David A. Hullender

Nonlinear induced disturbance rejection in inertial stabilization systems

A frequent problem in inertial stabilization control systems is the rejection of disturbances associated with moving components. Very often such disturbances are nonlinear and time varying. A prime example is the relative motion of components within a gimbal; in this case, nonlinear bearing friction induces a destabilizing torque from base motion to the component being stabilized. This paper presents a linear quadratic Gaussian algorithm, based on a simple first-order linear stochastic differential equation, for estimating and compensating in real time a particular class of disturbances that can be modeled as a plus or minus unknown slowly changing random value which is characterized by nonlinear Coulomb friction. Results of computer simulations testing the control algorithm are presented along with actual measurements from a laboratory brassboard system. The results reveal a noteworthy improvement in disturbance rejection as compared with a conventional PI controller with notch filters.

Estimation of Receiver Aircraft States and Wind Vectors in Aerial Refueling

A square root unscented Kalman filter is used to estimate the states of a receiver aircraft and the components of the wind the aircraft is exposed to as it flies behind the tanker aircraft. The wind is the superposition of time-varying prevailing wind, turbulence, and the tanker’s wake-induced wind. The system update of the estimator uses the nonlinear aircraft model, augmented by a nonlinear wind model, obtained from the translational dynamics of the aircraft. The aircraft state estimates are successfully used in controlling the position of the receiver aircraft relative to the tanker flying straight level and making turns. Although the performance of the estimation and control is very dependent on the covariance and correlation time constants of the sensor measurement errors, the estimated state feedback performs better than measured state feedback with higher levels of measurement noise and turbulence intensity.

Estimation of Aircraft States and Wind Exposure

This paper presents an application of the Square Root Unscented Kalman Filter (SRUKF) to the estimation problem of aircraft system states and the atmospheric wind the aircraft is exposed to. The aircraft is controlled by an LQR-based feedback controller to y the aircraft with commanded airspeed, altitude and yaw rate. The estimation is based on measurements from conventional auto-pilot sensors. Simulation experiments show that the estimation algorithm can successfully estimate the states of the aircraft model as well as time-varying wind vector.

Single Phase Compressible Steady Flow in Pipes

In general, the computation of single phase subsonic mass velocity of gas flowing through a pipe requires a computerized iterative analysis. The equations for the friction factor for laminar and turbulent flow are used to obtain explicit equations for the subsonic mass velocity as a function of the pressures at the ends of a pipe. Explicit equations for mass velocity are presented. Included within the equations is a heat transfer ratio, which can vary between 0 for adiabatic flow conditions to 1 for isothermal flow conditions. The use of this heat transfer ratio also enables the formulation of an explicit equation for the gas temperature along the pipe for nonisothermal flow conditions. The explicit equations eliminate the need for an iterative solution. Laboratory data are used to support the accuracy of the model.

Self-tuning controller for nonlinear inertial stabilization systems

The ability to compensate for disturbances resulting form nonlinear phenomena such as Coulomb friction in inertial stabilization systems has been demonstrated to be feasible when the plant dynamics of the system are accurately modeled. However, for cases where the plant in unknown or changing, a self-tuning control algorithm is desired to prevent instability. This paper formulates such a self-tuning control algorithm with specific application to systems with inherent nonlinearities. The ability of the algorithm to self- tune and compensate for nonlinear induced disturbances is demonstrated for an inertial stabilization gimbal control system with Coulomb type bearing friction.

Nonlinear-induced disturbance rejection in inertial stabilization systems

A frequent problem in inertial stabilization control systems is the rejection of disturbances associated with moving components. Very often such disturbances are nonlinear and time varying. A prime example is the relative motion of components within a gimbal; in this case, nonlinear bearing friction induces a de-stabilizing torque from base motion to the component being stabilized. This paper presents an LQG algorithm, based on a simple first order linear stochastic differential equation, for estimating and compensating in real time a particular class of disturbances that can be modeled as a plus or minus unknown slowly changing random value such as is characterized by nonlinear Coulomb friction. Results of computer simulations testing the control algorithm are presented along with actual measurements from a laboratory brassboard system. The results reveal a noteworthy improvement in disturbance rejection as compared with a conventional PI controller with notch filters.

A Simplified Method for Formulating the Simulation Diagram for Systems Containing Lines With Fluid Transients

The overall objective of this paper is to present a simplified approach to formulating a time domain simulation diagram for a dynamic system containing liquid or gas lines with significant fluid transients without having to use questionable simplifying assumptions for the fluid transients model. To achieve this objective, formulation of a two-port model for the fluid transients in a line that is compatible with any line termination conditions and represented by rational polynomial transfer functions is presented. This linear two-port model is first achieved by obtaining an input/output causality matrix for a line with linear flow resistances representing transition losses or flow restrictions at each end. The laminar flow “Dissipative Model” for fluid transients that accounts for nonlinear frequency dependent friction effects and thermal effects in gas lines is used in the formulation in order to achieve the most comprehensive model for axial flow in a constant diameter tube. The next step in achieving the overall objective is to obtain rational polynomial transfer function approximations for the three transfer functions in the reformulated “Dissipative Model”. These rational polynomial transfer function approximations are obtained from least-squares curve fits in the frequency domain of the exact transfer functions from the “Dissipative Model”. Then, two step-by-step procedures, using these transfer functions, for drawing a simulation diagram for a dynamic system containing fluid lines are presented.© 2003 ASME

EVALUATION OF QUASI-LINEAR TECHNIQUES FOR NONLINEAR PROCESSES WITH RANDOM INPUTS

Publisher Summary This chapter discusses the evaluation of quasi-linear techniques for nonlinear processes with random inputs. It describes several approaches are mentioned for modeling of nonlinear processes with either deterministic or stochastic inputs. Quasilinear modeling techniques have been popular especially for systems with random inputs because of their simplicity in obtaining closed form solutions. These techniques require that the probability density functions for the system variables either be known or assumed. The chapter presents a model for a nonlinear process that is representative of a guideway profile with constrained irregularities. It also highlights relative merits of two quasilinear techniques in approximating the nonlinearity.