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A method of transverse control which makes use of nonlinear formulations is presented. The strategy is utilized to stabilize a vehicle. The vehicle is autonomously guided and takes its control inputs from an optical sensing system. Additionally, the velocity of the vehicle is dictated by a longitudinal controller, which is also discussed.
Differential geometric system and control theory is used to develop a new dynamic system feedback technique for robot task space commands. The nonlinear robot arm system is feedback-linearized and simultaneously is output-decoupled by an appropriate nonlinear feedback and nonlinear coordinate transformation. On the joint space level, the scheme only commands drive forces or torques or their equivalent quantities addressed to the joint drives. An important property of the technique is that the planned and commanded task space trajectory together with its time derivatives directly drive the robot arm through a linear system model. A method for task space motion planning matching the requirements of the new scheme is briefly presented. The implications of the new technique for second and third order model robot arms with and without force feedback measuremnts and for two or more dynamically cooperating robot arms are discussed.
A piecewise linear method of analyzing the effects of discontinuous nonlinearities on control system performance is described. The limit cycle oscillatory behavior of the system resulting from the nonlinearities is described in terms of a sequence of linear system transient responses. The equations are derived which relate the initial and the terminal conditions of successive transients and the boundary conditions imposed by the non-linearities. The method leads to a convenient computation algorithm for prediction of limit cycle characteristics resulting from discontinuous nonlinearities such as friction, deadzones, and hysteresis.
This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.
An algorithm is presented for obtaining a reduced order or simplified nonlinear model of a nonlinear plant. The method provides a systematic approach for quickly finding the optimal simplified model of the system. Controllers are then designed around this nonlinear model and are used to control the original plant. An example design, for the F-8 aircraft, illustrates that the simplified model does indeed enable the design of a linear controller whose performance is indistinguishable from higher order optimal controllers for the original nonlinear plant. The net result is a simplified design procedure for effectively controlling complex nonlinear systems.
This paper addresses the problem of vibration prediction and vibration reduction in helicopters by means of active control methodologies. The nonlinear equations of a coupled rotor/flexible-fuselage system have been derived using computer algebra, thus relegating this tedious task to the computer. In the solution procedure the trim state and vibratory response of the helicopter are obtained in a single pass by using a harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter in all the rotor and fuselage degrees of freedom. Using this solution procedure, the influence of the fuselage flexibility on the vibratory response is studied. In addition, it is shown that the conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. A new scheme called MHHC, having multiple higher harmonic pitch inputs, was used to accomplish this task of simultaneously reducing both the vibratory hub loads and fuselage vibratory response. In addition, the uniqueness of this MHHC scheme is explained in detail.
The present article reports on active control and parameter updating techniques for thermal models based on the network approach.
Feedback control laws are presented for stabilization models of a hoop/column antenna. A brief review of linear and nonlinear feedback control laws is included. A method that is computable on a microprocessor and assures closed loop stability is explained and compared to a linear control law model.
To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.
Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.
The results of flight tests to determine the characteristics of spoiler roll control systems on three different light aircraft are summarized. Comparisons are made with wind tunnel data where available. Flight tests indicate that excellent roll characteristics can be achieved with spoilers. Yaw coupling with roll control inputs is virtually eliminated. Roll rates remain high when flaps are deployed at low speed. Very mild nonlinearities in control effectiveness exist, and there was no deadband or lag detected.
The results of flight tests to determine the characteristics of spoiler roll control systems on three different light aircraft are summarized. Comparisons are made with wind tunnel data where available. Flight tests indicate that excellent roll characteristics can be achieved with spoilers. Yaw coupling with roll control inputs is virtually eliminated. Roll rates remain high when flaps are deployed at low speed. Very mild nonlinearities in control effectiveness exist and there was no deadband or lag detected.
Mathematical model for rats nonlinear time-varying glucocorticoid secretion control mechanism, obtaining time dependent characteristics of hypothalamic-hypophyseal complex
This report provides a brief summary of the research work performed over the duration of the cooperative research agreement between NASA Langley Research Center and Kansas State University. The cooperative agreement which was originally for the duration the three years was extended by another year through no-cost extension in order to accomplish the goals of the project. The main objective of the research was to develop passivity-based robust control methodology for passive and non-passive aerospace systems. The focus of the first-year's research was limited to the investigation of passivity-based methods for the robust control of Linear Time-Invariant (LTI) single-input single-output (SISO), open-loop stable, minimum-phase non-passive systems. The second year's focus was mainly on extending the passivity-based methodology to a larger class of non-passive LTI systems which includes unstable and nonminimum phase SISO systems. For LTI non-passive systems, five different passification. methods were developed. The primary effort during the years three and four was on the development of passification methodology for MIMO systems, development of methods for checking robustness of passification, and developing synthesis techniques for passifying compensators. For passive LTI systems optimal synthesis procedure was also developed for the design of constant-gain positive real controllers. For nonlinear passive systems, numerical optimization-based technique was developed for the synthesis of constant as well as time-varying gain positive-real controllers. The passivity-based control design methodology developed during the duration of this project was demonstrated by its application to various benchmark examples. These example systems included longitudinal model of an F-18 High Alpha Research Vehicle (HARV) for pitch axis control, NASA's supersonic transport wind tunnel model, ACC benchmark model, 1-D acoustic duct model, piezo-actuated flexible link model, and NASA's Benchmark Active Controls Technology (BACT) Wing model. Some of the stability results for linear passive systems were also extended to nonlinear passive systems. Several publications and conference presentations resulted from this research.
The vortical flow over a delta wing contributes an important part of the lift - the so called nonlinear lift. Controlling this vortical flow with its favorable influence would enhance aircraft maneuverability at high angle of attack. Several previous studies have shown that control of the vortical flow field is possible through the use of blowing jets. The present experimental research studies vortical flow control by applying a new blowing scheme to the rounded leading edge of a delta wing; this blowing scheme is called Tangential Leading Edge Blowing (TLEB). Vortical flow response both to steady blowing and to unsteady blowing is investigated. It is found that TLEB can redevelop stable, strong vortices even in the post-stall angle of attack regime. Analysis of the steady data shows that the effect of leading edge blowing can be interpreted as an effective change in angle of attack. The examination of the fundamental time scales for vortical flow re-organization after the application of blowing for different initial states of the flow field is studied. Different time scales for flow re-organization are shown to depend upon the effective angle of attack. A faster response time can be achieved at angles of attack beyond stall by a suitable choice of the initial blowing momentum strength. Consequently, TLEB shows the potential of controlling the vortical flow over a wide range of angles of attack; i.e., in both for pre-stall and post-stall conditions.
Two mechanisms internal to the pilot that affect performance during a tracking task are: 1) Pilot equalization (i.e. lead/lag); and 2) Pilot gain (i.e. sensitivity to the error signal). For some applications McRuer's Crossover Model can be used to anticipate what equalization will be employed to control a vehicle's dynamics. McRuer also established approximate time delays associated with different types of equalization - the more cognitive processing that is required due to equalization difficulty, the larger the time delay. However, the Crossover Model does not predict what the pilot gain will be. A nonlinear pilot control technique, observed and coined by the authors as 'amplitude clipping', is shown to improve stability, performance, and reduce workload when employed with vehicle dynamics that require high lead compensation by the pilot. Combining linear and nonlinear methods a novel approach is used to measure the pilot control parameters when amplitude clipping is present, allowing precise measurement in real time of key pilot control parameters. Based on the results of an experiment which was designed to probe workload primary drivers, a method is developed that estimates pilot spare capacity from readily observable measures and is tested for generality using multi-axis flight data. This paper documents the initial steps to developing a novel, simple objective metric for assessing pilot workload and its variation over time across a wide variety of tasks. Additionally, it offers a tangible, easily implementable methodology for anticipating a pilot's operating parameters and workload, and an effective design tool. The model shows promise in being able to precisely predict the actual pilot settings and workload, and observed tolerance of pilot parameter variation over the course of operation. Finally, an approach is proposed for generating Cooper-Harper ratings based on the workload and parameter estimation methodology.
This paper, assuming steady wind and zero sideslip, presents a discrete-time mathematical model to obtain a control law and three-dimensional flight path to guide an aircraft in a given time from a given initial state (position, velocity and heading) to a prescribed final state subject to the constraints on airspeed acceleration, and pitch and bank angles of the aircraft. For ease in implementing the control law, the control inputs are assumed to be delayed and are applied in a sequential fashion. The guidance problem is formulated as a discrete nonlinear optimal control problem with time delays in dynamics and a cost functional of Bolza form. With a quadratic penalty function to handle terminal constraints on velocity and heading, a solution technique to the control problem based on conjugate gradient algorithm is investigated. Numerical examples are presented to illustrate the applicability of this approach to solution of a terminal area guidance problem in an automated air traffic control environment.