A New Control Performance Evaluation Based on LQG Benchmark for the Heating Furnace Temperature Control System

Abstract

Temperature control systems are a series of processes with large time-delay and non-linear characteristics. Research shows that using fractional-order modeling and corresponding control strategies can better control these processes. At the same time, the existing studies for control performance assessment are almost committed to the integer order control systems, and the methods used in few literatures on performance assessment of fractional order systems are also one-sided. This paper applies the linear quadratic Gaussian (LQG) evaluation benchmark to the performance evaluation of fractional-order control systems for the first time, starting with the LQG evaluation benchmark considering the input and output performance. The LQG benchmark can be obtained by the analytical algorithm, which simplifies the complexity of LQG solution. Finally, taking the application of the fractional predictive function control (FO-PFC) controller in the experiment of industrial heating furnace temperature control as an example, the effectiveness of the LQG benchmark is verified.

Logic adaptive optimization model for dynamic temperature compensation of heating furnace based on proportion‐integral‐derivative position algorithm

“…When there is only proportional control in the temperature control system, there is still some error in the output characteristics of the temperature control system. Its transfer function is: the multi‐mode control output of differential and integral of the mixed gas pressure deviation of the gas heating furnace is defined as [15] $$$$\begin{equation}_a^RD_t^ve\left( x \right) = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\dfrac{{{d}^ne\left( x \right)}}{{d_x^n}}}\\[15pt] {\dfrac{{{d}^n}}{{d_x^n}}\dfrac{1}{{\Gamma (n - v)}}\displaystyle\int_{a}^{t}{{\dfrac{{e\left( x \right)}}{{{{(x - y)}}^{v - n + 1}}}dy}}} \end{array} } \right.\end{equation}$$$$…”

On the Linear–Quadratic–Gaussian Control Strategy for Fractional-Order Systems

“…As an alternative approach, the well-known method designed for discrete-time fractional-order systems based on the Grünwald-Letnikov difference is presented in [33,34]. Furthermore, the fractional-order Linear-Quadratic-Gaussian controller is investigated in terms of control performance assessment in [35,36]. However, the LQG scheme acts as a benchmark of other control algorithms' quality in this context.…”