Criteria of optimal control and LQR-optimization of the electric drive

The article presents the analysis of quality control criteria systems of electromechanical objects. The synthesis of control systems is performed in temporal, frequency domains and in state space. In the first case are the main criteria of minimum energy consumption for control and maximum performance. For their a power infinitely small and infinitely large power realization are required, respectively compromise control resolves these contradictions. Particular cases of these criteria are low current, low heat losses and the integral criterion of quality of transient processes. In the frequency domain optimization problem is solved using modular criteria (MO) and symmetrical (SO) Optima. These criteria are also inconsistent optimizing transient processes on the task or perturbation. The paradox is resolved by incorporating the low-pass filter or by using the compromise criterion the optimum (CO). The main drawback of the criteria of MO, SO and CO are not subject to the internal feedback of the control object is eliminated during the synthesis of the correction device in the state space. A mathematical model of the control object is set of vector-matrix equations, and the quality functional in the form of quadratic forms unites the criteria of minimum energy consumption for control and maximum performance. As an example the synthesis of linear-quadratic regulator (LQR controller) for an electromechanical plant (TC-DC motor) specified in the state-space matrices A, B, C and D was considered. The curves of voltage, current and angular velocity were obtained. An appropriate choice of the matrices of the LQR controller proved the possibility of direct motor start without soft starter. The methods of mathematical modeling in MATLAB comparative evaluation of the considered criteria were used. The study in the space of states gives results which are the closest to the properties in industrial control systems.