Compensator for constant relative stability in process control systems

Process control systems are designed for a closed-loop peak magnitude of 2dB, which corresponds to a damping coefficient () of 0.5 approximately. With this specified constraint, the designer should choose and/or design the loop components to maintain a constant relative stability. However, the manipulative variable in almost all chemical processes will be the flow rate of a process stream. Since the gains and the time constants of the process will be functions of the manipulative variable, a constant relative stability cannot be maintained. Up to now, this problem has been overcome either by selecting proper control valve flow characteristics or by gain scheduling of controller parameters. Nevertheless, if a wrong control valve selection is made then one has to account for huge loss in controllability or eventually it may lead to an unstable control system. To overcome these problems, a compensator device that can bring back the relative stability of the control system was proposed. This compensator is similar to a dynamic nonlinear controller that has both online and offline information on several factors related to the control system. The design and analysis of the proposed compensator is discussed in this article. Finally, the performance of the compensator is validated by applying it to a two-tank blending process. It has been observed that by using a compensator in the process control system, the relative stability could be brought back to a great extent despite the effects of changes in manipulative flow rate.

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

Convergence problems in a class of model reference adaptive control systems

A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. Convergence problems in this attractive class of systems have been investigated in this paper using concepts from hyperstability theory. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. A boundedness condition on the input to the linear part of the system has been taken into account in the analysis - this condition appears to have been missed in the previous applications of hyperstability theory. Sufficient conditions for the convergence of the adaptive gain to the desired value are also given.

Stability of control systems with time delay

To find the approximate stability limit on the forward gain in control systems with small time delay, this note suggests approximating the exponential in the characteristic equation by the first few terms of its series and using the Routh–Hurwitz criterion. This approximation avoids all the time-consuming graphical work and gives a somewhat pessimistic maximum bound for the gain constant.

Control of a Duct Flow Network for Wind Display in a Virtual Environment

Control of flow in duct networks has a myriad of applications ranging from heating, ventilation, and air-conditioning to blood flow networks. The system considered here provides vent velocity inputs to a novel 3-D wind display device called the TreadPort Active Wind Tunnel. An error-based robust decentralized sliding-mode control method with nominal feedforward terms is developed for individual ducts while considering cross coupling between ducts and model uncertainty as external disturbances in the output. This approach is important due to limited measurements, geometric complexities, and turbulent flow conditions. Methods for resolving challenges such as turbulence, electrical noise, valve actuator design, and sensor placement are presented. The efficacy of the controller and the importance of feedforward terms are demonstrated with simulations based upon an experimentally validated lumped parameter model and experiments on the physical system. Results show significant improvement over traditional control methods and validate prior assertions regarding the importance of decentralized control in practice.

A Networked Control Systems Perspective for Wide-Area Monitoring Control of Smart Power Grids

This paper presents a networked control systems (NCS) framework for wide area monitoring control of smart power grids. We consider a scenario in which wide area measurements are transmitted to controllers at remote locations. We model the effects of delays and packet dropouts due to limited communication capabilities in the grid. We also design a robust networked controller to damp wide-area oscillations based on information obtained from Wide Area Monitoring Systems (WAMS), and analyze the improvement in system stability due to networked control. With communication integration being an important feature of the smart grid, detailed consideration of the effects of communication is essential in the control design for future power systems. We believe that this work is an essential step in this direction.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Micro-satellite angular rate estimation using second-order sliding mode observer

Development of computationally efficient and accurate attitude rate estimation algorithm using low-cost commercially available star sensor arrays and processing unit for micro-satellite mission is presented. Our design reduces the computational load of least square (LS)-based rate estimation method while maintaining the same accuracy compared to other rate estimation approaches. Furthermore, rate estimation accuracy is improved by using recently developed fast and accurate second-order sliding mode observer (SOSMO) scheme. It also gives robust estimation in the presence of modeling uncertainties, unknown disturbances, and measurement noise. Simulation study shows that rate estimation accuracy achieved by our LS-based method is comparable with other methods for a typical commercially available star sensor array. The robustness analysis of SOSMO with respect to measurement noise is also presented in this paper. Simulation test bench for a practical scenario of satellite rate estimation uses moment-of-inertia variation and environmental disturbances affecting a typical micro-satellite at 500km circular orbit. Comparison studies of SOSMO with 1-SMO and pseudo-linear Kalman filter show that satisfactory estimation accuracy is achieved by SOSMO.