The system of a multi-motor frequency-cascade electric drive based on asynchronous motors with a phase-rotor, which is characterized by synchronous-asynchronous speed control, is considered. Synchronous regulation is carried out by varying the frequency of the voltage on the stator of the electric motors, and asynchronous regulation is carried out by changing the counter-emf introduced into the rectified rotor current circuit. By formal transformations, expressions are obtained that determine the basic static characteristics of an electric motor with the considered control method and its T-shaped equivalent circuit. As a result of the conversion of the obtained equivalent circuit, the asynchronous motor was presented as an equivalent source of EMF, which allowed a formal transition to the equivalent circuit of the rectified rotor current circuit, to obtain a dynamic model and draw up a block diagram of the electric motor with frequency-cascade control. We also obtained a linearized dynamic model of an asynchronous electric motor with frequency-cascade control, structurally corresponding to the asynchronous-valve cascade, which, taking into account the relevant features, allows the use of classical methods of synthesis of closed-loop control systems.

Mathematical Model of Asynchronous Motor with Frequency-Cascade Regulation

Multi-channel object control is required in many technical systems and technological setups. Typically, the number of controlled output values of the object is the same as the number of inputs used to control the object. There are examples of using two or more input channels to control a single output value of an object. This is justified by the fact that different control channels have evident different shortcomings, and hence different advantages. In particular, this is efficient if one of the control channels is limited in speed, and the other is limited in the control range. If there are no evident differences in the advantages of different control channels, such redundant control is not used. There are no publications on the efficiency of using redundant management of multi-channel objects. Analytical methods for calculating controllers, even with non-redundant control, are extremely complex, and for the case of second-order objects with delay, there are no adequate analytic methods. This explains the lack of publications on the redundant control of multi-channel objects, since this task is extremely difficult for analytical methods. The emergence of software tools for mathematical modeling (simulation) and numerical optimization removed the problem of calculating of complex regulators for complex sophisticated. The use of such software makes allows investigating the usefulness of excessive control on numerical examples. This paper is devoted to the investigation of the expediency of controlling a second-order object of dimenslon $3\times 2$ with a delay. It is shown that even if there are no visible bases for using all three control channels, this gives a significant positive effect. A control method was developed and grounded with approbation, including a set of test actions, regulator structures and cost functions.

Controlling a Second-Oorder Multichannel Object of Dimension $3\times 2$ with Delay

The control of multi-channel objects is relevant for many areas of science and technology. The presence of multiple links from each input to each output inside the object complicates the control problem extremely. Solving this problem by creating separate loops from each exit to each input is impossible. To solve this problem, a multichannel controller is necessary, that is, a controller containing the demanded transfer functions from each of its inputs to each output. There are many methods for calculating multi-channel controllers, but the overwhelming majority of them can be used only for the simplest models of the object. If each transfer function in the matrix model of the object contains delay links, none of the analytical methods for calculating the regulator is acceptable. This problem can be solved only by numerical optimization methods. In this paper, the method of numerical optimization of a regulator for a multi-channel object is proposed and investigated in the case when the transfer function of each channel is a product of a second-order filter and a pure delay link. A simple application of the numerical optimization method yields a system in which transient processes are characterized by overshoot exceeding 50%. The paper suggests a modification of the cost function for calculating the regulator by the method of numerical optimization. The effectiveness of the suggested solution is demonstrated, recommendations on the use of the proposed method are given.

Aleksander V. Liapidevskiy

Papers

Controlling a Second-Oorder Multichannel Object of Dimension $3\times 2$ with Delay

Controlling of Second-Order Two-Channel Object with Delay