A global convergence criterion for discrete-time multivariable adaptive systems

The paper deals with the basic problem of adjusting a matrix gain in a discrete-time linear multivariable system. The object is to obtain a global convergence criterion, i.e. conditions under which a specified error signal asymptotically approaches zero and other signals in the system remain bounded for arbitrary initial conditions and for any bounded input to the system. It is shown that for a class of up-dating algorithms for the adjustable gain matrix, global convergence is crucially dependent on a transfer matrix G(z) which has a simple block diagram interpretation. When w(z)G(z) is strictly discrete positive real for a scalar w(z) such that w-1(z) is strictly proper with poles and zeros within the unit circle, an augmented error scheme is suggested and is proved to result in global convergence. The solution avoids feeding back a quadratic term as recommended in other schemes for single-input single-output systems.

Sequential design of decentralized control systems

Our main result is a new sequential method for the design of decentralized control systems. Controller synthesis is conducted on a loop-by-loop basis, and at each step the designer obtains an explicit characterization of the class C of all compensators for the loop being closed that results in closed-loop system poles being in a specified closed region D of the s-plane, instead of merely stabilizing the closed-loop system. Since one of the primary goals of control system design is to satisfy basic performance requirements that are often directly related to closed-loop pole location (bandwidth, percentage overshoot, rise time, settling time), this approach immediately allows the designer to focus on other concerns such as robustness and sensitivity. By considering only compensators from class C and seeking the optimum member of that set with respect to sensitivity or robustness, the designer has a clearly-defined limited optimization problem to solve without concern for loss of performance. A solution to the decentralized tracking problem is also provided. This design approach has the attractive features of expandability, the use of only 'local models' for controller synthesis, and fault tolerance with respect to certain types of failure.

Position and Feed-Rate Control for Contouring Numerical-Control Systems

Numerical control (NC) for contouring operations requires precise control of position and feed rate for approximating the contour by linear moves of the cutter. A control scheme, for generating linear moves with desired slopes for the cutter, is described. This scheme provides for nine successive linear moves, and may be either expanded or implemented in succession, for approximating a contour.

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.

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.

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.

An account of chronological developments in control of distributed parameter systems

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum.Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references.

Broadcast Control Mechanism for Positional Consensus in Multiagent Systems

In this paper, a strategy for controlling a group of agents to achieve positional consensus is presented. The problem is constrained by the requirement that every agent must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming (LP) formulation that is computationally less intensive than earlier proposed methods. Moreover, a random perturbation input in the control command that helps the agents to come close to each other even for a large number of agents, which was not possible with an existing strategy in the literature, is introduced. The method is extended to achieve positional consensus at a prespecified location. The effectiveness of the approach is illustrated through simulation results. A comparison between the LP approach and the existing second-order cone programming-based approach is also presented. The algorithm was successfully implemented on a robotic platform with three robots.

Some new concepts in nonlinear systems

Some new concepts characterizing the response of nonlinear systems are developed. These new concepts are denoted by the terms, the transient system equivalent, the response vector, and the space-phase components. This third concept is analyzed in comparison with the well-known technique of symmetrical components. The performance of a multiplicative feedback control system is represented by a nonlinear integro-differential equation; its solution is obtained by the principle of variation of parameters. The system response is treated as a vector and is resolved into its space-phase components. The individual effects of these components on the performance of the system are discussed. The suitability of the technique for the transient analysis of higher order nonlinear control systems is discussed.

A New Liquid Level Sensor for Process-Control Applications

Many process-control systems are air-operated. In such an environment, it would be desirable and economical to use pneumatic sensors. Bubble-back pressure sensors perform quite satisfactorily, but in case of viscous inflammable and slurry-like liquids with a tendency to froth, this level sensor is inadequate. The method suggested in this paper utilizes a pneumatic capacitor, one boundary of which is formed by the liquid level, to modulate a fluid amplifier feedback oscillator. The absence of moving parts and economy obtained makes this method attractive for process-control applications. The system has been mathematically modeled and simulated on an IBM 360/44 digital computer. Experimental values compare fairly well with the theoretical results. For the range tested, the sensor is found to have a linear frequency variation with the liquid level Extended running in the laboratory shows that the system is very reliable. This system has been found insensitive to temperature variations of up to 15ðC.

Modeling stochastic hybrid systems

Stochastic hybrid systems arise in numerous applications of systems with multiple models; e.g., air traffc management, flexible manufacturing systems, fault tolerant control systems etc. In a typical hybrid system, the state space is hybrid in the sense that some components take values in a Euclidean space, while some other components are discrete. In this paper we propose two stochastic hybrid models, both of which permit diffusion and hybrid jump. Such models are essential for studying air traffic management in a stochastic framework.

Terminal Impact Angle Constrained Guidance Laws Using Variable Structure Systems Theory

In this brief, variable structure systems theory based guidance laws, to intercept maneuvering targets at a desired impact angle, are presented. Choosing the missile's lateral acceleration (latax) to enforce sliding mode, which is the principal operating mode of variable structure systems, on a switching surface defined by the line-of-sight angle leads to a guidance law that allows the achievement of the desired terminal impact angle. As will be shown, this law does not ensure interception for all states of the missile and the target during the engagement. Hence, additional switching surfaces are designed and a switching logic is developed that allows the latax to switch between enforcing sliding mode on one of these surfaces so that the target can be intercepted at the desired impact angle. The guidance laws are designed using nonlinear engagement dynamics for the general case of a maneuvering target.

Turbine emulator for development of variable speed microhydro power generation systems

Variable speed operation of microhydro power plants is gaining popularity due to the benefits that accrue from their use and the development of suitable generator control systems. This paper highlights the benefits of variable speed systems over conventional systems and also proposes a simple emulator for hydraulic turbines that operate in variable speed fixed flow rate mode. The emulator consists of an uncontrolled separately excited DC motor with additional resistors and has performance characteristics similar to that of the hydraulic turbine.