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3 Ładziński R.

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Dynamic systems with a finite degrees of freedom number

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Ładziński R.

Archives of Control Sciences

2014

tom Vol. 24, no. 2

207--234

Taking as a starting point the law of conservation of the total energy of the system, and introducing two basic state functions - the Lagrangian and the Rayleigh function, the general form of the equation of motion for any dynamic system with a finite number of degrees of freedom is derived. The theory is illustrated by considering the rotating - type electromechanical energy converter with six degrees of freedom being the model of all essentially important types of DC and AC machines, including rotating power amplifiers, induction - and synchronous type motors - all of them discussed from both, the steady-state and the transient point of view. In the next part of the paper there is described a simple electric circuit with its model characterized by the holonomic constraints of the velocity-type. Finally, there is presented the kinematics and dynamics of the interesting mechanical system - the gyroscope placed on the rotating Earth.

An outline of the linear control system synthesis by a proper, stable rational functions approach

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Ładziński R.

Archives of Control Sciences

1998

tom Vol. 7, no. 3/4

241-265

In the process of designing controllers for linear multivariable plants specially effective are algebraic methods which require from the transfer matrices of both, the plant and the controller to be presented in coprime fractional form with factorization carried on with respect to the ring of exponentially-stable, proper real-rational functions. The main objective of the paper is to show that this form of representation with simultaneous parametrization of all linear controllers that provide internal stability of the closed-loop system can be achieved in the simplest and most natural way by analysing the system shown in Fig. 3 - the so-called basic structure. Problems of choosing the parameter to meet some important design specifications, viz. a robust asymptotic tracking of the reference signal with disturbance and noise rejection are also considered and illustrated by two representative examples covering the area of continuous- and discrete-time systems.

On reducing the order ot the stabilizing compensator for a linear multivariable plant

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Ładziński R.

Archives of Control Sciences

1998

tom Vol. 7, no. 1/2

69-98

The text covers an in-depth study on the order of the compensator applied in a feedback system for stabilization of the linear, time-invariant, n-th order, multivariable plant. It is shown that all such compensators evolve from the n-th order structure depicted in two forms in Fig. 2 (dotted lines). Presentation includes the so-called reduced and subreduced order compensators and the case of a static output feedback, i.e. the compensator of order zero. All theoretical considerations are supported by examples, in which various types of compensators are synthesized.