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

Nonlinear regulation in constrained input discrete-time linear systems

The use of composite linear and non-linear feedback laws for the control of constrained input discrete-time linear systems is re-examined. By making use of the delta operator formulation of a discrete-time system, an apparent restriction on the magnitude of the non-linear control law is removed, and the similarities between the continuous and discrete-time solutions to the problem are elucidated. In order to develop the results, unconstrained systems are treated initially, but it is shown that, locally, the sufficient conditions for the stabilization of such systems are actually equivalent to those for the stabilization of the corresponding constrained systems

Output Violation Compensation for Systems with Output Constraints

The problem of output constraints in linear systems is considered, and a new methodology which helps the closed loop respect these limits is described. The new methodology invokes ideas from the antiwindup literature in order to address the problem from a practical point of view. This leads to a design procedure very much like that found in antiwindup design. First, a linear controller ignoring output constraints is designed. Then, an additional compensation network which ensures that the output limits are, as far as possible, respected is added. As the constraints occur at the output, global results can be obtained for both stable and unstable plants

Design of Flight Controllers based on Simplified LPV model of a UAV

Design of Flight Controllers based on Simplified LPV model of a UA

Publications of A. G. J. MacFarlane from SIR ALISTAIR G. J. MACFARLANE. 9 May 1931 — 2 November 2021

Sir Alistair MacFarlane was a gifted engineer with a fascination for feedback control systems from his industrial experience on radar systems through to his university research on multivariable control system design. He managed to excel in both practical design and mathematical analysis. He was also exceptionally effective, charismatic and visionary in leadership positions at both Cambridge and Heriot-Watt universities

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 plant's 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

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 ${cal L}_{1}$ 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

Cubature H-∞ Information Filter and its Extension

State estimation for nonlinear systems with Gaussian or non-Gaussian noises, and with single and multiple sensors, is presented. The key purpose is to propose a derivative free estimator using concepts from the information filter, the H∞H∞ filter, and the cubature Kalman filter (CKF). The proposed estimator is called the cubature H∞H∞ information filter (CH∞IFCH∞IF); it has the capability to deal with highly nonlinear systems like the CKF, like the H∞H∞ filter it can estimate states with stochastic or deterministic noises, and similar to the information filter it can be easily extended to handle measurements from multiple sensors. A numerically stable square-root CH∞IFCH∞IF is developed and extended to multiple sensors. The CH∞IFCH∞IF is implemented to estimate the states of a nonlinear permanent magnet synchronous motor model. Comparisons are made with an extended H

Clearance of Nonlinear Flight Control Laws using Hybrid Evolutionary Optimization

The application of two evolutionary optimization methods, namely, differential evolution and genetic algorithms, to the clearance of nonlinear flight control laws for highly augmented aircraft is described. The algorithms are applied to the problem of evaluating a nonlinear handling quality clearance criterion for a simulation model of a high-performance aircraft with a delta canard configuration and a full-authority flight control law. Hybrid versions of both algorithms, incorporating local gradient-based optimization, are also developed and evaluated. Statistical comparisons of computational cost and global convergence properties reveal the benefits of hybridization for both algorithms. The differential evolution approach in particular, when appropriately augmented with local optimization methods, is shown to have significant potential for improving both the reliability and efficiency of the current industrial flight clearance proces

Deterministic Model: Robustness Analysis of the Period and Amplitude of the Internal cAMP Oscillations with Respect to Perturbations in the Model Parameters and Initial Conditions

<p>The first row shows the distribution in the period of the deterministic model for one cell with 5%, 10%, and 20% perturbations, and the second row shows the amplitude distribution. The peak bar at 20 min for the period distributions represents the number of cells that are not oscillating. The proportion of cells that are not oscillating increases from 2% to 25% as the size of the perturbation increases. The distributions of the amplitudes also show a similar tendency, i.e., the mean value decreases and the standard deviation increases as the magnitude of the perturbation increases. Each plot is the result of 100 simulations for different random samples of the model parameters, the cell volume, and initial conditions using a uniform distribution about the nominal values.</p