There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper is concerned with the state estimation problem for a class of discrete-time singularly perturbed systems with distributed time-delays. During the data transmission through a network channel of limited bandwidth, for the sake of collision avoidance and energy saving, a dynamic event-triggered scheme is employed to schedule the data communication from the sensors to the designed estimator. First, for a given singular perturbation parameter (SPP), by constructing a novel Lyapunov–Krasovskii SPP-dependent functional, sufficient conditions are obtained to guarantee the exponentially mean-square ultimate boundedness of the error dynamics of the state estimation. Furthermore, in the case that the SPP does not exceed a predefined upper bound, a design algorithm is developed for the desired state estimator ensuring that the error dynamics is exponentially mean-square ultimately bounded. In this case, by solving certain matrix inequalities, the estimator gain is characterized without needing to know the exact SPP (as long as it stays below the given upper bound). Moreover, the ultimate bound of the error dynamics is estimated. Finally, simulation results are given to confirm the validity and advantages of the proposed design scheme of the state estimator.

Dynamic Event-Triggered State Estimation for Discrete-Time Singularly Perturbed Systems With Distributed Time-Delays

The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

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Comparison of Riemann and Lebesque sampling for first order stochastic systems

This brief concentrates on controller design for flexible string systems subjected to external disturbances, input constraints, and state constraints. The hyperbolic barrier Lyapunov function and auxiliary systems are adopted to develop boundary constrained control with a disturbance observer for restraining vibrations, eliminating input and state constraints, and tackling external disturbances. The suggested control can ensure the input and state constraints and achieve asymptotic stability in the controlled system. With appropriate design parameters, the simulation results obtained verify the control performance.

Boundary Constrained Control of Flexible String Systems Subject to Disturbances

Robots have become an integral part of industrial automation. Their ultimate role and contribution in this sector is essentially a function of the associated control strategy to ensure precision, r...

Optimal and Robust Control of Multi DOF Robotic Manipulator: Design and Hardware Realization

This brief proposes an event-triggered composite control of a two time scale system. A periodic sampling requirement is relaxed and both slow and fast states of the system decide independently when transmitting their current measurements based on a time-dependent triggering rule. The distinct feature of this scheme is that it does not require synchronized measurement updates of its slow and fast dynamics. Further, the theory of singular perturbation is used to decouple the system into slow and fast subsystems, and stability of the system is established. The proposed control strategy guarantees convergence of system states to an adjustable region around origin excluding the Zeno behavior. Simulation results manifest the effectiveness of the proposed approach.

Event-Triggered Composite Control of a Two Time Scale System

this work presents a comparative study of two different control strategies for a flexible single-link manipulator. The dynamic model of the flexible manipulator involves modeling the rotational base and the flexible link as rigid bodies using the Euler Lagrange's method. The resulting system has one Degree-Of-Freedom (one DOF) and it provide freedom to increase the degree as well. Two types of regulators are studied, the State-Regulator using Pole Placement, and the Linear-Quadratic regulator (LQR). The LQR is obtained by resolving the Ricatti equation, in this work, we apply and compare two strategies to control the tip of the flexible link: state-feedback and linear quadratic regulator. These regulators are designed to reduce tip vibrations and increase system stability due to the flexibility of the arm.

Comparison of Pole Placement and LQR Applied to Single Link Flexible Manipulator

This article propose a hybrid fractional order PIDcontroller which is optimized with classical proportional integralderivative controller (PID) gives an exquisite response. Here thetwo tuning method are used to evaluate the parameters of PIDcontroller, first one is Ziegler-Nichols and other one is Astrom-Hagglund method. The parameters of FO-PID controller in useas the proportional constant, integral constant are by Ziegler-Nichols and derivative constant by Astrom-Hagglund method. In order to obtain required solutions, two non-linear equationsare derived to find the fractional order of the integral term andderivative term The step response shows the benefits of abovediscussed hybrid fractional order PID controller when comparingwith existing controller. Simulated results are carried by matlab2012(a).

Design of Optimal PID[FOPID] Controller for Linear System

This paper describes the framework for event triggered control of a plant possessing two time scales. The periodic sampling requirement is relaxed and states are sampled based on a triggering rule. The dynamic trigger function where event triggering threshold varies with time has been used. Triggering function parameters are different for slow and fast states and events are detected independently in the two subsystems. This also allows the sensors for slow and fast states to be geographically distributed in the network. Further singular perturbation technique is used to decouple the system into fast and slow subsystems and stability of the overall system is investigated. It is proved that the closed loop system asymptotically converges to an adjustable region around the equilibrium point and a minimum bound on inter-execution time is also guaranteed. Asymptotic stability may also be obtained if the parameters of trigger function are adequately selected. Simulation results manifest the efficacy of the proposed approach and verify the theoretical analysis.

Event triggered control of two time scale system

In this paper, a polytopic model of an uncertain buck converter with parasitic resistances is obtained in continuous conduction mode. Although linear quadratic regulators (LQRs) provide good stability and are optimal but they do not ensure robustness for the highly uncertain system. Therefore, A robust LQR designing method for power converters is presented using linear matrix inequalities (LMIs) to ensure robust stability of highly uncertain systems and the output is analyzed in the presence of line and load perturbations. In addition, an input voltage feedforward gain is included in this closed loop converter system to achieve a good line regulation. It is shown that with feedforward, there is no transient due to the line voltage perturbations. The results of the proposed approach are verified through simulation.

Manisha Bhandari

Papers

Event-Triggered Composite Control of a Two Time Scale System

Comparison of Pole Placement and LQR Applied to Single Link Flexible Manipulator

Design of Optimal PID[FOPID] Controller for Linear System

Event triggered control of two time scale system

An LMI approach for robust LQR control of PWM buck converter with parasitics