A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes

A computationally tractable unified finite word length closed-loop stability measure is derived which is applicable to fixed-point, floating-point and block-floating-point representation schemes. Both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure. For each arithmetic scheme, the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it. Numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes.     

Direct Method Based Control System for an Autonomous Quadrotor

This paper proposes a real time control algorithm for autonomous operation of a quadrotor unmanned air vehicle. The quadrotor is a small agile vehicle, which as well as being a excellent test bed for advanced control techniques could also be suitable for internal surveillance, search and rescue and remote inspection. The proposed control scheme incorporates two key aspects of autonomy; trajectory planning and trajectory following. Using the differentially-flat dynamics property of the system, the trajectory optimization is posed as a non-linear constrained optimization within the output space in the virtual domain, not explicitly related to the time domain. A suitable parameterization using a virtual argument as opposed to time is applied, which ensures initial and terminal constraint satisfaction. The speed profile is optimized independently, followed by the mapping to the time domain achieved using a speed factor. Trajectory following is achieved with a standard multi-variable control technique and a digital switch is used to re-optimize the reference trajectory in the event of infeasibility or mission change. The paper includes simulations using a full dynamic model of the quadrotor demonstrating the suitability of the proposed control scheme.     

Design of poiseuille flow controllers using the method of inequalities

This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral （PI） controllers. In the second one, the MoI is combined with McFarlane and Glover＇s H∞ loop-shaping design procedure in a mixed-optimization approach.     

Reduction of controller fragility by pole sensitivity minimization

Presents a method for the reduction of controller fragility. The method is based on the sensitivity of closed-loop poles to perturbations in the controller parameters. By means of a state space parameterization of the controller, the closed-loop pole sensitivity can be reduced. A controller fragility measure based on the closed-loop pole sensitivity is proposed. Conditions for the optimal state-space realization of the controller are presented, along with a numerical method for obtaining the solution     

Optimised configuration of sensors for fault tolerant control of an electro-magnetic suspension system

For any given system the number and location of sensors can affect the closed-loop performance as well as the reliability of the system. Hence, one problem in control system design is the selection of the sensors in some optimum sense that considers both the system performance and reliability. Although some methods have been proposed that deal with some of the aforementioned aspects, in this work, a design framework dealing with both control and reliability aspects is presented. The proposed framework is able to identify the best sensor set for which optimum performance is achieved even under single or multiple sensor failures with minimum sensor redundancy. The proposed systematic framework combines linear quadratic Gaussian control, fault tolerant control and multiobjective optimisation. The efficacy of the proposed framework is shown via appropriate simulations on an electro-magnetic suspension system.     

Finite word length stability issues in an l1 framework

The paper addresses the digital controller structure problem for the closed loop stability of a feedback digital control system subject to finite word length (FWL). A new method of maximizing the stability subject to perturbations in the digital controller implementation is proposed. The approach is based on structured perturbation theory in an l₁ framework, and unlike some previous approaches, can be simply extended to consider closed loop nominal performance and closed loop robust performance and stability. The method is demonstrated with application examples.     

Comments on “On the structure of digital controllers withfinite word length consideration”

In the above-mentioned paper by Li (ibid. vol.43 (1998)), a condition is presented as necessary and sufficient to give the optimal realization of state space controllers for minimal sensitivity of all closed-loop eigenvalues subject to finite word-length effects. The condition is shown here not to be sufficient. In addition, the condition for minimal sensitivity of a single closed-loop eigenvalue presented in the above-mentioned paper is not complete. The complete conditions are presented in this paper     

Kolmogorov-Chaitin Complexity of Digital Controller Implementations

The complexity of linear, fixed-point arithmetic digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for state-space realizations, parallel and cascade realizations, and for a newly proposed generalized implicit state-space realization. The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure. The results show that from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have lower complexity and better performance, than lower-order controllers with longer word-length.