Girish Deodhare

Design of non-overshooting feedback control systems

The authors consider the problem of designing non-overshooting feedback control systems when the input is a step. They also consider the more general problem of designing controllers to optimally track a step with some predetermined amount of allowable overshoot. It is shown that both these problems always have a solution (under some standard assumptions). It is then shown that the counterpart of this problem, that is, the problem of designing non-undershooting feedback control systems, need not have a solution in general, but it is proved that one can always design a feedback controller to achieve as little percentage of undershoot as desired. Most of the work deals with discrete-time single-input single-output systems though some extensions of the techniques to continuous-systems are discussed.<<ETX>>

l/sub 1/-optimality of feedback control systems: the SISO discrete-time case

Controllers that optimally reject a class of disturbances are considered. The problem of determining when a stabilizing control is l/sub 1/-optimal for a given plant is studied for some stable weighting function. This problem belongs to the class of inverse problems in optimal control introduced by Kalman. It is shown that for a given plant, the set of all the H/sub infinity /-optimal controllers (obtained by considering all stable weighting functions with no zeros on the unit circle) is actually contained in the corresponding set of l/sub 1/-optimal controllers. It is also demonstrated that an l/sub 1/-optimal controller, unlike an H/sub infinity /-optimal controller, can remain l/sub 1/-optimal for the same plant for a wide range of nontrivially different weighting functions. >

Some results on l/sub 1/-optimality of feedback control systems: the SISO discrete-time case

A study is made of the problem of determining when a stabilizing controller is l/sub 1/-optimal for a given plant for some stable weighting function. This problem belongs to the class of inverse problems in optimal control introduced by R.E. Kalman (1964). Only SISO discrete-time plants are considered. The authors give a characterization of all the possible l/sub 1/-optimal compensators for a given plant with different weights under some assumptions on the plant and the allowable weights. A few results are also obtained in the general case (i.e. without making overly restrictive assumptions on the plant and allowable weights). In particular, it is shown that, for a given plant, the set of all the H/sub infinity /-optimal controllers, obtained by considering all stable weighting functions with no zeros on the unit circle, is actually contained in the corresponding set of l/sub 1/-optimal controllers. The authors also show that an l/sub 1/-optimal controller (unlike an H/sub infinity /-optimal controller) can remain l/sub 1/-optimal for the same plant for a wide range of nontrivially different weighting functions. They characterize some of these weighting functions.<<ETX>>

Flight Control System Clearance Using Static Tests at Iron Bird

The Indian Light Combat Aircraft (LCA) has flown more than 485 flights so far without encountering any major faults in the flight safety critical fly-by-wire control software. This is partly due to the stringent quality control process and rigorous testing of the Control Laws (CLAW) and Air Data System Algorithms (ADS) carried out on various ground platforms such as Iron bird before flight. The pass/fail criteria for the tests carried out at the Iron bird test rig are defined based on the tolerance bounds provided on the expected results which take into account the characteristics of the associated hardware. These tolerance bounds guarantee that the correctness in functionality of the modules (CLAW, ADS) is retained, if the set of bounded inputs generate a set of bounded outputs. The processing of tolerance bounds is an algorithmic development that plays an important role in defining the acceptance criteria for the tests and enables clearance (certification) of the different modules. This paper presents the procedure used for the clearance of the static tests of the CLAW and ADS on the Iron Bird platform. The details on the pass/fail criteria for the static tests and the tool developed for generating the bounds are also described. The tolerance bounds for static tests were evolved based on manufacturer’s data, testers experience and engineering judgment gathered during various levels of testing of ADS and CLAW algorithms. This process yielded excellent results and was accepted as a formal clearance methodology for the onboard safety critical software.

A FEEDBACK LINEARISATION BASED NONLINEAR CONTROLLER SYNTHESIS TO RECOVER AN UNSTABLE AIRCRAFT FROM POST- STALL REGIME

Dynamics of the aircraft configuration considered in this paper shows a unique characteristic that mere are no stable attractors in the entire high angle of attack flight envelope. As a result, once the aircraft has departed from die normal flight regime, no standard technique can be applied to recover me aircraft. In mis paper, using feedback linearisation technique, a nonlinear controller is designed at high angles of attack which is engaged after the aircraft departs from normal flight regime. This controller stabilises the aircraft into a stable spin. Then a set of synthetic pilot inputs are applied to cause an automatic transition from the spin equilibrium to low angles of attack where the second controller is connected. This controller is a normal gain scheduled controller designed to have a large domain of attraction at low angles of attack. It traps me aircraft into a low angle of attack level flight This entire concept of recovery has been verified using six degree of freedom nonlinear simulation. Feedback linearisation technique used to design a controller ensures internal stability only if the nonlinear plant has stable zero dynamics. Since zero dynamics depend upon the selection of outputs, a new method of choosing outputs is described to obtain a plant which has stable zero dynamics.

Clearance of Flight-Control-System Software with Hardware-in-Loop Test Platform

The Indian Light Combat Aircraft has flown more than 2000 flights, including trainer and naval variants, without encountering any major faults in the flight safety-critical fly-by-wire control software. This is partly due to the stringent quality control and rigorous testing of the control-law and air-data-system algorithms carried out on various ground platforms before flight. One of these ground test platforms is the hardware-in-loop test platform (Iron Bird). The processing of tolerance bounds to define the pass/fail criteria is an algorithmic development. It guarantees the correctness of the modules, if the set of inputs generates a set of outputs within processed tolerance bounds. This paper presents the philosophy behind the design of test cases and the tools developed to evaluate the control-law and air-data-system modules on the Iron Bird platform, and the procedure to clear the test results. The computation of tolerance bounds and algorithms for their processing have been evolved over a period ba...

Guaranteed Stability of Polynomials Under Application of a Uniform Nonnegative Polynomial Mapping on Coefficients

This note presents a new result for the guaranteed stability of polynomials under uniform non-negative polynomial mapping on the coefficients.