Tarunraj Singh

Robust Time-Delay Control

A method is presented to minimize residual vibration of structures or lightly damped servomechanisms. The method, referred to as the proportional plus multiple delay control, involves the use of multiple time delays in conjunction with a proportional part to cancel the dynamics of the system in a robust fashion. An interesting characteristic of the controller involves addition of a basic single time-delay control unit in cascade to the existing controller, for every additional requirement of robustness

Shaped Input Control of a System With Multiple Modes

This paper describes a method for limiting vibration in flexible systems that have more than one characteristic frequency and mode. It is only necessary to have knowledge of the component mode frequencies and damping ratios in order to be able to calculate the timing and magnitudes of the impulse sequence used in the shaping. Only two impulses, in the nonrobust case, or three impulses in a more robust case, are necessary regardless of the number of component frequencies. Simple tests are established to determine when this technique can be used and examples are presented.

Uncertainty propagation for nonlinear dynamic systems using Gaussian mixture models

A Gaussian-mixture-model approach is proposed for accurate uncertainty propagation through a general nonlinear system. The transition probability density function is approximated by a finite sum of Gaussian density functions for which the parameters (mean and covariance) are propagated using linear propagation theory. Two different approaches are introduced to update the weights of different components of a Gaussian-mixture model for uncertainty propagation through nonlinear system. The first method updates the weights such that they minimize the integral square difference between the true forecast probability density function and its Gaussian-sum approximation. The second method uses the Fokker-Planck-Kohnogorov equation error as feedback to adapt for the amplitude of different Gaussian components while solving a quadratic programming problem. The proposed methods are applied to a variety of problems in the open literature and are argued to be an excellent candidate for higher-dimensional uncertainty-propagation problems.

Brief paper: Design of noise and period-time robust high-order repetitive control, with application to optical storage

Repetitive control is useful if periodic disturbances or setpoints act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period time is exactly known. The improved disturbance rejection at the periodic frequency and its harmonics is achieved at the expense of a degraded system sensitivity at intermediate frequencies. A convex optimization problem is defined for the design of high-order repetitive controllers, where a trade-off can be made between robustness for changes in the period time and for reduction of the error spectrum in-between the harmonic frequencies. The high-order repetitive control algorithms are successfully applied in experiments with the tracking control of a CD-player system.

Fuel/Time Optimal Control of the Benchmark Problem

Design of fuel/time optimal control of the benchmark two-mass/spring system is addressed in the frequency domain. The optimal control profile is represented as the output of a time-delay filter, where the amplitude of the time-delayed signals are constrainted to satisfy the control bounds. The time delays of the filter are determined by solving a parameter optimization problem that minimizes a weighted fuel/time cost function subject to the constraint that the tune-delay filter cancel all the poles of the system and the control profile satisfies the rigid-body boundary conditions. It is shown that three control structures exist: a three-switch profile corresponding to the time optimal control problem that changes to a six-switch profile corresponding to a cost function that includes a small weight on the fuel. As the weight on the fuel increases beyond a critical value, the control profile changes to a two-switch profile. The value of the critical weight that represents the transition of the control profile from a six-switch to a two-switch control profile is determined.

Robust time-delay control of multimode systems

This paper presents a procedure for the design of open loop controllers for flexible structures using multiple step inputs delayed in time. The controller attenuates the residual vibration by cancelling the complex poles of the system. Robustness is achieved by locating additional zeros at the cancelled poles of the system. The paper begins by addressing the control of a single mode and examines the effect of user selected time-delays on robustness and the reference input. Next, a procedure for the design of robust time-delay controllers for multiple modes with user selected time-delays is considered. This is followed by a design of a minimum time-delay controller, such that the step input magnitudes are constrained to values between 0 and 1. Two examples, a spring-mass system and a single-link flexible-arm robot are used to illustrate the effectiveness of the proposed controller.

Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation

A nonlinear filter is developed by representing the state probability density function by a finite sum of Gaussian density kernels whose mean and covariance are propagated from one time-step to the next using linear system theory methods such as extended Kalman filter or unscented Kalman filter. The novelty in the proposed method is that the weights of the Gaussian kernels are updated at every time-step, by solving a convex optimization problem posed by requiring the Gaussian sum approximation to satisfy the Fokker-Planck-Kolmogorov equation for continuous-time dynamical systems and the Chapman-Kolmogorov equation for discrete-time dynamical systems. The numerical simulation results show that updating the weights of different mixture components during propagation mode of the filter not only provides us with better state estimates but also with a more accurate state probability density function.

The higher order unscented filter

This article proposes a technique for the selection of the /spl sigma/-set for a probability distribution approximation filter, i.e., the unscented filter. The /spl sigma/-set is selected so as to capture the higher order input statistics. The Taylor series expansion is used to illustrate that the 3/sup rd/ order and higher statistics of the nonlinear transformation can be reproduced while the unscented filter captures the statistics up to the 3/sup rd/ order only. Two benchmark problems are used to corroborate the proposed solution.

Blood glucose control algorithms for type 1 diabetic patients: A methodological review

Abstract A method for optimal continuous insulin therapy for diabetes patients has been sought since the early 1970s. Although technical and medical advances have been made, a fully automated artificial pancreas to replace the functions of the natural organ is still a research aim. This review compares recent control algorithms for type 1 diabetic patients which automatically connect continuous glucose monitoring and insulin injection, without patient intervention. Black-box model and gray-box model based control strategies are described and their performances are evaluated, with a focus on their feasibility of implementation in a real-life situation. In conclusion, a satisfactory control strategy has not yet been proposed, mainly because most control algorithms rely on continuous blood glucose measurement which is not yet available. Modeling the effect of glucose ingestion as an external disturbance on the time evolution of blood glucose concentration, is now the norm for the control community. In contrast, the effects of physical activity on the metabolic system is not yet fully understood and remain an open issue. Moreover, clinical studies on evaluation of control performance are scarce. Therefore, research on blood glucose control needs to concentrate on advanced patient modeling, control optimization and control performance evaluation under realistic patient-oriented conditions.

Minimax Design of Robust Controllers for Flexible Systems

The design of robust time-delay and saturating controllers based on the range of expected variation of uncertain parameters from their nominal values is investigated. A minimax optimization problem is formulated with the objective of minimizing the maximum value of the cost function over the range of the uncertain parameter. By the adoption of the residual energy as the cost function, the optimization problem formulation is simple because it requires only one equation that is used both as the cost function and constraint. To expedite the optimization process, equations are derived for the gradient of the cost and constraint functions with respect to the parameters of the controller. The proposed technique is illustrated on two examples. The first is a spring-mass-dashpot and the second is the two-mass-spring benchmark problem.