Marc L. Steinberg

Adaptive Control of Feedback Linearizable Nonlinear Systems With Application to Flight Control

The question of output trajectory control of a class of input-output feedback linearizable nonlinear dynamical systems using state variable feedback in the presence of parameter uncertainty is considered. For the derivation of a control law, a hypersurface is chosen which is a linear function of the tracking error, its derivatives, and the integral of the tracking error. An adaptive control law is derived such that in the closed-loop system, the trajectory asymptotically converges to this hypersurface. For any trajectory evolving on this surface, the tracking error tends to zero. Based on these results, a new approach to the design of an adaptive flight control system is presented. In the closed-loop system, trajectory control of the sets of output variables roll angle, angle of attack, and sideslip angle ( ,#,/?) using aileron, rudder, and elevator control is presented. Simulation results are obtained to show that precise simultaneous longitudinal and lateral maneuvers can be performed in spite of large uncertainty in the aerodynamic parameters.

Comparison of Intelligent, Adaptive, and Nonlinear Flight Control Laws

Seven different nonlinear control laws for multiaxis control of a high-performance aircraft are compared in simulation. The control law approaches are fuzzy logic control, backstepping adaptive control, neural network augmented control, variable structure control, and indirect adaptive versions of model predictive control and dynamic inversion. In addition, a more conventional scheduled dynamic inversion control law is used as a baseline. In some of the cases, a stochastic genetic algorithm was used to optimize e xed parameters during design. The control laws are demonstrated on a six-degree-of-freedom simulation with nonlinear aerodynamic and engine models, actuator models with position and rate saturations, and turbulence. Simulation results include a variety of single- and multiple-axis maneuvers in normal operation and with failures or damage. The specie c failure and damage cases that are examined include single and multiple lost surfaces, actuator hardovers, and an oscillating stabilatorcase. Therearealso substantial differences between thecontrol law design and simulation models,which are used to demonstrate some robustness aspects of the different control laws.

Nonlinear predictive control of feedback linearizable systems and flight control system design

The question of output trajectory control of input-output feedback linearizable nonlinear dynamic systems using state variable feedback is considered. For the derivation of the predictive control law, a vector function s is chosen as a linear combination of the tracking error, its higher order derivatives, and the integral of the tracking error. The control law is obtained by the minimization of a quadratic function of the predicted value of s and the control input. It is shown that in the closed-loop system the trajectories are uniformly ultimately bounded in the presence of uncertainty in the system parameters. Based on these results, a flight control system for the trajectory control of the output variables pitch, sideslip, and roll angles (0, /3, ) using aileron, rudder, and elevator control is presented. Simulation results are obtained to show that precise simultaneous longitudinal and lateral maneuvers can be performed in spite of the uncertainty in the aerodynamic parameters.

Nonlinear adaptive and sliding mode flight path control of F/A-18 model

The question of inertial trajectory control of aircraft in the three-dimensional space is discussed. It is assumed that the nonlinear aircraft model has uncertain aerodynamic derivatives. The control system is decomposed into a variable structure outer loop and an adaptive inner loop. The outer-loop feedback control system accomplishes (x,y,z) position trajectory and sideslip angle control using the derivative of thrust and three angular velocity components (p,q,r) as virtual control inputs. Then an adaptive inner feedback loop is designed, which produces the desired angular rotations of aircraft using aileron, elevator, and rudder control surfaces to complete the maneuver. Simplification in the inner-loop design is obtained based on a two-time scale (singular perturbation) design approach by ignoring the derivative of the virtual angular velocity vector, which is a function of slow variables. These results are applied to a simplified F/A-18 model. Simulation results are presented which show that in the closed-loop system asymptotic trajectory control is accomplished in spite of uncertainties in the model at different flight conditions.

Effects of Control Allocation Algorithms on a Nonlinear Adaptive Design

Abstract : The effect of the choice of control allocation algorithm used in conjunction with a nonlinear adaptive control law is examined. In particular, an existing back stepping control law design is modified to allow the incorporation of various control allocation algorithms. Simulation results are presented for two separate adaptive control law designs and for a nonadaptive two-loop dynamic inversion controller. With the control law designs fixed, tracking maneuvers are simulated using four separate control allocation routines - Direct Allocation, Discrete Time Direct Allocation, Pseudo-inverse, and Weighted Pseudo-Inverse. System performance is then examined as a function of control allocation method. As expected, even though the remainder of the control law design remains fixed, system performance is directly impacted by the choice of control allocation algorithm. Further, some of the important control law/control allocation interactions are identified and their effects on overall system performance analyzed.

Nonlinear adaptive flight control with a backstepping design approach

Abstract : This paper examines the use of adaptive backstepping for multi-axis control of a high performance aircraft. The control law is demonstrated on a 6 Degree-of-Freedom simulation with nonlinear aerodynamic and engine models, actuator models with saturation, and turbulence. Simulation results are demonstrated for large pitch-roll maneuvers, and for maneuvers with failure of the right stabilator. There are substantial differences between the control law design and simulation models, which are used to demonstrate some robustness aspects of this control law. Actuator saturation is shown to be a considerable problem for this type of controller. However, the flexibility of the backstepping design provides opportunities for improvement. In particular, the Lyapunov function is modified so that the growth of integrated error and the rate of change of parameter growth are both reduced when the surface commands are growing at a rate that will likely saturate the actuators. In addition, the deadzone technique from robust linear adaptive control is applied to improve robustness to turbulence.

HIGH-FIDELITY SIMULATION TESTING OF CONTROL ALLOCATION METHODS

This paper describes high-fidelity simulation testing of some of the more popular advanced control allocation techniques integrated with two separate dynamic inversion control laws. The allocation methods include variations of quadratic programming, linear programming, direct allocation, cascaded generalized inverse, and weighted pseudo-inverse. Results are presented for single and multi-axis pitch and roll maneuvers with and without actuator failures. A velocity vector roll is also considered for the no failure case. Results show that a robust control law can mask differences in the various control allocation routines and lead to similar performance from both optimal and sub-optimal allocation methods. Furthermore, the current results illustrate that the closed-loop performance does not directly follow from the openloop measures that are widely used in the literature.

High-fidelity simulation testing of intelligent and adaptive aircraft control laws

This paper compares the robustness of seven popular adaptive and intelligent control approaches using a high fidelity aircraft simulation. The control laws were originally developed and tuned using a lower fidelity simulation of the same aircraft, which is significantly different from the high fidelity simulation used to generate all results in, this paper. The control law approaches examined are fuzzy logic, linearly and nonlinearly parameterized neural network approaches, an indirect adaptive version of dynamic inversion, variable structure, and a hybrid approach that combines direct and indirect adaptive elements. In addition, a conventional scheduled dynamic inversion controller is used as baseline. The approaches are demonstrated on a high fidelity six degree-of-freedom simulation with nonlinear aerodynamic and engine models, actuator models with position and rate saturations, and turbulence. Simulation results are given for single and multi-axis pitch and roll maneuvers in both nominal and failed cases.

A Comparison of Neural, Fuzzy, Evolutionary, and Adaptive Approaches for Carrier Landing

Abstract : This paper compares in simulation six control approaches for an automated carrier landing design problem. The key requirements of this problem are that the aircraft must remain within tight bounds on a three dimensional flight path while approaching the ship, and then touch down in a relatively small area with acceptable sink rate, angular attitudes and speed. Further, this must be accomplished with limited control authority for varying conditions of ship motion, air turbulence, radar tracking noise/data delays, and ship air wake. The control law approaches examined are: fuzzy logic, two neural network approaches, indirect adaptive and non-adaptive versions of dynamic inversion, and a hybrid approach that combines direct and indirect adaptive elements. In some of the cases, a genetic algorithm was used to optimize fixed parameters during design. The approaches were demonstrated on a 6 Degree-of-Freedom simulation with nonlinear aerodynamic and engine models, actuator models with position and rate saturations, and turbulence. Simulation results include statistics for landing with damage to both control and lifting surfaces in different environmental conditions.

Human system performance metrics for evaluation of mixed-initiative heterogeneous autonomous systems

This paper describes a set of human system performance metrics and their implementation and use in a series of operator experiments for mixed initiative control of multiple heterogeneous unmanned systems. The focus of the work is on technologies that support the control of five to ten air, sea, and undersea vehicles with a common human interface. The individual systems have significant differences both physically and with regards to their onboard level and type of autonomy. This includes some ability of the operator to modify the autonomy levels relative to particular types of autonomous decision-making. This paper will describe the set of metrics and experience in applying them including implementation factors and their utility. Finally, it will describe some lessons learned.