Jesse B. Hoagg

Internal Model Control in the Shift and Delta Domains

We construct multivariable internal model controllers in the shift and delta domains. To do so, we develop a linear algebraic approach to the multivariable command following and disturbance rejection problem that facilitates a unified treatment of the differential, shift, and delta domains.

Adaptive Control of the NASA Generic Transport Model Using Retrospective Cost Optimization

We provide a detailed description of retrospective-cost based adaptive control, which is 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 sign of the high-frequency gain as well as 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 information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known, and no matching conditions are required. We apply this adaptive control technique to NASA’s Generic Transport Model to illustrate disturbance rejection under unknown, reduced controller authority.

Direct adaptive dynamic compensation for minimum phase systems with unknown relative degree

We consider parameter-monotonic direct adaptive control for single-input-single-output minimum-phase linear time-invariant systems with knowledge of the sign of the high-frequency gain (first nonzero Markov parameter) and an upper bound on the magnitude of the high-frequency gain. The first part of the paper is devoted to fixed-gain analysis of single-parameter high-gain-stabilizing controllers. Two novel fixed-gain dynamic compensators are presented for stabilizing minimum-phase systems. One compensator stabilizes systems with arbitrary-but-known relative degree, while the other utilizes a Fibonacci series construction to stabilize systems with unknown-but-bounded relative degree. Next, we provide a general treatment of parameter-monotonic adaptive control, including a result that guarantees state convergence to zero. This result is then combined with the high-gain-stabilizing controllers to yield parameter-monotonic direct adaptive dynamic compensation for minimum-phase systems with either arbitrary-but-known or unknown-but-bounded relative degree

Discrete-Time Adaptive Command Following and Disturbance Rejection with Unknown Exogenous Dynamics

We present an adaptive controller that requires limited model information for stabilization, command following, and disturbance rejection for multi-input, multi-output minimum-phase discrete-time systems. Specifically, the controller requires knowledge of the open-loop systems relative degree and a bound on the first nonzero Markov parameter. Notably, the controller does not require knowledge of the command or disturbance spectrum as long as the command and disturbance signals are generated by Lyapunov-stable linear systems. Thus, the command and disturbance signals are combinations of discrete-time sinusoids and steps. In addition, the controller uses feedback action only and thus does not require a direct measurement of the command or disturbance signals. We prove global asymptotic convergence for command following and disturbance rejection

On the Zeros, Initial Undershoot, and Relative Degree of Collinear Lumped-Parameter Structures

This paper considers collinear lumped-parameter structures where each mass in the structure has a single degree of freedom. Specifically, we analyze the zeros and relative degree of the single-input, single-output (SISO) transfer function from the force applied to an arbitrary mass to the position, velocity, or acceleration of another mass. In particular, we show that every SISO force-to-motion transfer function of a collinear lumped-parameter structure has no positive (real open-right-half-plane) zeros. In addition, every SISO force-to-position transfer function of a spring-connected collinear lumped-parameter structure has no non-negative (real closed-right-half-plane) zeros. As a consequence, the step response does not exhibit initial undershoot. In addition, we derive an expression for the relative degree of SISO force-to-position transfer functions. The formula depends on the placement of springs and dashpots, but is independent of the values of the spring constants and damping coefficients. Next, we consider the special case of serially connected collinear lumped-parameter structures. In this case, we show that every SISO force-to-position transfer function of a serially connected collinear lumped-parameter structure is minimum phase, that is, has no closed-right-half-plane zeros. The proofs of these results rely heavily on graph-theoretic techniques.

Deadbeat internal model control for command following and disturbance rejection in discrete-time systems

Internal model control is an established technique in continuous-time linear control but has not been developed for discrete-time systems in the shift and delta domains. In this paper, we present a new linear algebraic solution to the multivariable command following and disturbance rejection problem that unifies continuous and discrete time. Furthermore, we present deadbeat internal model control for discrete-time systems in the shift and delta domains

Adaptive control of a flexible membrane using acoustic excitation and optical sensing

Flexible membranes are envisioned as a key component of large, lightweight, space-based systems. This paper focuses on the problem of adaptive disturbance rejection, that is, the rejection of external disturbances with unknown spectral content. It describes the design and operation of a laboratory testbed involving a exible membrane with acoustic excitation and optical sensing. The ARMARKOV adaptive disturbance rejection algorithm is used to reject single- and dual-tone disturbances without knowledge of the disturbance spectrum and with limited modeling of the membrane dynamics.

Broadband adaptive disturbance rejection for a deployable optical telescope testbed

Broadband adaptive disturbance rejection is demonstrated on the artificial white-light source of the deployable optical telescope (DOT) developed by the Air Force Research Laboratory (AFRL). Large deployable optical systems are envisioned as the future of space telescopes. These systems are require active control for disturbance rejection. In this paper, we consider a multi-input, multi-output discrete-time adaptive disturbance rejection algorithm. The algorithm requires knowledge of some Markov parameters of the system from the control signal inputs to the performance variables. No information about the disturbance spectrum is required. We demonstrate broadband disturbance rejection numerically on an identified model of DOTs white-light source and experimentally on the system itself.

On the zeros, initial undershoot, and relative degree of lumped-mass structures

This paper considers lumped-mass structures where each mass in the structure has a single degree of freedom. Specifically, we analyze the zeros and relative degree of the single-input single-output (SISO) transfer function from the force applied to an arbitrary mass to the position, velocity, or acceleration of another mass

Investigation of Cumulative Retrospective Cost Adaptive Control for Missile Application

A cumulative retrospective cost adaptive control algorithm is augmented to a gain-scheduled three loop autopilot to assess performance in a nonlinear three-degree-of-freedom missile model. The cumulative retrospective cost adaptive controller requires minimal model information; specifically estimates of the relative degree, 1st nonzero Markov parameter, and nonminimum phase zeros of the linearized missile model. A rate gyro sensor failure is applied to the model and the performance of the control techniques is investigated through an analysis of air-to-air intercept scenarios. The results indicate that an adaptive controller can, to some degree, improve the missile’s ability to engage a target when such a failure occurs. Nomenclature m Missile mass Iyy Missile Inertia g Acceleration due to gravity X;Z Inertial position in the X-Z plane U Inertial velocity component along the body frame x-axis of the center of gravity (CG) W Inertial velocity component along the body frame z-axis of the CG Vm Magnitude of missile velocity M Mach number Az;P Acceleration component along body frame z-axis at pointP along the body x-axis Angle of attack Pitch angle q Body rate Air density Sref Reference area dref Reference length Cx Aerodynamic force coefficient along the body frame x-axis Cz Aerodynamic force coefficient along the body frame z-axis Cm Aerodynamic moment coefficient along the body y-axis at the CG q Dynamic pressure p Tail fin angle T Thrust along body frame x-axis