Optimal actuator placement and static load compensation for a class of distributed parameter systems

Adaptive structures where actuators are incorporated into a building structure have the potential to reduce resource consumption in construction industry drastically. However, the performance of static load compensation depends to a large extend on the actuator placement. This paper presents optimal actuator placement for systems with distributed parameters based on the Gramian compensability matrix. To provide a general framework for different kind of loads, static loads are discretized as Dirac impacts. The resulting optimal actuator placement is robust against unknown load amplitudes, as load profiles are only considered qualitatively in the cost function. Further, the optimal control input for a given load results directly from the optimization problem. The procedure is illustrated for a Kirchhoff-Love plate and integrated fluidic actuators.

NUMERICAL ALGORITHM OF COMPUTATIONAL EXPERIMENT OF THE APPLIED OPTIMAL CONTROL PROBLEM IN SYSTEMS WITH DISTRIBUTED PARAMETERS

Stages of computing experiment of the developed algorithm by means of the final and differential scheme for the solution of applied problems of optimum control of the processes described by the solutions of elliptic type are given n article.

METHODS OF SYNTHESIS OF REGULATORS FOR HYDRODYNAMIC CONTROL SYSTEMS WITH DISTRIBUTED PARAMETERS

An important problem of choosing a method for synthesizing regulators for constructing a system for controlling the parameters of hydrolithospheric processes is considered. The article deals with the issues of system analysis and synthesis of control systems with distributed parameters. The existing ways of solving mathematical equations describing models with spatial coordinates are shown. The main methods when there are solutions to the mathematical model are identified: analytical construction of optimal regulators and the structural method of analysis. Methods of approximation in cases where there is no solution to the mathematical model are described: methods of finite-dimensional approximation; decomposition of bilinear control systems; frequency method. The main provisions of the methods for solving the problem of discretization in partial derivatives are given. The preference of the frequency method of regulator synthesis in the creation of control systems for hydrolithospheric processes is shown. A hodograph is obtained in the form of logarithmic amplitude and phase frequency surfaces, which can be used to interpret the Nyquist stability criterion from graphs. A frequency method for the synthesis of multidimensional systems is considered, when the input effects to a distributed controller are implemented as a discrete function in space. The condition under which the object belongs to the class of spatially invariant objects is shown. It is concluded that the frequency method of regulator synthesis is the most convenient tool for creating systems with distributed parameters.

FIRST-ORDER METHODS FOR GENERALIZED OPTIMAL CONTROL PROBLEMS FOR SYSTEMS WITH DISTRIBUTED PARAMETERS

The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.

METHODS FOR PROBLEMS OF VECTOR GENERALIZED OPTIMAL CONTROL OF SYSTEMS WITH DISTRIBUTED PARAMETERS

The paper develops the theory of existence and necessary optimality conditions for optimal control problems with a vector quality criterion for systems with distributed parameters and generalized impacts. The concept of $(K, e, \epsilon)$-approximate efficiency is investigated. Necessary conditions for $(K, e, \epsilon)$-approximate efficiency of admissible controls in the form of variational inclusions are proved. Methods for solving problems of vector optimization of linear distributed systems with generalized control are proposed. Convergence of algorithms with errors is proved.

MODELING IN SYSTEMS WITH DISTRIBUTED PARAMETERS TAKING INTO ACCOUNT DISSIPATION

A method for modeling systems with distributed parameters, taking into account dissipation, is presented. For the modeling, we used the method of replacing the direct calculations of resonant frequencies by interpolating the values. Models are developed in MATLAB in Simulink. LAFC was obtained and compared with the time characteristic obtained in models without dissipation and taking into account dissipation at a resonant frequency.