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In the paper it is investigated, under which conditions a time variable state transformation can be used to change a periodic autonomous system realization into a form with constant real coefficients. Conditions for the transformation to be periodic are further considered, and it is shown that the necessary and sufficient condition to meet the conditions is in that two specific matrices must be similar to each other. The properties of the matrices and the transformation are studied, and the discussion is then extended to input-output systems. An approach to design stabilizing control laws for these kinds of periodic systems is outlined.

Grinding systems are often modelled by multivariable impulse response or weighting function matrices. These kind of models are very suitable for design of model predictive controllers. Two predictive control algorithms have been developed and tested with two simulated models of grinding systems. Their design is based on decoupling of the steady state interactions. The dynamic interactions cannot be eliminated but their strengths are reduced by dynamic compensation.

The time for material to pass through a plug flow vessel is modelled by a delay function. If the flow rate is time-variable, the varying delay is difficult to calculate analytically even for general test functions of the flow rate. In this paper, the properties of delay functions are studied theoretically. Two different methods for the simulation of the delay are derived. Several examples are studied, in which known analytical solutions as well as simulations of delay functions are presented.

The paper presents a new method for modelling of complex processes containing unkown qualitative varlables. The method is based on grouping the input-output-palrs of the model into a finite nunlber of clusters each representing different values of unknown qualitative variables. An online clustering algorithm is derived from assumption that each cluster consists of realizations of some normally distributed random vector. An expert control system using the cluster model together WIth sImple static linear models for decision of necessary control actions is outlined. The method has been applied to real data from mineral processes.

A physical continuous flow process of unknown structure is identified under constant and variable flow rates by testing it in a well instrumented laboratory enviroment. The pH numbers of its input and output streams are measured continuously, converted to concentrations of reaction invariant components and used as inputs to the recursive parameter estimation algorithm. This is first written in terms of time, in order to obtain the weighting function of the process under constant flow. The same algorithm is then rewritten in terms of an integrated flow variable which has been shown to bring the variable flow processes to constant parameter form, and used for identification under variable flow. In both cases the identification converges to a weighting function estimate which includes a minor random component only, and produces the continuous output with good accuracy. Independent tests with an impulselike input at three different flow rates are used as a check of the results. The method is considered applicable to predictive and other model based controls of time-varying processes.

The pilot manufacturing cell processes objects which belong to a product family. They arrive at the cell on a conveyor on which they lie in random order and in random positions and orientations. They are picked up and handled, drilled, milled and measured in several stages; all operations and their sequences follow each other automatically. A high degree of flexibility is reached through the use of a camera sensor, an industrial robot, programmable and NC machine tools and control computers, as components of the cello A rather large software system has been developed for recognition and adaptive handling of objects, for cell control and for external communication with a standard CAD/CAM system. The system is used for instruction and demonstration of the technology and serves research by offering a test bed for FM programs of various levels of sophistication. Its operation under dynamic programming and knowledge based controls is illustrated by reported test runs.

Dynamic model of the rotary grinding mill with variable material flow is a superposition of the kinetic grinding process and the flow pattern characterized by the residence time distribution. A dimensionless residence variable is introduced by integrating the slurry flow through the mill and the time varying model is brought to invariant form by application of this variable. A recursive on-line identification method is developed for open and closed grinding loops by parametrizing the residence distribution with a set of unknown amplitude readings. With Extended Kalman Filter, both the kinetics and the residence distribution are estimated under variable process flow.

Models of continuous flow vessels with variable volume and flow are studied and methods are developed for their recursive identification. New, composite variables have been introduced recently and it has been proven that many time-variable flow systems have only constant parameters, if they are modelled as functions of such variables, assuming their flow patterns are invariant under changes of flow and volume. The recursive prediction error algorithm is now first formulated in terms of the variable which matches to the case of constant volume and variable flow, and the process is identified by estimating a set of 20 successive, equidistant values of the weighting function. Similar algorithms are then written and identifications executed in the cases of variable volume and flow. The study is extended to the case of a flow pattern which changes independently of the simultaneous variation of the total flow and volume, and the parameters of the pattern are tracked. The identifications of the simulated processes prove the superiority of the approach with regard to algorithms written in terms of the regular time variable. Extension of the method to estimation of chemical reaction parameters is discussed against this background.

Properties of the descriptor form representation of linear time-invariant multivariable systems have been studied using polynomial system methodology. A new normal form for the input-output equivalence on descriptor form representations has been presented. This normal form makes the complicated and partly misleading controllability and observability considerations presented in the literature clear and easy to carry out.

Thermal shocks influencing onto oscillators will complicate the design of the phase and frequency locked loops. Due to thermal shocks the frequencies of crystals can run away from their nominal frequencies by tens or even more than 100 Hz in a second. Nokia mobile phones has made in the cooperation with laboratory of system engineering at the University of Oulu studies to manage the affect of thermal shocks in tracking loops. The results indicate that the influence of thermal shocks mostly can be compensated in the currently known conditions.

The polynomial systems theory for time-varying and distributed parameter systems is briefly introduced. The theory is applied to design of a vision based control system for exact positioning of a camera above a moving object. The algebraic structure needed here is a ring of skew polynomials with skew polynomial coefficients. Both an observer for estimating nonmeasurable outputs and a stabilizing controller are designed.

A new method for modelling of complex processes containing unknown qualitative variables is presented. The method is based on clustering the input-output-pairs of the model into a finite number of clusters each representing a different value of unknown qualitative variables. The clustering algorithm is derived from the assumption that each cluster consists of realizations of a normally distributed random vector. The method has been tested by simulated process model and real data from mineral processes.

Models of continuous flow vessels with variable volume and flow are studied and methods are developed for their recursive identification. New, composite variables have been introduced recently and it has been proven that many time-variable flow systems have only constant parameters, if they are modelled as functions of such variables, assuming their flow patterns are invariant under changes of flow and volume. The recursive prediction error algorithm is now first formulated in terms of the variable which matches to the case of constant volume and variable flow, and the process is identified by estimating a set of 20 successive, equidistant values of the weighting function. Similar algorithms are then written and identifications executed in the cases of variable volume and flow. The study is extended to the case of a flow pattern which changes independently of the simultaneous variation of the total flow and volume, and the parameters of the pattern are tracked. The identifications of the simulated processes prove the superiority of the approach with regard to algorithms written in terms of the regular time variable. Extension of the method to estimation of chemical reaction parameters is discussed against this background.

This paper deals with canonical forms and invariants for linear time-invariant differential and difference systems. The signal spaces of differential systems are regarded as modules over the ring C[p] of polynomials in the differentiation operator p with complex coefficients. Systems are considered as sets of input-output pairs (u,y;) satisfying modulo equations of the form A(p)y= B(p)u, where A{p) and B(p) are matrices with entries in C[p]. It is shown that under certain conditions all S3Tstem matrices [A(p) — B(p)] associated with a given system are equivalent in the sense that they can be obtained from each other by elementary row operations. The main result is that every system matrix can be brought to a unique canonical upper triangular (CUT) form. Difference systems are considered similarly by replacing p by a shift operator. For these systems there exists a CUT-form which is strongly dependent on causality.

Dynamic model of the rotary grinding mill is described as a superposition of the kinetic grinding process and the flow pattern expressed by the residence time distribution. The model of a system with a closed grinding loop is obtained as a combination of models of its components. Dynamics of the system have been simulated, after the model has been reduced to correspond to a binary grain size distribution. The numerically obtained impulse responses of this multivariable model are now converted to frequency responses, and appropriate controllers are designed by means of the Nyquist arrays. By means of the known, mostly nonlinear dependences of the model on the various inputs, the controllers can be retuned without a physical testing, e.g. after a permanent change of the average value of an input variable has been observed.

The controllability indices for multivariable linear systems are defined by selecting linearly independent columns of the controllability matrix. The two selection schemes yield Hermite indices and Kronecker indices. To express the information on uncontrollable modes “augmented” indicca arc introduced. For structured systems defined to have their parameters either fixed at zero or independent and free there exist generic indices, i.e. indices which are actual indices for “almost all” free parameter values. The generic indices can be determined using graph—theoretic methods. Observability indices are defined and studied in an analogous way. The relationships between the indices and a polynomial matrix representation of the system are given and applied to improve a feedback compensator design method based on the polynomial matrix representation. New methods for removing uncontrollable and unobservable modes are also given.

Steady state models of open and closed grinding loop are derived, Starting from the dynamic model of the rotary mill and the models of the other components. The parameters have been evaluated by sampling and analyses, and by computation based on the models. Use of the models for control and optimization of the steady state is explained. The dynamic models are also studied in order to develop recursive on-line methods for parameter and state estimation. Ooth a general, infinite dimensional state space model and a slightly simpler finite dimensional model are presented and their use for estimation and control is discussed.

A special vision system for the exact positioning and feedback. control of manipulators has been developed. The visual sensor is mounted on the gripper of the manipulator. The output of the system consists of the 2-dimensional position and orientation deviations from the taught nominal ones and they are transmitted to the manipulator control system via standard serial or parallel connections. The system is insensitive with respect to variations in its operating environment because it is based on matching local features of the image contours using the Hough-transform methodology. The prototype system has so far been realized by software using a laboratory-scale vision system but some most time consuming operations will be replaced by special hardware in the near future.

The basic theory for analysis and synthesis of differential systems using polynomial matrix representation is considered. Concepts like controllability, observability, stability etc. are defined and methods based on elementary row operations for checking them are given. As an example of synthesis methods an algorithm for synthesis of observers is given. A similar algorithm for synthesis of feedback compensators has been presented elsewhere. Computer aided design of multivariable control systems is performed interactively using a program which enables manipulation of polynomial matrices, and a simulation program that uses polynomial matrices as models of differential systems. The program for manipulation of polynomial matrices performs row operations and other transformations, calculates determinants and their roots etc. Synthesis problems can also be considered by studying different regulator compositions, constructing estimators and feedback compensators. The simulation program communicates with the manipulation program by means of polynomial matrices stored in files. Simulation results are presented by graphic displays or by separate plotter and design decisions can be based on these results. The use of the CAD package is demonstrated by considering an observer synthesis problem.

This paper briefly presents the fundamental facts of the polynomial systems theory as applied by Rosenbrock, Wolovich and others. The theory utilizes an operator algebra which is a natural generalization of the usual operational calculus based on the Laplace and Z-transforms. It is shown how this operator algebra can be used in an efficient way for solving a number of typical problems relating to the analysis and synthesis of linear time-invariant feedback systems and estimators.

The paper suggests an algorithm for the multi variable control of an lndustrial sulphide ore grinding plant. The algorithm is based on the linear-quadratic gaussian control theory with a moving time horizon The dynamic process model with two inputs and two outputs is obtained by fitting simple low order linear time-invariant models to measured inputoutput pairs. Characteristic to the model are the long time delays The model is brought to the state space form, in which the time delays are described by additional state components. The inputs are replaced by input increments, for the purpose of avoiding imbalances of stationary values and of assigning quadratic costs to input changes Because of disturbances both in the process and in the measuring equipment Kalman filter is used for state estimation. In order to carry out the setpoint changes faster, the estimated state is corrected by tne corresponding change of coordinates The control algorithm has been tested both by simulation runs and by implementation in the control of the plant. The weighting and covariance matrices were used as tuning parameters. The test runs showed that the algorithm can be tuned rather easily and satisfactory results were obtained The steady state interactions were almost completely compensated and the transient interactions were within acceptable limits

Problems dealing with combined hydro/thermal power systems are very difficult to solve due to their many uncertainties. In order to do their solution possible to non-specialist decision-makers, too, the problems have to be formulated in an appropriate way. In this paper a simulation model based on dynamic programming and statistical time series is presented. The model has been applied to a decision making situation, where the estimation and cognition of risks have had a decisive importance.

The basic theory for analysis and synthesis of differential systems using polynomial matrix representation is considered. Concepts like controllability, observability, stability etc. are defined and methods based on elementary row operations for checking them are given. As an example of synthesis methods an algorithm for synthesis of observers is given. A similar algorithm for synthesis of feedback compensators has been presented elsewhere. Computer aided design of multivariable control systems is performed interactively using a program which enables manipulation of polynomial matrices, and a simulation program that uses polynomial matrices as models of differential systems. The program for manipulation of polynomial matrices performs row operations and other transformations, calculates determinants and their roots etc. Synthesis problems can also be considered by studying different regulator compositions, constructing estimators and feedback compensators. The simulation program communicates with the manipulation program by means of polynomial matrices stored in files. Simulation results are presented by graphic displays or by separate plotter and design decisions can be based on these results. The use of the CAD package is demonstrated by considering an observer synthesis problem.