Performance Assessment of FO-PID Temperature Control System Using a Fractional Order LQG Benchmark

Rongxuan Li,Hongbo Zou,Feng Wu,Pingzhi Hou

doi:10.1109/access.2020.3004701

Rongxuan Li, Hongbo Zou + Show 2 more

Open Access

https://doi.org/10.1109/access.2020.3004701

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Abstract

In this paper, a fractional order LQG benchmark is proposed for the control performance assessment of fractional order control systems. Similar to the conventional LQG benchmark, the fractional order LQG performance benchmark curve is determined by the numerical calculation method, which avoids the calculation of the complex interaction matrix. The fractional order process model is discretized via fractional order calculus. Meanwhile, the fractional order integral is introduced into the conventional LQG cost function. Then solving the linear quadratic Gaussian problem under the fractional order model and fractional control, the optimal input and output variances are determined for different weighting factors and the performance curves can be achieved. The comparison between fractional order LQG and the conventional LQG shows the improvement of the proposed benchmark under the same condition. The proposed benchmark can provide a more direct and superior reference standard to evaluate the performance of fractional order control system. Finally, a case study of fractional order PID(FO-PID) controller in industrial heating furnace temperature control experiment with model matching and model mismatch conditions is used to verify the effectiveness of the proposed benchmark.

Highlights

The research on control performance assessment of control loops can be traced back to 1970
We can intuitively find that input variance and output variance can be reduced to a certain extent by adjusting fractional order PID parameters in the case of model matching and model mismatch, so that the performance point is close to FO-linear quadratic Gaussian (LQG) performance tradeoff curve, this indicates that the control performance of the controller has been greatly improved after parameter adjustment as expected
In this paper, A fractional order LQG benchmark is developed for the performance assessment on fractional order systems

Summary

INTRODUCTION

The research on control performance assessment of control loops can be traced back to 1970. In 2019, an improved entropy benchmark for performance assessment of common cascade control system was proposed by Zhang et al [24], which combined entropy with output mean value and deal with the inconsistency of the minimum variance benchmark in evaluating non-Gaussian disturbance systems. The corresponding optimal achievable performance is calculated for all processes belonging to the fractional model sets controlled by PID-type controller This method is based on classical minimum variance theory that maximum performance is strongly influenced by the process normalized dead time and only used for evaluating the process controller with fixed structure. On the basis of conventional LQG benchmark(based on the integer order model), we can consider an novel LQG benchmark that based on fractional order process model and fractional order control to achieve the performance assessment problem under fractional order systems with fractional order controller. The performance of FO-PID has studied under the model matching and the model mismatch

FRACTIONAL ORDER CALCULUS

SIMULATION CASE

FRACTIONAL ORDER LQG TRADEOFF CURVE

CONCLUSION