# Optoelectronics, Instrumentation and Data Processing (v.51, #5)

Structural-parametric synthesis of time-optimal distributed parameter control systems with interval uncertainty of the plant characteristics by E. Ya. Rapoport; I. S. Levin

*(429-440)*. This work is devoted to a possible way to construct time-optimal closed systems for incompletely determined linear models of distributed-parameter control plants of parabolic type, which provides real-time identification of their parametric characteristics according to the results of monitoring the state of the plants. The structural-parametric synthesis of the proposed controllers is based on the alternance method of designing optimal software controls. The paper gives an example (of independent interest) of constructing a time-optimal system for the control of the process of induction heating under typical conditions of interval uncertainty of the initial temperature and heat losses.

**Keywords:**distributed-parameter plants; time-optimal control; alternance method; switching function; structural-parametric synthesis; interval uncertainties

Alternance method of structural-parametric synthesis of cascade automatic control systems by Yu. E. Pleshivtseva; A. A. Afinogentov

*(441-448)*. This work is devoted to the technique of solving the problem of structural-parametric synthesis of typical controllers in a multiloop cascade automatic control system, which is developed on the basis of the alternance method of parametric optimization that provides the maximum degree of invariance of local control loops relative to external perturbations with given limitations on the peak of amplitude-frequency characteristics of closed loops of the synthesized automatic control system. The task of optimizing the subsystem for controlling the fuel oil temperature in a multiloop control system of primary oil refining on an atmospheric and vacuum crude distillation unit is considered as an example, which is of independent interest.

**Keywords:**structural-parametric synthesis; cascade control system; alternance method of optimization; mathematical programming problem; typical controllers

Estimation of directly unmeasurable external perturbations using functional observers by A. Z. Asanov; D. N. Dem’yanov

*(449-455)*. It is shown that the problem of estimating unmeasurable external perturbations from a mathematical point of view is equivalent to estimating some of the state variables of an extended plant. An algorithm for estimating unmeasurable external perturbations using a functional observer is proposed, and conditions for the solvability of the synthesis problem are formulated. The resulting solution is obtained using the method of matrix canonization.

**Keywords:**external perturbations; estimation; functional observer; synthesis algorithm; matrix canonization

Aircraft attitude control by Yu. N. Zolotukhin; A. A. Nesterov

*(456-461)*. The problem of control of the aircraft attitude in a three-dimensional space is considered. The attitude is described by the Euler angles between the axes of the body-fixed coordinate system and the Earth frame. A method of calculating the torque driving the aircraft to a prescribed attitude is proposed. A controller implementing this method is presented. Results of simulations are reported.

**Keywords:**aircraft; attitude; attitude control; torque

Self-adjusting system with a reference model for control of underwater vehicle motion by A. V. Lebedev; V. F. Filaretov

*(462-470)*. A method of synthesis of a self-adjusting multichannel system with a reference model for centralized control of autonomous underwater vehicle motion is developed. Conditions of selfadjustment process stability with allowance for dynamic reciprocal effects and kinematic relations between all control channels in the presence of parametric nonstationarity of the complete nonlinear mathematical model of the vehicle are obtained. The amplitude of the self-adjustment signal is formed as a function of coordinates and reference-input signals in order to reduce the control signal magnitude. The developed system ensures a high quality of control of an underwater vehicle with significant variations of its parameters.

**Keywords:**control system; autonomous underwater vehicle; reference model; self-adjustment

Synthesis of PID controllers for nonlinear nonstationary plants by A. S. Vostrikov; G. A. Frantsuzova

*(471-477)*. A possible approach to the calculation of standard controller parameters based on the localization method is considered. It is shown that the controllers designed in this way completely solve the problem of stabilization of first- and second-order nonlinear nonstationary plants. Variants of implementation of standard controllers and recommendations for calculating their parameters are presented and the properties of the obtained automatic systems are investigated. It is noted that a general characteristic feature of systems with the proposed PID controller is the occurrence of fast motion components against the background of slow work processes. Results of numerical modeling illustrate the main properties of the systems considered.

**Keywords:**control; PID controller; nonlinear plant; localization method; multirate processes

Robust correction of dynamic plants in automatic control systems by A. B. Filimonov; N. B. Filimonov

*(478-484)*. A two-step procedure for solving problems of robust control of dynamic plants with uncertainties is proposed. Plant dynamics is first subjected to robust correction by means of a high-gain control loop in accordance with a given reference model. Since the corrected plant model is now known, standard control methods are then used. This approach is implemented in a two-loop control system: the inner loop provides robust correction of a plant, and the outer loop is responsible for the achievement of the control objective.

**Keywords:**uncertain plant; high gain; robust correction; reference dynamics; two-loop control system

Root coordinates in the design of SISO control systems by A. V. Chekhonadskikh

*(485-495)*. We study pole placement in SISO linear control systems with low-order controllers is studied. A method for finding critical (including optimal and suboptimal) pole placement in closedloop systems is theoretically justified and demonstrated on an example. Using critical root diagrams and root polynomials, it is possible to analytically express the parameters of a suboptimal controller in terms of root coordinates, in particular, the real and imaginary parts of characteristic roots. The resulting algebraic equations and inequalities allow specifying the left-most shift of the pole placement domain and the greatest relative stability (possibly taking into account oscillation) without cumbersome calculations.

**Keywords:**SISO linear control systems; low-order controller; optimal pole placement; R-graduation; critical root diagrams; root polynomials

Robust leader–follower formation control of mobile robots by the structural synthesis method by Yu. N. Zolotukhin; K. Yu. Kotov; A. S. Mal’tsev; A. A. Nesterov; M. A. Sobolev; M. N. Filippov; A. P. Yan

*(496-504)*. A problem of control of the motion of mobile robots with a differential drive in a leader–follower formation is considered. The proposed method of structural synthesis allow one to form control inputs for robots–followers only on the basis of information about the relative positions of the followers and the leader without using the absolute values of the spatial coordinates of the robots. The algorithm efficiency is confirmed by results of numerical experiments.

**Keywords:**leader–follower formation; control of a formation of mobile robots; structural synthesis of automated control systems; forced motion

Information-control system for mobile robots by V. F. Filaretov; D. A. Yukhimets; E. Sh. Mursalimov

*(505-511)*. An approach is proposed for constructing an information-control system (ICS) for controlling the motion of mobile robots (MRs) of various types and purposes. This ICS consists of universal components with data exchange through interfaces independent of the MR hardware. The use of this system appreciably decreases the cost of the development of a new generation of mobile robots.

**Keywords:**mobile robot; information-control system; data fusion; software architecture

Modeling the process of measuring radial and axial displacements of complex-shaped blade tips by S. Yu. Borovik; M. M. Kuteynikova; P. E. Podlipnov; Yu. N. Sekisov; O. P. Skobelev

*(512-522)*. This paper gives brief descriptions of the distinctive features of the method of measuring radial and axial displacements of complex-shaped blade tips (employed in turbines) using a distributed cluster of single-coil eddy current sensors (SCECS) with a sensitive element (SE) in the form of conductor strips, known models of the electromagnetic interaction of SCECS SEs with the controlled and adjacent blades, and a measuring circuit (MC) with a cluster of two SCECSs designed for computational experiments. Results of experiments in the form of families of conversion functions (dependences of the equivalent inductances of SEs or digital codes at the MC output on the desired radial and axial displacements of the blade tip) and families of influence functions of adjacent blades on the equivalent inductances of the SE and the MC output codes are considered..

**Keywords:**complex-shaped blade tips; radial and axial displacements; single-coil eddy current sensor; influence of adjacent blades; conversion and influence functions

Adaptive periodic servo-system for nonlinear control-affine objects by E. L. Eremin; E. A. Shelenok

*(523-529)*. A problem of constructing a combined adaptive control system for periodic modes of a control-affine a priori uncertain nonlinear dynamic object is considered. At the stage of simulation modeling, the quality of the resulting control system is illustrated.

**Keywords:**adaptive control; combined algorithm; periodic signal generator; stationary observer; hyperstability criterion

Analysis of the error of measuring the capacity of semiconductor structures at a high Frequency by V. N. Vyukhin

*(530-535)*. The error of measuring the capacity of semiconductor structures at a high frequency by an integrator-based measurement circuit is studied theoretically and experimentally. Relations derived for calculating this error allow one to choose the measurement circuit parameters correctly for particular conditions.

**Keywords:**measuring the capacity of semiconductor structures; measurement error; test signal; measurement circuit; capacity divider; integrator