Optimal Identification and Metaheuristic PID Control of a Two-Tank System

Dan Stefanoiu,Janetta Culita

doi:10.3390/electronics10091101

Abstract

In the modern optimization context, this paper introduces an optimal PID-based control strategy for a two-tank installation, namely ASTANK2. The process model was identified by using raw and spline smoothed measured data, respectively. Two PID controller configurations, a standard (regular) one (PID-R) and a non-standard one (PID-N), were considered for each type of model, resulting in four regulators. The optimal tuning parameters of each regulator were obtained by a searching approach relying on a combination of two metaheuristics. Firstly, an improved version of the Hill Climbing algorithm was employed to comprehensively explore the searching space, aiming to find fairly accurate tuning parameters. Secondly, an improved version of the Firefly Algorithm was proposed to intensively refine the search around the previously found optimal parameters. A comparative analysis between the four controllers was achieved in terms of performance and robustness. The simulation results showed that all optimal controllers yielded good performance in the presence of exogenous stochastic noise (bounded error tracking, setpoint tracking, reduced overshoot, short settling time). Robustness analysis is extensive and illustrates that the PID-R controllers are more robust to model uncertainties, whilst PID-N controllers are more robust to tracking staircase type references.

Highlights

There is a variety of complex control strategies, in control engineering practice, the Proportional–Integral–Derivative (PID) control structures are the most widely used, owing to their simple structure, good stability [3], high reliability, reasonable closed loop performance and robustness [4,5,6].The key problem in designing a PID controller ensuring these features is to tune the parameters accurately and efficiently
Before running Advanced Hill Climbing Algorithm (AHCA) and IFA, the PID-R regulators were tuned by means of the well-known Ziegler–Nichols empirical method [7]
The resulting parameters of PID-R controllers are listed in Table 3

Summary

Introduction

The key problem in designing a PID controller ensuring these features is to tune the parameters accurately and efficiently. This is a challenging task when dealing with industrial processes that usually are modelled as multi-variable systems, with nonlinear dynamics and a large number of tunable variables [5]. The PID tuning methods evolved from empirical (Ziegler–Nichols [7,8], Cohen–Coon) and analytical (internal model, pole placement, gain-phase margin [9]) to adaptive and optimization-based [5]. Unlike the empirical and analytical methods that provide weak or only satisfying performance, the optimization techniques applied to PID tuning yield good performance (disturbance rejection, set-point tracking) and robustness [4,10,11]. In recent decades, the problem of designing an optimal PID controller that drives the systems into a desired behavior has increasingly captured the interest of the automatic control community

Objectives

Methods

Results

Conclusion