SYNTHESIS AND RESEARCH OF A COMBINED CASCADE REGULATOR WITH ADVANCED COMPENSATION FOR CONTROLLING THE THERMAL MODE OF A CEMENT FURNACE
https://doi.org/10.33815/2313-4763.2025.2.31.041-051
Abstract
Improving energy efficiency and stabilizing product quality are critical challenges for the modern cement industry, especially with the widespread adoption of alternative fuels with highly variable characteristics. This study aims to develop and validate a combined cascade controller with feedforward compensation for controlling the sintering zone temperature of a rotary cement kiln. The proposed system integrates the advantages of a cascade structure, featuring a fast inner heat load loop and a precise outer temperature loop, with a feedforward channel that actively compensates for the main measured disturbance—the calorific value of alternative fuel.
The research is based on a dynamic model of the kiln's "fuel flow - temperature" channel, approximated as a second-order transfer function with a significant time delay. The control requirements were formalized considering technological constraints, dynamic performance, robustness, and energy efficiency. The synthesis of the combined controller involved two key steps: (1) tuning the parameters of the cascade PID controller using the modulus optimum method with subsequent detuning for robustness, resulting in parameters 𝐾𝑝=0.0032 (kg/s)/°C, 𝑇𝑖=1470 s, 𝑇𝑑=223 s, which provide stability margins of 𝜙𝑚≈52∘ and 𝐴𝑚≈8.9 dB; (2) determining the optimal feedforward compensation coefficient 𝐾𝑓𝑓𝑜𝑝𝑡=0.73 based on a variance analysis that accounts for errors in estimating the fuel's calorific value. A discrete control algorithm suitable for implementation in na industrial PLC was developed, incorporating anti-windup mechanisms and rate-of-change limits.
The effectiveness of the proposed control system (Strategy C) was evaluated through simulation in MATLAB/Simulink and compared with two baseline strategies: a single-loop PID controller (Strategy A) and a cascade PID controller without feedforward compensation (Strategy B). Stochastic disturbances in fuel calorific value were generated using a first-order autoregressive (AR1) model. Simulations covered three operational scenarios: steady-state operation, step change in alternative fuel share, and high fuel variability conditions.
The results demonstrate the superior performance of the combined feedforward-feedback strategy. In the steady-state regime, it reduced the root-mean-square deviation of temperature by 51.2% (from 24.8°C to 12.1°C) and the settling time by 34.5% (from 58 min to 38 min) compared to the basic PID controller. The overshoot was also minimized. Furthermore, the specific heat consumption decreased by 2.8%, from 3.38 MJ/kg to 3.285 MJ/kg. In the high-variability scenario (CV = 25%), the combined system showed enhanced robustness, maintaining a temperature standard deviation of 18.7°C, which is 51.4% lower than the basic controller. The economic impact was estimated, showing potential annual fuel cost savings of up to UAH 14.1 million for a kiln with a capacity of 3000 tons of clinker per day.
The study confirms that integrating feedforward compensation of measurable disturbances into a cascade control structure is a highly effective approach for enhancing control quality, dynamic response, and energy efficiency in processes with large inertia and delay, operating on fuels with unstable characteristics. The proposed methodology for controller synthesis and the obtained results are of significant practical value for designing automation systems in energy-intensive industries transitioning to circular economy models.
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