A homotopy approach for stabilizing single-input systems with control structure constraints

A linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized. Some examples of feedback realizations which impose constraints on the gain vector are: static output feedback, constant gain feedback for several operating points of a system, and two-controller feedback. We consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them. Each of these problems is cast into a problem of solving a system of equalities and inequalities. In this formulation, the coefficients of the quadratic and linear factors of the closed-loop characteristic polynomial are the variables. To solve the system of equalities and inequalities, a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework. Our method is illustrated with an example for each class of control structure constraint.

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.

A transputer-based extended hypercube

The Extended Hypercube is a new approach in multiprocessor architectures, which reduces the communication burden on the processor elements. We propose a scheme for implementing such an architecture using INMOS transputers as the processor and controller elements to achieve a very high computation to communication ratio.

Decentralized Parallel Operation of Inverters Sharing Unbalanced and Nonlinear Loads

In this paper, a wireless control strategy for parallel operation of three-phase four-wire inverters is proposed. A generalized situation is considered where the inverters are of unequal power ratings and the loads are nonlinear and unbalanced in nature. The proposed control algorithm exploits the potential of sinusoidal domain proportional+multiresonant controller ( in the inner voltage regulation loop) to make the system suitable for nonlinear and unbalanced loads with a simple and generalized structure of virtual output-impedance loop. The decentralized operation is achieved by using three-phase P/Q droop characteristics. The overall control algorithm helps to limit the harmonic contents and the degree of unbalance in the output-voltage waveform and to achieve excellent power-sharing accuracy in spite of mismatch in the inverter output impedances. Moreover, a synchronized turn on with consequent change over to the droop mode is applied for the new incoming unit in order to limit the circulating current completely. The simulation and experimental results from-1 kVA and -0.5 kVA paralleled units validate the effectiveness of the scheme.

Optimal scheduling of a processor executing a communication protocol stack

We consider the problem of optimally scheduling a processor executing a multilayer protocol in an intelligent Network Interface Controller (NIC). In particular, we assume a typical LAN environment with class 4 transport service, a connectionless network service, and a class 1 link level protocol. We develop a queuing model for the problem. In the most general case this becomes a cyclic queuing network in which some queues have dedicated servers, and the others have a common schedulable server. We use sample path arguments and Markov decision theory to determine optimal service schedules. The optimal throughputs are compared with those obtained with simple policies. The optimal policy yields upto 25% improvement in some cases. In some other cases, the optimal policy does only slightly better than much simpler policies.

Relationship between the controllability grammian and closed-loop eigenvalues: the single input case

The controllability grammian is important in many control applications. Given a set of closed-loop eigenvalues the corresponding controllability grammian can be obtained by computing the controller which assigns the eigenvalues and then by solving the Lyapunov equation that defines the grammian. The relationship between the controllability grammian, resulting from state feedback, and the closed-loop eigenvalues of a single input linear time invariant (LTI) system is obtained. The proposed methodology does not require the computation of the controller that assigns the specified eigenvalues. The closed-loop system matrix is obtained from the knowledge of the open-loop system matrix, control influence matrix and the specified closed-loop eigenvalues. Knowing the closed-loop system matrix, the grammian is then obtained from the solution of the Lyapunov equation that defines it. Finally the proposed idea is extended to find the state covariance matrix for a specified set of closed-loop eigenvalues (without computing the controller), due to impulsive input in the disturbance channel and to solve the eigenvalue assignment problem for the single input case.

Ultracapacitor Based Ride Through System for Control Power Supplies in High Power Converters

High power converters are used in variable speed induction motor drive applications. Riding through a short term power supply glitch is becoming an important requirement in these power converters. The power converter uses a large number of control circuit boards for its operation. The control power supply need to ensure that any glitch in the grid side does not affect any of these control circuit boards. A power supply failure of these control cards results in shut down of the entire system. The paper discusses the ride through system developed to overcome voltage sags and short duration outages at the power supply terminals of the control cards in these converters. A 240VA non-isolated, bi-directional buck-boost converter has been designed to be used along with a stack of ultracapacitors to achieve the same. A micro-controller based digital control platform made use of to achieve the control objective. The design of the ultracapacitor stack and the bidirectional converter is described the performance of the experimental set-up is evaluated.

Modeling and Field Oriented Control of Salient Pole Wound Field Synchronous Machine in Stator Flux Coordinates

This paper describes the field oriented control of a salient pole wound field synchronous machine in stator flux coordinates. The procedure for derivation of flux linkage equations along any general rotating axes including stator flux axes is given. The stator flux equations are used to identify the cross-coupling occurring between the axes due to saliency in the machine. The coupling terms are canceled as feedforward terms in the generation of references for current controllers to achieve good decoupling during transients. The design of current controller for stator-flux-oriented control is presented. This paper proposes the method of extending rotor flux closed loop observer for sensorless control of wound field synchronous machine. This paper also proposes a new sensorless control by using stator flux closed loop observer and estimation of torque angle using stator current components in stator flux coordinates. Detailed experimental results from a sensorless 15.8 hp salient pole wound field synchronous machine drive are presented to demonstrate the performance of the proposed control strategy from a low speed of 0.8 Hz to 50 Hz.

Gain calibration of CCD systems at VBO

The system gain of two CCD systems in regular use at the Vainu Bappu Observatory, Kavalur, is determined at a few gain settings. The procedure used for the determination of system gain and base-level noise is described in detail. The Photometrics CCD system at the 1-m reflector uses a Thomson-CSF TH 7882 CDA chip coated for increased ultraviolet sensitivity. The gain is programme-selected through the parameter 'cgain' varying between 0 and 4095 in steps of 1. The inverse system gain for this system varies almost linearly from 27.7 electrons DN-1 at cgain = 0 to 1.5 electrons DN-1 at cgain = 500. The readout noise is less than or similar 11 electrons at cgain = 66. The Astromed CCD system at 2.3-m Vainu Bappu Telescope uses a GEC P8603 chip which is also coated for enhanced ultraviolet sensitivity. The amplifier gain is selected in discrete steps using switches in the controller. The inverse system gain is 4.15 electrons DN-1 at the gain setting of 9.2, and the readout noise approximately 8 electrons.

Waveform synthesis using Walsh functions International Journal of Electronics

A software and a microprocessor based hardware for waveform synthesis using Walsh functions are described. The software is based on Walsh function generation using Hadamard matrices and on the truncated Walsh series expansion for the waveform to be synthesized. The hardware employs six microprocessor controlled programmable Walsh function generators (PWFGs) for generating the first six non-vanishing terms of the truncated Walsh series. Improved approximation to a given waveform may be achieved by employing additional PWFGs.

Matrix method for eigenstructure assignment - The multi-input case with application

The eigenvalue and eigenstructure assignment procedure has found application in a wide variety of control problems. In this paper a method for assigning eigenstructure to a linear time invariant multi-input system is proposed. The algorithm determines a matrix that has eigenvalues and eigenvectors at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenstructure. Solution of the matrix equation, involving unknown controller gams, open-loop system matrices, and desired eigenvalues and eigenvectors, results hi the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint can easily be overcome by a negligible shift in the values. Application of the procedure is illustrated through the offset control of a satellite supported, from an orbiting platform, by a flexible tether.

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Matrix method for eigenstructure assignment - The multi-input case with application

The eigenvalue and eigenstructure assignment procedure has found application in a wide variety of control problems. In this paper a method for assigning eigenstructure to a Linear time invariant multi-input system is proposed. The algorithm determines a matrix that has eigenvalues and eigenvectors at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenstructure. solution of the matrix equation, involving unknown controller gains, open-loop system matrices, and desired eigenvalues and eigenvectors, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint can easily be overcome by a negligible shift in the values. Application of the procedure is illustrated through the offset control of a satellite supported, from an orbiting platform, by a flexible tether,

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Composite material and piezoelectric coefficient uncertainty effects on structural health monitoring using feedback control gains as damage indicators

This article addresses uncertainty effect on the health monitoring of a smart structure using control gain shifts as damage indicators. A finite element model of the smart composite plate with surface-bonded piezoelectric sensors and actuators is formulated using first-order shear deformation theory and a matrix crack model is integrated into the finite element model. A constant gain velocity/position feedback control algorithm is used to provide active damping to the structure. Numerical results show that the response of the structure is changed due to matrix cracks and this change can be compensated by actively tuning the feedback controller. This change in control gain can be used as a damage indicator for structural health monitoring. Monte Carlo simulation is conducted to study the effect of material uncertainty on the damage indicator by considering composite material properties and piezoelectric coefficients as independent random variables. It is found that the change in position feedback control gain is a robust damage indicator.