Matthew C. Turner

A new perspective on static and low order anti-windup synthesis

By viewing the anti-windup problem as a decoupled set of subsystems and relating this configuration to a general static anti-windup set-up, LMI conditions are established which guarantee stability and performance of the resulting closed-loop system. The approach taken, and the mapping used for the performance index, are logical and intuitive–-and, it is argued, central to the ‘true’ anti-windup objective. The approach enables one to construct static anti-windup compensators in a systematic and numerically tractable manner. The idea is extended to allow low-order anti-windup compensators to be synthesized, which, while being sub-optimal, can improve transient performance and possess several desired properties (such as low computational overhead and sensible closed-loop pole locations). In addition, low-order anti-windup synthesis is often feasible when the corresponding static synthesis is not.

A Tutorial on Modern Anti-Windup Design

In this paper, several constructive linear and nonlinear anti-windup techniques are presented and explained. Two approaches, namely direct linear anti-windup (DLAW) and model recovery anti-windup (MRAW), are described in an algorithmic way, in order to illustrate their main features. Hereafter, theoretical conditions ensuring stability and performance, their applicability, their accompanying guarantees, and their merits and deficiencies are given. The possible extensions to less standard problem settings are also briefly discussed.

Linear quadratic bumpless transfer

A method for bumpless transfer using ideas from LQ theory is presented and shown to reduce to the Hanus conditioning scheme under certain conditions.

Practical implementation of a novel anti-windup scheme in a HDD-dual-stage servo-system

Two novel discrete anti-windup (AW) techniques are applied to a dual-stage actuator of an experimental hard disk drive system. The techniques, one low order, the other full order, employ convex l/sub 2/-performance constraints in combination with linear-matrix-inequality-optimization methods. It is shown that the AW compensators can improve the performance of the nominal dual-stage servo-system when the secondary actuator control signal saturates at its allowable design limits. Also, stability is achieved despite saturation of both the secondary actuator and the voice-coil-motor actuator. Practical results show that the performance of each AW compensator is superior to another well-known ad-hoc AW technique, the internal model control AW scheme. The main contribution of the paper is the application of theoretically rigorous AW methods to an industrially relevant servo system.

Linear matrix inequalities for full and reduced order anti-windup synthesis

This work considers the design of fixed-order antiwindup compensators guaranteeing stability and a given level of L2 performance. The main results show how the design of such a compensator can be cast as a nonconvex optimization problem. It is demonstrated how, under given conditions, this optimization problem can be reduced to a standard LMI (linear matrix inequality) feasibility problem, and situations in which these compensators coincide with those in the literature are described. Moreover, given this formulation, an algorithm for the construction of anti-windup compensators which meet an optimal C2 performance bound is proposed. Furthermore, a lower bound on the C2 performance achievable is shown to be precisely the greater of that predicted by the bounded real lemmas for the linear open-loop plant and for the linear unsaturated closed-loop system.

Discrete-time and sampled-data anti-windup synthesis: stability and performance

The anti-windup (AW) problem is formulated in discrete time using a configuration which effectively decouples the nominal linear and nonlinear parts of a closed loop system with constrained plant inputs. Conditions are derived which ensure an upper bound on the induced l 2 norm of a certain mapping which is central to the anti-windup problem. Results are given for the full-order case, where a solution always exists, and for static and low-order cases, where a solution does not necessarily exist, but which is often more appealing from a practical point of view. The anti-windup problem is also framed and solved for continous-time systems under sampled-data control. It is proved that the stability of the anti-windup compensator loop is equivalent to a purely discrete-time problem, while a hybrid induced norm is used for performance recovery. The performance problem is solved using linear sampled-data lifting techniques to transpose the problem into the purely discrete domain. The results of the paper are demonstrated on a flight control example.

On the Existence of Stable, Causal Multipliers for Systems With Slope-Restricted Nonlinearities

The stability of a feedback interconnection of a linear time invariant (LTI) system and a slope-restricted nonlinearity is revisited. Unlike the normal treatment of this problem, in which multipliers are explicitly chosen and then stability conditions checked, this technical note derives existence conditions for a sub-class of these multipliers, namely those which are L 1 bounded, stable, causal and of order equal to the LTI part of the system. It is proved that for the single-input-single-output case, these existence conditions can be expressed as a set of linear matrix inequalities and thus can be solved efficiently with modern optimization software. Examples illustrate the effectiveness of the results.

Anti-windup synthesis using Riccati equations

The aim of this paper is to give a novel solution to the full order anti-windup (AW) compensation problem for stable systems with input saturation. The solution is obtained by “completing the square” in three steps and requires the solution to a single bounded-real Riccati equation, characterized by the open-loop plants norm. The Riccati equation plays the role of the LMIs usually found in anti-windup synthesis, but, in addition to its numerical advantages, it yields a family of anti-windup compensators with the same performance. This family of compensators is parameterized by a matrix which is intimately linked with both the poles of the anti-windup compensator and the robustness properties of the closed-loop saturated system. Thus, this matrix allows a robust anti-windup problem to be solved in a straightforward and intuitive manner. The effectiveness of the proposed technique is demonstrated on a simple example.

Anti-windup compensation of rate saturation in an experimental aircraft

This paper describes the design, flight testing and accompanying analysis of two anti-windup (AW) compensators for an experimental aircraft - the German Aerospace Centers (DLR) advanced technologies testing aircraft (ATTAS). The AW compensators were designed to reduce the deleterious effects of rate-saturation of the aircrafts actuators on handling qualities. The AW compensators were flight-tested and assessed using the resulting pilot comments, in the form of handling qualities ratings (HQRs) and pilot-involved-oscillation ratings (PIORs), and flight test data. These media demonstrate that the AW compensators improved the predictability and handling of the aircraft. The results also provide an initial understanding of the relationship between the theory and design choices for AW controllers and the response of the piloted aircraft during periods of rate saturation.

Robust control applications

Abstract This paper (first presented as a plenary lecture at the Fifth IFAC Symposium on Robust Control Design, Toulouse, July 2006) demonstrates the practical importance of robust control theory by describing its application to two non-trivial practical control problems. Part 1 considers helicopter control and Part 2 addresses saturation problems in high-performance head-positioning servo systems in high-density hard-disk drives. In Part 1, we present the design and flight test of a new batch of H ∞ controllers for the Bell 205 helicopter. At the heart of each controller is an H ∞ loop-shaping controller, augmented with a hand-tuned reference filter to improve tracking performance and to reduce a perceived phase lag which pilots had complained of previously. Flight testing revealed that, with such an architecture, it was relatively easy to get Level 1 handling qualities ratings in low aggression manoeuvres. Further fine tuning resulted in Level 1 qualities for high aggression manoeuvres and one controller performed to Level 1 standard in all manoeuvres tested. In Part 2, we consider how robust control techniques can be used to design anti-windup compensators to counter performance and stability problems associated with saturating actuators in state-of-the-art hard-disk drive servo systems. A promising two-stage approach is given and illustrated with experimental results.