George Meyer

Nonlinear control design for slightly non-minimum phase systems: application to V/STOL aircraft

Abstract There has been a great deal of excitement recently over the development of a theory for explicitly linearizing the input-output response of a nonlinear system using state feedback. One shortcoming of this theory is the inability to deal with non-minimum phase nonlinear systems. Highly maneuverable jet aircraft, such as the V/STOL Harrier, belong to an important class of a slightly non-minimum phase nonlinear systems. The non-minimum phase character of aircraft is a result of the small body forces that are produced in the process of generating body moments. In this paper, we show that, while straightforward application of the linearization theory to a non-minimum phase system results in a system with a linear input-output response but unstable internal dynamics, designing a feedback control based on a minimum phase approximation to the true system results in a system with desirable properties such as bounded tracking and asymptotic stability.

Brief paper: Application of nonlinear transformations to automatic flight control

This paper presents the results of an application of transformations (from nonlinear to linear systems) to the design of a helicopter autopilot. The topics covered are (1) a review of the transformation theory and its use in the design approach, (2) a description of the helicopter mathematical model, (3) the construction of the transformation from the nonlinear system to the linear system, and (4) a discussion of the system performance.

Stable inversion for nonlinear systems

Abstract There have been two recent major developments in output tracking for nonlinear systems, and our first main contribution is to relate these. Under appropriate assumptions, we show that the bounded.solution of the partial differential equation of Isidori and Byrnes for each trajectory of an exosystem must be given by an integral representation formula of Devasia, Chen and Paden. Under restrictive hypotheses, Devasia, Chen and Paden develop a Picard process that converges to the solution of the integral equation. This solution to the integral equation is also a bounded solution to a dynamical equation driven by the desired outputs. In aircraft applications our nonlinear systems are perturbations of ‘pure-feedback systems’ with outputs, and we find a solution to the stable inversion problem i.e. finding bounded controls and bounded state trajectories in response to bounded output signals, in two steps. The first step ignores the perturbation error and computes the major part of the desired control and corresponding state trajectory. The second step computes the remaining control and states by finding a noncausal and stable solution to an ‘error-driven dynamical equation’. In other words, the method of Devasia, Chen and Paden is applied to an ‘error system’ and not to the full system. This two-step procedure is the second main contribution of this paper. Throughout this paper it is assumed that our nonlinear systems have vector relative degree.

Lagrangian Delay Predictive Model for Sector-Based Air Traffic Flow

A control theoretical model of sector-based air traffic flow is derived using hybrid automata theory. This model is Lagrangian, because it models the properties of the system along its trajectories. A subset of this model is used to generate analytic predictions of air traffic congestion: A dynamic sector capacity is defined and derived that is used fo rp redicting the time it takes to overload a given portion of airspace. This result links the Lagrangian approach with Eulerian models, which account for temporal variations of parameters in a fixed volume. To determine the accuracy of predictions, an air traffic flow simulator is designed and validated. The simulator is then used to show that flow scheduling and conflict resolution may be decorrelated by reducing aircraft density.

The design of exact nonlinear model followers

A practical approach to the design of control systems for strongly nonlinear, multivariable, time-dependent plants is described. The structure of the control system is that of an exact model follower. The model dynamics are decoupled, linear, constant, and of the order of the plant. The plant state and controls are transformed so that the plant, when viewed through these transformations, looks like the simple model. Regulation of disturbances is accomplished by means of the transformed state and controls. Conditions for transformability into linear models, the appropriate models, and the construction of the transformations are discussed. The approach is illustrated on a trajectory autopilot for a helicopter.

Synthesis and Viability of Minimally Interventive LegalControllers for Hybrid Systems

In this paper, we study the control of Composite Hybrid Machines (CHMs) subject to safety specifications. CHMs are a fairly general class of hybrid systems modeled in modular fashion as the concurrent operation of Elementary Hybrid Machines (EHMs). The formalism has a well-defined synchronous-composition operation that permits the introduction of the controller as a component of the system. The task of a legal (safety) controller is to ensure that the system never exits a set of specified legal configurations. Among the legal controllers, we are particularly interested in designing a minimally-interventive (or minimally-restrictive) one, which interferes in the systems operation only when constraint violation is otherwise inevitable. Thus, a minimally interventive safety controller provides maximum flexibility in embedding additional controllers designed for other control objectives to operate concurrently, while eliminating the need to re-investigate or re-verify the legality of the composite controller with respect to the safety specification. We describe in detail an algorithm for controller synthesis and examine the viability of a synthesized controller as related to the possibility of Zenoness, where the system can undergo an unbounded number of transitions in a bounded length of time.

Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints

We examine a class of hybrid systems called Composite Hybrid Machines (CHMs), that consist of the concurrent (and partially synchronized) operation of Elementary Hybrid Machines (EHMs). Legal behavior is specified by a set of illegal configurations that the CHM may not enter, and is to be achieved by the concurrent operation of the CHM with a suitably designed legal controller. A legal controller is minimally restrictive if, when composed to operate concurrently with another legal controller, it will never interfere with the operation of the other controller. We focus attention on the problem of synthesizing a minimally restrictive legal controller, whenever a legal controller exists. We present an algorithm for the synthesis of minimally restrictive legal controllers for CHMs with rate-limited dynamics, where legal guards are conjunctions or disjunctions of atomic formulas in the dynamic variables (of the type x ≤ x0 or x ≥ x0).

Nonlinear Controller Design for Flight Control Systems

Abstract There has been a great deal of excitement recently over the development of a theory for explicitly linearizing the input-output response of a nonlinear system using state feedback. One shortcoming of this theory is the inability to deal with non-minimum phase nonlinear systems. Highly maneuverable jet aircraft, such as the V/STOL Harrier, belong to an important class of a slightly non-minimum phase nonlinear systems. The non-minimum phase character of these aircraft is clue in part to a slight coupling between rolling moments and lateral accelerations. In this paper, we show that, while straightforward application of the linearization theory to a non-minimum phase system results in a system with a linear input-output response but unstable internal dynamics, designing a feedback control based on a minimum phase approximation to the true system results in a system with desirable properties such as bounded tracking and asymptotic stability.

Automated conflict resolution procedures for air traffic management

The current air traffic control system (ATC) requires aircraft to travel along set route segments along prescribed flight corridors on the highway system in the sky. Under this paradigm, airline operational centers (AOC) do not have direct control once the aircraft is on a cleared flight plan. Continuing to fly on a prespecified route, however, can substantially increase costs due to emerging situations like changing weather patterns, missed connections, and traffic congestion along the route. The paper discusses a conflict resolution methodology for air traffic management. The applicability of this methodology to advance the free flight paradigm is considered.

Decoupled Conflict-Resolution Procedures for Decentralized Air Traffic Control

This article addresses the decoupling of conflict resolution procedures (CRPs) for decentralized, en-route, air traffic control. The main contribution of this article is to identify necessary and sufficient conditions to decouple CRPs. Additionally, the article demonstrates the existence of such decentralized en-route CRPs, which guarantee global conflict resolution.