MATHEMATICAL DESCRIPTION AND OPTIMIZATION BY THE QUADRATIC QUALITY CRITERION OF AUTOMATIC CONTROL SYSTEMS USING PULSE WIDTH MODULATION OF SIGNALS

An approach to the optimization of complex digital automatic control systems (ACS) is proposed, in which the conversion of control signals into a sequence of pulses with time modulation is used. The requirements for actuators in many applications necessitate the use of such a conversion to achieve proportional regulation of the output value in accordance with the input control signal. A generalized description of digital automatic control systems of the specified type and an equivalent transformation of their discrete equations of motion, which is based on the reduction of such equations to the Hammerstein form, are proposed. Such a transformation significantly simplifies the mathematical description of digital ACSs and requires fewer resources for computational implementation. For ACSs, using pulse-width modulation of the control signal, the synthesis algorithm has been improved. A feature of the proposed approach is the inclusion in the criterion of optimality of energy costs for control in the form of a dependence on the length of control pulses. Functional dependencies are obtained that establish the form of the law of pulse polarity change and analytical description of the optimal modulation characteristic of the pulse-width converter of the control signal according to the given quadratic quality criterion and parameters of the invariable continuous part of the system.