive controllers as well as the non-adaptive baseline controller in a variety of dynamic maneuvers and precision flying tasks designed to uncover potential deficiencies in the handling qualities of the aircraft, and adverse interactions between the pilot and the adaptive controllers. The work was completed as part of the Integrated Resilient Aircraft Control Project under NASA s Aviation Safety Program.
A prime obstacle to the widespread use of adaptive control is the degradation of performance and possible instability resulting from the presence of unmodeled dynamics. The approach taken is to explicitly include the unstructured model uncertainty in the output error identification algorithm. The order of the compensator is successively increased by including identified modes. During this model building stage, heuristic rules are used to test for convergence prior to designing compensators. Additionally, the recursive identification algorithm as extended to multi-input, multi-output systems. Enhancements were also made to reduce the computational burden of an algorithm for obtaining minimal state space realizations from the inexact, multivariate transfer functions which result from the identification process. A number of potential adaptive control applications for this approach are illustrated using computer simulations. Results indicated that when speed of adaptation and plant stability are not critical, the proposed schemes converge to enhance system performance.
An approach in which the manipulator inverse is used as a feedforward controller is employed in the adaptive control of manipulators in order to achieve trajectory tracking by the joint angles. The desired trajectory is applied as an input to the feedforward controller, and the controller output is used as the driving torque for the manipulator. An adaptive algorithm obtained from MRAC theory is used to update the controller gains to cope with variations in the manipulator inverse due to changes of the operating point. An adaptive feedback controller and an auxiliary signal enhance closed-loop stability and achieve faster adaptation. Simulation results demonstrate the effectiveness of the proposed control scheme for different reference trajectories, and despite large variations in the payload.
An averaging analysis of indirect, discrete-time, adaptive control systems is presented. The analysis results in a signal-dependent stability condition and accounts for unmodeled plant dynamics as well as exogenous disturbances. This analysis is applied to two discrete-time adaptive algorithms: an unnormalized gradient algorithm and a recursive least-squares (RLS) algorithm with resetting. Since linearization and averaging are used for the gradient analysis, a local stability result valid for small adaptation gains is found. For RLS with resetting, the assumption is that there is a long time between resets. The results for the two algorithms are virtually identical, emphasizing their similarities in adaptive control.
An application of Model Reference Adaptive Control (MRAC) to the position and force control of flexible manipulators and robots is presented. A single-link flexible manipulator is analyzed. The problem was to develop a mathematical model of a flexible robot that is accurate. The objective is to show that the adaptive control works better than 'conventional' systems and is suitable for flexible structure control.
This paper presents a stable discrete-time adaptive law that targets modeling errors in a direct adaptive control framework. The update law was developed in our previous work for the adaptive disturbance rejection application. The approach is based on the philosophy that without modeling errors, the original control design has been tuned to achieve the desired performance. The adaptive control should, therefore, work towards getting this performance even in the face of modeling uncertainties/errors. In this work, the baseline controller uses dynamic inversion with proportional-integral augmentation. Dynamic inversion is carried out using the assumed system model. On-line adaptation of this control law is achieved by providing a parameterized augmentation signal to the dynamic inversion block. The parameters of this augmentation signal are updated to achieve the nominal desired error dynamics. Contrary to the typical Lyapunov-based adaptive approaches that guarantee only stability, the current approach investigates conditions for stability as well as performance. A high-fidelity F-15 model is used to illustrate the overall approach.
Adaptive control techniques are well suited to nonlinear applications, such as wind turbines, which are difficult to accurately model and which have effects from poorly known operating environments. The turbulent and unpredictable conditions in which wind turbines operate create many challenges for their operation. In this paper, we design an adaptive collective pitch controller for a high-fidelity simulation of a utility scale, variable-speed horizontal axis wind turbine. The objective of the adaptive pitch controller in Region 3 is to regulate generator speed and reject step disturbances. The control objective is accomplished by collectively pitching the turbine blades. We use an extension of the Direct Model Reference Adaptive Control (DMRAC) approach to track a reference point and to reject persistent disturbances. The turbine simulation models the Controls Advanced Research Turbine (CART) of the National Renewable Energy Laboratory in Golden, Colorado. The CART is a utility-scale wind turbine which has a well-developed and extensively verified simulator. The adaptive collective pitch controller for Region 3 was compared in simulations with a bas celliansesical Proportional Integrator (PI) collective pitch controller. In the simulations, the adaptive pitch controller showed improved speed regulation in Region 3 when compared with the baseline PI pitch controller and it demonstrated robustness to modeling errors.
A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.