The Fastest Response Algorithm for Thermal Plants with a Time Delay: Application in a Hybrid System Containing a PID Controller and an Automatic Tuning Unit

The article discusses matters concerned with improving the performance of automatic closed-loop control systems of thermal plants with a time delay in responding to a change in the setpoint. The improvement is achieved by applying the fastest response algorithm (FRA) according to the Pontryagin maximum principle and using linear prediction of the controlled variable. It is shown that, during operation with switching the maximum control outputs applied to a plant with a time delay, linear prediction is inefficient, and self-oscillations may occur in the system. The technical solution proposed for eliminating self-oscillations implies the use of a hybrid closed-loop control system comprising an FRA, a PID controller, and an automatic controller tuning (ACT) unit, which performs the function of determining the plant model parameters and optimizing the controller parameters. The actuator is considered as a proportional section that is used as part of the plant. The control limitations are related to the level of the control output applied to the plant. The ACT unit comprises accelerated controller tuning algorithms that use active plant identification methods based on analyzing the response to an impulse input and two cycles of the excited self-oscillations. These algorithms make it possible to determine four parameters of the second-order plant model with a time delay. The self-oscillations occurring in systems with the FRA and plants with a time delay are eliminated at the end of the transient by making a switchover to PID control. Four embodiment versions of a system with the FRA are analyzed, specifically, those with and without control output reversal and also with using the plant simulation model without a time delay that is obtained from the ACT operating in parallel with the plant. For practical embodiment of the MSRA as part of a hybrid system, it is recommended to use its version without control output reversal. Relations for calculating the controlled variable prediction coefficient in terms of the plant model parameters in a wide range are obtained. Two examples of using the hybrid system equipped with industry-grade controllers for a temperature control system are given: one with the electric heater power controlled using a pulse-width modulator and the other with a constant speed actuator.