The article deals with the application of fractional order desired forms to extend the range of possible fractional controllers adjustment in the synthesis of electromechanical systems loops and to provide better quality of transition processes as compared with integer order controllers. Experimental tests of the fractional order controllers, synthesized by proposed approaches in the control system of frequency converter-induction motor speed, have confirmed the effectiveness in terms of the expansion of adjusting capabilities of PI ^γ D ^μ controller as compared with the classical PID-controller.

The approximation of a fractional order PI^λD^μ-controller transfer function using a chain fraction theory is considered. Analytical expressions for the approximation of $s^{\pm \alpha }$ components of the transfer functions of PI^λD^μ-controllers were obtained through the application of the chain fraction theory. Graphs of transition functions and frequency characteristics of D^μ (α = μ = 0.5) and I^λ (α = λ = −0.5) parts for five different decomposition orders were obtained and analyzed. The results showed the possibility of applying the approximation of the PI^λD^μ-controller transfer function by the method of chain fractions with different valuesof λ and μ. For comparison, the transfer functions with the same order polynomials, obtained by the methods of Oustaloup transformation and chain fractions, were approximated for α = ±0.5. The analysis proved the advantages of using the chain fraction method to approximate the transfer function of the PI^λD^μ-controller. The performed approximation opens up the possibility of developing engineering methods for the technical implementation of PI^λD^μ-controllers. The accuracy of the same order transfer function approximation is higher when the method of chain fractions is used. It has been established that the adequacy of the frequency characteristics of the transfer functions obtained by the chain fraction method also depends on the approximation order.

The intelligent point multi-sensor fire detector with smoke and heat sensors has been proposed using a fuzzy correction block synthesized on the basis of fuzzy logic theory. The algorithm of the work of this block has been developed: the forms and parameters of the input and output membership functions have been established; based on expert knowledge, a base of fuzzy rules that describe the state of the environment in the room has been compiled. According to the developed algorithm of work, the fuzzy correction block recognizes the change in temperature and smoke concentration in the room and generates the required output signal. This allows you to detect a fire at the early stage. The work of this fire detector has been investigated on the developed digital model of the fuzzy correction block.

The approximation of high order transfer function using particle swarm optimization method through a range of proposed fractional order transfer functions (models) has been carried out and the accuracy of such approximation has been estimated by comparing transition and frequency characteristics. The advantages of transition function approximation of induction generator with self-excitation by using fractional order transfer functions have been elucidated.

The model of an alternating current single-phase collector motor in the MATLAB Simulink environment has been developed and researched on the basis of the data obtained through project design calculation, during which all the motor parameters required for the mathematical model have been obtained. It has offered considerable opportunities for applying this approach in further research of this motor type. The model of such motor has been also developed and investigated on the basis of an existing universal motor model in the library of MATLAB Simulink and the data obtained from project design calculation. A comparative analysis of the results obtained on both models has allowed for the conclusion about high degree of their coincidence and the possibility of their application for further studies.

The approximation of high order transfer function of an experimental electromechanical system by means of using particle swarm optimization method together with a proposed simple fractional order transfer function with zero and pole has been carried out and the accuracy of such approximation has been assessed through comparison of transition and frequency characteristics. The advantages of transition function approximation of induction generator with self-excitation by using fractional order transfer function with zero and pole have been displayed.