EMS control system design for a Maglev vehicle - a critical system

For the effective operation of a magnetically levitated (maglev) vehicle using electro-magnetic suspension, it is necessary that the airgap between the guideway and the levitating magnets is maintained. Such systems, where the output is required to remain strictly within bounds, are known as critical systems. This paper describes the design of the suspension system for a high-speed maglev vehicle which ensures that the airgap is maintained

Ellipsoidal Calculus, Singular Perturbations and the State Estimation Problems for Uncertain Systems

One of the basic elements of dynamic modelling of complex systems is the linkage and synchronization of subsystems that develop in different time scales. The relevant techniques applied here are related to a singular perturbation theory for differential systems. A more complicated issue arises for uncertain systems described by differential inclusions, for which an appropriate theory is being developed. In order to make the theory constructive, some further steps are necessary. These are presented in this paper, where a computer-implementable "ellipsoidal" version is given. The results are particularly relevant to the linkage of models related to environmental, demographic and economic problems

Prospects of a mathematical theory of human behavior in complex man-machine systems tasks

A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued

On Viable Solutions for Uncertain Systems

One of the problems that arises in the theory of evolution and control under uncertainty is to specify the set of all the solutions to a differential inclusion that also satisfy a preassigned restriction on the state space variables (the "viability" constraint). The latter set of "viable" trajectories may be described by either a new differential inclusion whose right-hand side is formed with the aid of a contingent cone to the restriction map or by a variety of parametrized differential inclusions each of which has a relatively simple structure. The second approach is described here for a linear-convex differential inclusion with a convex valued restriction on the state space variables

On the Modified maximum Principle in Estimation Problems for Uncertain Systems

The present report is devoted to the problems of estimating the state of a linear dynamic system on the basis of on-line observation. It is assumed that the disturbances in the system inputs and in the current measurements are uncertain, a set-membership description of their values being only given in advance. A considerable number of problems concerning systems of the above type are covered by the theory of control and observation under uncertainty conditions. The main problems of this paper deal with the description of certain informational domains that are consistent with the results of available measurements of the state space variables. Here we consider the case when the disturbances in the system dynamics and in the observation equation are subjected to instantaneous (or "geometric") constraints. One approach to the problem based on an imbedding procedure of the primary problem into an auxiliary one of linear-quadratic estimation theory is given in the paper. The proposed procedure involves certain quadratic forms to bound the uncertainties in the modified problem. This method allows one to derive an appropriate maximum principle that is satisfied by system trajectories leading to boundary points of the informational domain

Optimal Adaptive Control Methods for Structurally Varying Systems

The problem of simultaneously identifying and controlling a time-varying, perfectly-observed linear system is posed. The parameters are assumed to obey a Markov structure and are estimated with a Kalman filter. The problem can be solved conceptually by dynamic programming, but even with a quadratic loss function the analytical computations cannot be carried out for more than one step because of the dual nature of the optimal control law. All approximations to the solution that have been proposed in the literature, and two approximations that are presented here for the first time are analyzed. They are classified into dual and non-dual methods. Analytical comparison is untractable; hence Monte Carlo simulations are used. A set of experiments is presented in which five non-dual methods are compared. The numerical results indicate a possible ordering among these approximations.

Set Membership Parameter Estimation and Design of Experiments Using Homothety

In this note we address the problems of obtaining guaranteed and as good as possible estimates of system parameters for linear discrete–time systems subject to bounded disturbances. Some existing results relevant for the set–membership parameter identification and outer–bounding are first reviewed. Then, a novel method for characterizing the consistent parameter set based on homothety is offered; the proposed method allows for the utilization of general compact and convex sets for outer–bounding. Based on these results, we consider the one–step input design and identifiability problems in set–membership setting. We provide a guaranteed approach for the one–step input design problem, by selecting optimal inputs for the purpose of parameter estimation. As optimality criterion, the dimension and the outer– bounding volume of the “anticipated ” consistent parameter set is considered. We furthermore derive a sufficient criterion for (one–step) parameter identifiability, i.e. when a point estimate for a parameter can be guaranteed for all possible measurements

Hydrothermal modeling for optimum temperature control : an estimation-theoretic approach

Originally presented as part of the first author's thesis, (Environmental Engineer) in the M.I.T. Dept. of Civil EngineeringA short-term temperature forecasting (STF) system is proposed to predict and control plant intake and discharge temperatures at Salem Harbor Electric Generating Station. It is desired to minimize receiving-water (i.e., intake-water) temperatures during peak power demand periods, in order to minimize the cost of complying with the maximum discharge water temperature limit. This study addresses the hydrothermal modeling requirements of an STF system. An important element of an STF system is a predictive model of plant intake water temperatures. For application to Salem Harbor Station, strict model performance criteria exist, defining a model development problem: Develop a simple model to predict plant intake water temperatures 24 hours ahead, predicting daily peak intake temperatures within 10F on 90% of the days, and using only existing measurements. An estimation-theoretic approach to model development is used, which quantifies and minimizes the uncertainties in the model. The approach employs optimal filtering and full-information maximum- likelihood (FIML) estimation to obtain optimum parameter estimates. A two-basin, two-layer hydrothermal model of Salem Harbor is developed. The model computes hourly intake temperatures, incorporating tidal flushing, stratification, surface heat exchange, and wind advection of the plume. Twenty-eight model parameters and five noise statistics are estimated from intake-temperature data. Preliminary best-fit parameter values are obtained subjectively, followed by FIML parameter estimation using a data base of 96 hourly measurements (7/29 - 8/2/74). The model is tested for 106 days (5/17- 9/20/74) and various performance measures are computed, including sum- of-squares of measurement residuals (S), whiteness (P), percent of daily peak temperature predictions within 10F of actual (T), and others. Visual inspection of 24-hour intake temperature predictions shows that the two-basin, two-layer model performs qualitatively well. However, the model fails statistical tests on S and P, indicating structural weaknesses. FIML estimation yields physically unrealistic values for certain parameters, probably compensating for inadequate model structure. Despite structural flaws in the two-basin, two-layer model, FIML estimation yields parameters with consistently better performance than the preliminary estimates (by a small amount). It is concluded that the two-basin, two-layer model is presently unsuitable for STF use, largely due to structural weaknesses. Possible corrections are suggested; however, a statistical model of hourly temperatures appears to offer greater potential accuracy than physically-derived models. FIML parameter estimation is shown to be useful for water quality model development on a real system, particularly after subjective model development has been exhausted.New England Power Company under the MIT Energy Laboratory Electric Power Progra

Impacts of global warming on reservoir systems management

Issued as Reports [nos. 1-5], Draft final report, and Final report, Project E-20-68