Sahhjendra N. Singh

A modified algorithm for invertibility in nonlinear systems

The algorithm of Hirschorn [1] for the construction of inverses of nonlinear systems is modified, and new sufficient conditions for invertibility and inverse system for a larger class of systems are obtained. For the systems which do not satisfy the invertibility, conditions, a characterization of input space on which the input-output map is injective is derived.

Decoupling of invertible nonlinear systems with state feedback and precompensation

For a class of nonlinear invertible systems considered by Hirschorn [1], a decoupling control synthesis using state feedback and precompensation is presented. Two examples which include decoupling of vertical and horizontal path angles of a terrain-following airplane are presented.

Output feedback non-linear decoupled control synthesis and observer design for manoeuvring aircraft

This paper presents an application of decoupling theory for designing a controller with output feedback in rapid, non-linear aeroplane manoeuvres. For simplicity in control law derivation, only momenta caused by aileron, rudder and elevator are considered, and control forces are neglected. For a class of non-linear systems, a method for designing an observer is presented. Using this approach, angle of attack and sideslip are constructed. An approximate observer is obtained by neglecting the derivatives of roll rate and aileron deflection. The non-linear controller is synthesized using estimated angle of attack and sideslip obtained from the approximate observer. Simulated responses of the closed-loop system, including the control forces, show that the neglected forces have no significant effects and the large, simultaneous lateral and longitudinal manoeuvres can be precisely performed. The control law shows only a small effect of wind gust.

Generalized functional reproducibility condition for nonlinear systems

A new sufficient condition for the existence of control to generate a given real analytic function as the output of a large class of multivariable nonlinear control system is derived. Furthermore, a prefilter (right-inverse system) is constructed to generate the required control.

Invertibility of observable multivariable nonlinear systems

Based on the algorithm of Hirschorn [1] for obtaining inverses, sufficient conditions for invertibility of observable multivariable nonlinear systems are derived. For observable and invertible systems, a static left-inverse system is constructed. For certain noninvertible systems, the sufficient condition yields a characterization of input space on which the input-output map is injective.

Functional reproducibility of multivariable nonlinear systems

Based on the algorithm of Hirschorn [1] for the construction of inverses, a sufficient condition for the existence of control to generate a given real analytic function as the output of a multivariable nonlinear control system is derived. Furthermore, a prefilter (right-inverse system) is constructed to generate the required control.

Ultimate boundedness control of set points of mismatched uncertain linear systems

This paper describes an approach to the control of non-zero set points of a class of uncertain linear systems based on the theory of ultimate boundedness. Unlike previous works, here it is not required that uncertainties satisfy the so-called matching conditions. A sufficient condition for the existence of a state transformation (which can also be extended to non-linear systems) for the transformation of the mismatched system into a matched system is derived. A control low for controlling non-zero set points in the new state space is also developed. For illustration, an application to the control of a simple power system with varying load and uncertain parameters is considered. It is seen that the approach of this paper is useful in obtaining a proper state space in which it is possible to prescribe desired set points. Simulation results are presented to show the effectiveness of the controller.

Reproducibility in nonlinear systems using dynamic compensation and output feedback

The question of functional reproducibility of multivariable nonlinear systems with unknown initial state is considered. A sufficient condition for the existence of control to generate a given real analytic function as the output of a composite system consisting of a compensator in cascade with a nonlinear plant is derived. A static prefilter (right-inverse system) with only measured output feedback is constructed to generate the required control input to the composite system.

Stability of Gyro in a Vehicle Spinning with Uncertain Angular Velocity

The analysis of a single-axis rate gyroscope mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using circle criterion, it is shown that the gimbal motion is globally asymptotically stable if Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. A simple analytical relation for the selection of gyro parameters for stability is derived.

Stability of Gyro with Harmonic Nonlinearity in Spinning Vehicle

A stability analysis of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain angular velocity ¿z about the spin axis of the gyro is presented. The complete nonlinear equation of motion, which includes the fundamental and second harmonic nonlinear terms, arising due to ¿z, is considered. For time-varying ¿z(t), using the circle criterion, it is shown that the gimbal motion is globally asymptotically stable if the Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. For the case of uncertain constant ¿z, using the Lyapunov approach, conditions for global asymptotic stability (GAS) and asymptotic stability are derived. Stable regions in parameter space of the gyro and state space are obtained. Analytical relations for the selection of gyro parameters are derived.