Multi-objective meta-heuristic optimization in intelligent control: A survey on the controller tuning problem

Highlights

• Conflicting control requirements demand multi-objective meta-heuristic optimization for tuning.

• Multi-objective meta-heuristics are powerful techniques for controller tuning.

• The review covers the multi-objective metaheuristic optimization in controller tuning.

• The full steps of the controller tuning process in works published from 2001 to 2019 are reviewed.

• Possible research trends for multi-objective controller tuning are stated.

Abstract

Multi-objective optimization has been adopted in many engineering problems where a set of requirements must be met to generate successful applications. Among them, there are the tuning problems from control engineering, which are focused on the correct setting of the controller parameters to properly govern complex dynamic systems to satisfy desired behaviors such as high accuracy, efficient energy consumption, low cost, among others. These requirements are stated in a multi-objective optimization problem to find the most suitable controller parameters. Nevertheless, these parameters are tough to find because of the conflicting control performance requirements (i.e., a requirement cannot be met without harming the others). Hence, the use of techniques from computational intelligence and soft computing is necessary to solve multi-objective problems and handle the trade-offs among control performance objectives. Meta-heuristics have shown to obtain outstanding results when solving complex multi-objective problems at a reasonable computational cost. In this survey, the literature related to the use of multi-objective meta-heuristics in intelligent control focused on the controller tuning problem is reviewed and discussed.

Introduction

Dynamic systems are found in problems from many contexts such as financial [1], medical [2], mechanical [3], chemical [4], electrical [5], and social [6]. These systems are required to have desirable behaviors to generate useful applications. These behaviors are achieved by using a suitable control strategy.

The analysis of dynamic systems to design successful controllers is concerned to control engineering. Since the emergence of PID control by Elmer Sperry in 1910, there have been more concerns about tuning procedures that guarantee the best performance of the PID controller. In this, the controller parameters, which compromise the overall operation and performance of a dynamic system, must be properly set. Ziegler and Nichols introduced the first tuning rules in 1942 [7], and after that, several tuning rules have been proposed. Nevertheless, some of them have been focused on stabilizing linear systems [8], [9], and they are not suitable for nonlinear dynamic systems. Other tuning approaches involve nonlinear systems [10] and aim to obtain the control parameters that fulfill the stability conditions. However, the latter approach does not guarantee specific response characteristics. Consequently, one of the main problems in this control engineering area is controller tuning.

Controller tuning has been addressed by using different methods which can be classified as in [11]:

• Analytical methods where different tools from control theory are used to find the controller parameters by analyzing the closed-loop system stability. For instance, for linear systems [8], [9] described by their frequency response, root locus method, etc. and for nonlinear systems [10] from the Lyapunov stability analysis.

• Heuristic methods in which the controller parameters are manually chosen based on empirical knowledge of an expert designer that uses the information of the controlled variable measurements to establish proper parameter-performance relationships. Ziegler–Nichols [12] and Cohen–Coon [13] are two widely used heuristic methods.

• Optimization methods in which a mathematical programming problem that takes into account different performance criteria is stated and then solved by an optimizer to find a proper set of controller parameters. The reviewed works in this study fall into this class.

• Adaptive tuning methods obtain the controller parameters online by performing an identification together with one of the above methods.

The difficulty in tuning controllers is related to the complexity of the dynamic system to be governed [14]. In many cases, it can have structures that include highly nonlinear behaviors [15], a large number of tunable variables [16], and a large number of inputs and outputs [17]. Additionally, they can be subject to environmental or operational conditions such as uncertainties and disturbances, and several real-world limitations. These characteristics make the search harder for suitable controller parameters that achieve the desired performance.

Moreover, current applications demand meeting several performance specifications at a time, and they are usually in conflict [18]. They include but are not limited to high accuracy, efficient energy consumption, low cost, among others. The above also means that different controller parameter settings imply different satisfaction levels of the demands. Therefore, the tuning process becomes a non-trivial task.

Fortunately, the above multiple-demand controller tuning problem can be treated as a multi-objective mathematical programming one, which in turn can be handled by optimization or adaptive-optimization tuning methods. This approach allows using multi-objective optimization techniques to find a set of reliable controller configurations with different trade-offs (regarding their compliance with the tuning performance specifications). In this way, based on its preferences, the designer or decision-maker can choose the configuration alternative that best suits the demands of the application for its further implementation.

Due to the complexity of the multi-objective mathematical programming problem, also known as Multi-Objective Problem (MOP) in the controller tuning task, the use of computational intelligence or soft computing techniques must be necessary [19]. The use of these techniques in control engineering (in the context of multi-objective optimization and beyond) is defined by Ruano [20] as intelligent control. It conforms to a growing area of interest for research.

Among intelligent techniques, meta-heuristic optimizers have been widely used to solve many real-world optimization problems, as observed in [21], [22], [23]. This popularity is due to their parallelizable and relatively simple operation, their capability of handling very complex problems at a reasonable computational cost, and their applicability to a wide variety of contexts [24]. The above makes meta-heuristics suitable alternatives to handle the controller tuning problem.

In [25] and [26], the tuning approaches adopted for several control problems are analyzed with a particular focus on the optimization problem formulations, the used controller structures, and the controlled dynamic systems. In all cases, meta-heuristics have had outstanding advantages in controller tuning. The variety of available dynamic systems and controller structures entail to an extensive range of different tuning Multi-Objective Problem (MOP)s whose characteristics require the use of different types of meta-heuristics with particular search mechanisms to find the most suitable controller configurations. Hence, unlike the reported in [25] and [26], the present work is concerned to the review of full steps of the controller tuning process, from abstraction to validation, analyzing the addressed dynamic systems and controller structures, paying particular attention in the formulation of the related multi-objective optimization problems, emphasizing the adopted multi-objective meta-heuristic techniques and their search mechanisms, and observing the used decision-making approaches. The present work studies research items published from 2001 to 2019.

It is important to mention that several works in the specialized literature adopt an a priori preference articulation approach. In this way, a single-objective is constructed as a composition of the objectives in the MOP by establishing the importance of each objective based on higher-level preference information [27], [28], [29], [30], [31], [32], [33], [34], [35]. Then, a single-objective optimizer can be used to solve the new problem and obtain a single preferred controller parameter configuration. These works are out of the scope of the present survey.

The rest of this document is organized as follows. Sections 2 Multi-objective optimization — an overview, 3 The controller tuning problem give a background about multi-objective optimization through meta-heuristic techniques and multi-objective controller tuning, respectively. The general controller tuning process is described in Section 4 with the support of the surveyed research items. The conclusions and future directions derived from this survey are drawn in Section 5.