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

In this paper, we develop and implement Composite Nonlinear Feedback (CNF) control law for an inverted pendulum subject to actuator saturation. The inverted pendulum mounted over a cart is inherently unstable and nonlinear system. Our aim is to balance pendulum near to its vertically upright position while tracking the cart position for a given setpoint. CNF control law is proposed for asymptotical tracking of cart position and to make the process faster and smoother with fewer oscillations. The key to CNF control technique design is the combination of linear and nonlinear control where linear control gives quick rising time due to low damping ratio and nonlinear control provides high damping ratio to remove the overshoot resulting from linear part during tracking the reference. Simulations are performed to validate the theory and results are discussed.

Composite Nonlinear Feedback Control for Inverted Pendulum with Input Saturation

In this paper, we consider the event triggered control of the singularly perturbed linear system, where the communication between sensor and the controller/actuator is through a digital communication network and the transmission is based on some state dependent criterion. The models of slow and fast subsystems of the plant are added at the controller and are used for the estimation of states between the transmission times. Whenever the difference between estimated and actual states exceeds a certain threshold, controller is updated with the actual states of the plant provided by the sensor. This effectively reduces the communication frequency. The stability properties of overall closed loop system is studied and it is found that for sufficiently small value of singular perturbation parameter, system attains practical stability and by adequately selecting trigger function parameters, asymptotic stability is also achieved. A numerical example is shown to illustrate the results of the paper.

Event triggered control of singularly perturbec linear system based on its slow and fast model

PID controller gives satisfactory results up to second order as it is difficult to get desired response quality in third and higher order systems using analytical approach, as the number of zeros provided by PID controller is less than the order of the plant. PIDA (Proportional-Integral-Derivative-Acceleration) controllers are found to be suitable for third and higher order systems. This paper studies the design of PIDA controller using three different approaches i.e. Dorf Approach, Coefficient Diagram Method and Kitti's Method applied to speed control of 3-phase induction motor.

Comparative study of design of PIDA controller for induction motor

In this paper, a model-based control strategy is used for a networked control system. In place of a randomly estimated model of the plant, a model is determined using recursive least square estimation based on estimated states. The idea of model-based control is to reduce communication frequency, to meet the constraints of available bandwidth. It is noticed that smaller the error between plant and model, higher is the update interval. The model-based approach is applied to a classical problem of an inverted pendulum. The effectiveness of this approach is demonstrated using simulation results.

Control of an inverted pendulum in networked environment

This paper focuses on the Gravitational Search Algorithm (GSA) which depends on the law of gravity and law of motion GSA lacks the exploitation property To improve the exploitation skill, efficiency, and accuracy of GSA, a modified GSA (MGSA) is proposed The proposed algorithm keeps up a suitable stability between the exploitation and exploration skills of GSA by using an intelligence factor (IF) The MGSA is applied to speed control problem of an induction motor system Simulations results showed that the modified GSA performs better than GSA and Adaptive Tabu Search (ATS) in terms of computational time and closed-loop response

Manisha Bhandari

Papers

Composite Nonlinear Feedback Control for Inverted Pendulum with Input Saturation

Event triggered control of singularly perturbec linear system based on its slow and fast model

Comparative study of design of PIDA controller for induction motor

Control of an inverted pendulum in networked environment

Parameter Estimation for PID Controller Using Modified Gravitational Search Algorithm