Novel metaheuristic-based tuning of PID controllers for seismic structures and verification of robustness

Highlights

• Seismic structures with active tendons are investigated.

• Novel optimum tuning methods for controllers are proposed.

• Metaheuristics such as FPA, TLBO and JA are employed.

• PID type controllers are used.

Abstract

In the present study, an active structural control using metaheuristic tuned Proportional-Integral-Derivative (PID) type controllers is presented. The aim of the study is to propose a feasible active control application considering time delay and a feasible control force. In the optimum control methodology, near-fault directivity pulse was considered for ground motion. Three different metaheuristic algorithms are separately employed in the optimum tuning of PID parameters such as proportional gain, integral time and derivative time. The employed algorithms are Flower Pollination Algorithm, Teaching Learning Based Optimization and Jaya algorithm. The maximum control force limit is considered as a design constraint. The methodology contains the time delay consideration and a process to avoid the stability problem on the trial results during the optimization process. The method is explained in three stages as The Pre-Optimization Stage, The Dynamic Analysis Stage and The Optimization Stage. The optimum PID parameters of different algorithms are very different, but the performance of active control is similar since a similar control signal can be generated by different proportion of controller gains such as proportion, integral and derivative processes. As the conclusion of the study, the amount of control force must be chosen carefully since big control forces may resulted with stability problems if the control system has long delay.

Introduction

During strong ground motions, civil structures may suffer unsteady vibrations. These vibrations may be harmful in several ways. For example, internal forces resulting from the magnification of acceleration via earthquake may pass the safety limits for fracture protection of sections. Although vibrating civil structures are even built to carry these internal forces, vibrations may prevent the safety usage of the structure by disturbing individuals and process of machineries. For that reason, structural control methods have been developed for civil structures.

The active control methods including a source like a linear motor driven by a control algorithm can be also used in civil structures. Using active control to absorb vibrations of a device may be quite easy, but it may be problematic for huge mechanical systems without sensitively precise behavior because of several uncertainties. In that case, stability problem of active controlled structures must be handled by the prefect tuning of controller algorithm. For the uncertainties, several factors must be considered during optimum tuning and sensibility of optimum values must be validated. In the present study, the factors such as time delay and control force limitation are the main subject of the proposed method and then, the robustness of the proposed method is verified to show the feasibility of the active control approach that is effective on different ground accelerations.

The main idea of active control is to provide forces which are opposite to additional inertia force resulting from earthquakes by sensing and processing of structural responses with a controller. The control force on the structure can be generated according to several methods. Using active tendons that are crosswise pre-stress cable systems with changeable stress by a linear actuator driven by a controller have been proposed in several studies for structures. The additional control force has been also provided by active tuned mass dampers (ATMDs) [[1], [2], [3], [4], [5], [6], [7]]. For these systems, the control force has been generated by sensing structural responses and processing with the help of a control algorithm including H₂, H_inf, linear quadratic regulator (LQR), neural network control fuzzy logic control, sliding mode control (SMC) and Proportional–Integral–Derivative (PID) type controllers [[8], [9], [10]].

The oldest active structural control approaches have been proposed in 80s [[3], [4], [5], [6]]. Yang and Samali proposed active control for high structures suffering from wind excitations to reduce peak value of acceleration of structures [3]. In past studies, high buildings were also idealized as a cantilever beam for active control [4]. Experimental studies have also been provided for active control by considering the time delay factor of the control signal [6,7]. The classical control algorithms have been modified by the time. For non-linear structures, artificial neural networks have been utilized in the control algorithm [11]. A filtered sliding mode control (SMC) approach is proposed for active controlled structures to be more robust [12]. Aldemir and Bakioğlu developed a modified LQR for sub-optimal control of seismic structures [13]. SMC was combined with fuzzy logic theory to prevent the shattering effect of classical SMC for active control of structures [14]. The comparison SMC with PID [15] and PD/PID with LQR [16] in controlled structures were also discussed. Wavelet-based adaptive pole assignment method for structural control outperformed the LQR in minimization of time delay and maximizing resistance of structure [17]. A method called equivalent-input-disturbance for active control was developed by Miyamoto et al. [18]. For active control of three-dimensional structure with geometrical and material non-linearity, neuro-genetic algorithm, which is the combination of dynamic fuzzy wavelet neuroemulator and the floating point genetic algorithm, was proposed by Adeli and Jiang [19]. The efficiency of a hybrid LQR-PID controller for seismic structures equipped with ATMD was investigated by Heidari et al. [20]. The parametric uncertainties and time delay effects was considered by a proposed control method called neural based SMC with moving sliding surface [21]. Active tendon control systems for irregular structures considering soil-structure interaction effects have been proposed by using H_inf direct output feedback control algorithm [22] and LQR algorithm [23].

Nigdeli and Boduroğlu proposed PID controlled active structural control methodology to protect irregular structures from impulsive motions seen in near-fault ground motions [2]. As known, near fault ground motions cause two types of impulsive motions, namely flint step and directivity effects and the significant characteristic of impulsive motions are permanent displacement, high peak ground acceleration and velocity [24]. In FEMA P-695: Quantification of Building Seismic Performance Factors [25], historical near-fault ground motions were presented with and without pulses of directivity effect. The impulsive motion pulse models have been proposed by several studies [[26], [27], [28], [29]]. Also, several formulations to find the long period and peak velocity values of these pulses were proposed according to magnitude and soil condition of site according to regression analysis of historically recorded ground motions [30,31].

In order to avoid stability problems of active control systems by considering factors such as time-delay and feasibility of control force, a sensitive tuning of control algorithm must be done. In that case, the optimization of controller parameters is needed. The nature inspired metaheuristic methods are suitable to optimize structural control systems. In passive control of structures, several metaheuristic algorithms and machine learning techniques have been employed to find the optimum parameters of passive tuned mass dampers (TMDs) [[32], [33], [34], [35], [36], [37], [38]]. In active control of structures, the metaheuristic-based methods such as genetic Algorithm and bat algorithm, bees algorithm, differential evolution, firefly algorithm, harmony search and imperialist competitive algorithm have been employed [[39], [40], [41], [42]]. Also, Cuckoo Search algorithm [43] and Gases Brownian motion algorithm [44] were employed for PID controlled seismic structures.

In the present paper, a metaheuristic tuned PID controller is proposed for seismic structures. The optimization methodology is presented and the objective of the optimization is to minimize first story displacement under a directivity pulse to consider the efficiency of method for near-fault earthquakes. The design variables of the methodology are the parameters of PID controller, which are the coefficients of the gains of proportion, integral and derivative process. The methodology was investigated for three different metaheuristic algorithms; namely Flower Pollination algorithm (FPA) [45], Teaching Learning Based Optimization (TLBO) [46] and Jaya algorithm (JA) [47]. In the method, a time delay of the control signal is considered, and control force limit is used as a design constraint. Finally, the methodology was tested on a 10-story case structure to investigate the robustness of the active control proposal. Different cases of time delay and control force limits were considered in the structural responses under several near-fault earthquake records with pulses. Also, different time delay values than the considered ones in the optimization were investigated to validate the system performance.