A fractional order PID controller using MACOA for indoor temperature in air-conditioning room

https://doi.org/10.1016/j.jobe.2021.103295Get rights and content

Highlights

  • A hybrid control scheme for indoor temperature of an air-conditioning room is designed.

  • Reconstructing a modified ant colony optimization algorithm upgrades control quality.

  • Control performance of the proposed algorithm is superior to that of the other ones.

  • Simulation results may offer the reference guides for regulating the other parameters.

Abstract

Aiming at controlling indoor temperature of each air-conditioning room equipped with fan coil unit (FCU), this paper proposes a hybrid control system to deal with such problem, in which a fractional order PID controller for indoor temperature (IT-FOPIDC) and a three-position controller for supply air volume (SAV-TPC) are used to maintain steady indoor temperature, respectively. For the key problem of tuning parameters of IT-FOPIDC, a modified ant colony optimization algorithm (MACOA) is reconstructed, and it is tested to be feasible by the simulation results. Thus, an algorithm using this MACOA is designed to adaptively solve the satisfied values of five parameters of IT-FOPIDC to further upgrade the control quality of indoor temperature from software. In the meanwhile, SAV-TPC manipulates the corresponding flow rate of supply air discharged from FCU to provide the dynamic variation of cooling or heating load to an air-conditioning room. So these two controllers work together for achieving the desired indoor temperature. The corresponding numerical simulation of this hybrid control system is carried out and the results indicate that this algorithm using MACOA is reliable to tackle the key problem of tuning parameters of IT-FOPIDC so that the control quality of indoor temperature is obviously improved. Moreover, for the same IT-FOPIDC, the control performance of the other intelligent optimization algorithms is compared to that of the proposed algorithm using MACOA under the same scenario, simulation results also show the latter is superior to the former in terms of analyzing the dynamic responses of indoor temperature, which may offer the corresponding reference guides for regulating the key performance parameters in HVAC& R engineering.

Introduction

The increasing development of air-conditioning technology can offer more comfortable indoor environment so that the living quality, the efficiency of work and study and the effects of indoor activities associated with different people are improved to great degree [[1], [2], [3], [4]]. At present, because of their characteristics of compact size, easy installation, convenient operation and decentralized control, etc, FCUs that respectively offer cooling and heating load in summer and winter are widely used in these types of rooms like office, classroom and conference room in order to achieve the desired indoor temperature [[5], [6], [7], [8]]. The major components in an FCU are cooling\heating coil, circulating fan, the rectangular outlet for SA, the rectangular inlet with the filter for return air RA, and condensate water pan. The air-conditioning technical requirements of indoor temperature and relative humidity are guaranteed by the corresponding process of heat and moisture exchange between IA and SA sent from circulating fan [9,10], so FCU is thermal device in essence, its characteristic is described by the thermodynamic model [10]. For operating an FCU installed in an air-conditioning room safely and efficiently, the corresponding control scheme plays a fairly important role besides considering its own features. In the view of the control theory, FCU can be described by a first-order transfer function with gain and time constant through simplifying the related conditions and assumptions [11]. Like many industrial controlled plants or processes, an air-conditioning room equipped with FCU called the general controlled plant that has the dynamics characteristics with large time-delay, large inertia and non-linearity. Although traditional PID control method is widely used because it is simple, effective, better robust, and easily implemented, when the traditional PID controller, also known as integer order PID (IOPID) one, is applied to such controlled plant, the corresponding control indices of indoor temperature such as steady state error, overshoot, regulating time, etc. are generally undesirable [[12], [13], [14]].

Podlubny firstly [15] proposes fractional order PID (FOPID) controller, also known as PIλDμ one, which is a generalization of the conventional PID controller based on the theory of fractional order calculus. FOPID controllers have been demonstrated to provide more better control performance than IOPID ones in different kinds of industrial parameter control processes or plants [[15], [16], [17], [18]]. The main reason is that introducing an integrator of fractional order λ and a differentiator of fractional order μ can offer extra degrees of freedom for designing an FOPID controller. For a controlled plant or process with the time-varying structural parameters and non-linearity, an FOPID controller is more adaptive by adjusting the values of Kp, Ki and Kd, as well as λ and μ. That is to say, the dynamic response and robustness of a close-loop negative feedback control system adopting PIλDμ controller can be obviously improved. For example, Zeng et al. [17] present a novel FOPID controller design method for an automatic regulator voltage (AVR) system and design an improved multi-objective extremal optimization algorithm (IMOEOA) to tune parameters of the proposed FOPID controller. Extensive experimental results on an AVR system have shown that the proposed FOPID controller whose parameters tuned by IMOEOA provides better or at least competitive performance than non-dominated sorting genetic algorithm II-based FOPID and single-objective genetic algorithm-based FOPID controllers in terms of accuracy and robustness. An adaptively fast fuzzy fractional order PID controller (AFFFOPIDC) is proposed for pumped storage hydro unit (PSHU) with the reversible properties [19], and an improved gravitational search algorithm (IGSA) is designed for the optimized parameters selection of AFFFOPIDC. Simulation tests under different running conditions are utilized to demonstrate the feasibility and robustness of this AFFFOPIDC in comparison with other controllers, this AFFFOPIDC using IGSA outperforms the others in most cases. Yang et al. [20] design an adaptive fractional-order sliding-mode control (AFOSMC) approach for superconducting magnetic energy storage system (SMESS) in order to improve its dynamical responses against various operation conditions. Compared the control performance of conventional PID control, interconnection and damping assignment passivity-based control, sliding-mode control, and fractional-order sliding-mode control to that of AFOSMC under three scenarios, simulation results indicate that AFOSMC can greatly outperform the other control approaches in both tracking speed and overall costs on the performance of an SMESS. In Ref. [18]; a novel hybrid controller including an FOPIDC and a tilt-integral-derivative controller (TIDC) is proposed for providing better dynamic responses in interconnected multi-area power systems. By applying the Sine-Cosine algorithm (SCA) to the proposed hybrid controller, the optimized parameters of this hybrid controller are obtained and better dynamic responses are confirmed by the corresponding simulation results. Also, better coordination between FOPIDC and TIDC is obtained in comparison to the other coordinated controllers such as PID-based, TID-based, and FOPID-based ones. Belkhier et al. [21] introduce a new adaptive fractional order PID controller to design the desired dynamics of permanent magnet synchronous generators (PMSGs). This FOPIDC is tested under parameter variations and it is compared to a benchmark nonlinear control method such as sliding mode. Simulation results demonstrate clearly that the proposed FOPID control system can provide control performance improvement (low tracing errors, fast convergence response, and strong robustness) of a PMSG over the sliding mode. These results show that the control quality associated with FOPID controllers can be upgraded to a great degree. As a consequence, the research of different kinds of FOPID controllers and how to tuning the corresponding parameters has gained increasing attentions by the academic and industrial community [17,19,[22], [23], [24]], and the key problem focuses on designing the algorithms to solve the optimal values of PIλDμ controller parameters accurately and conveniently in order to adapt the time-varying structural parameters of the controlled plant in practice.

With development of evolutionary algorithms and swarm intelligent algorithms that are two typical representatives of intelligent algorithms in the past decades, both evolutionary algorithms-based methods [1,19,25] and swarm intelligent algorithms-based ones [[26], [27], [28]] are widely used to cope with the optimization problems in theoretical research, practical engineering, as well as control theories and fields because of their common features and functions such as high efficiency, parallel processing, implementing easily, etc [17]. More specifically, swarm intelligent algorithms, such as PSOA [28,29], ACOA [26,27,30], and artificial bee colony optimization algorithm [17], have been utilized for the design of different types of controllers, especially IOPID or FOPID ones. Among them, inspired by the ants’ foraging behavior, ACOA is developed and is formalized by the related scholars [30]. ACOA is a potential heuristic bionic swarm intelligent algorithm, and its application fields have been rapidly expanded due to the characteristics of positive feedback, parallelism, and robustness [26,27,29]. For example, the desired results of optimizing the solutions of the complicated problems or control schemes are conveniently obtained by ACOA. However, BACOA also has its shortages of weak diversity and the premature convergence in solving the optimal solutions for a specific problem [17,26,27,29].

From the above mention, FCUs are widely installed in different types of separate rooms due to their special characteristics [[9], [10], [11]]. Especially for an ACS-FCU, indoor temperature can characterize its operation performance and provide the comfortable degree to people in those rooms, and its practical effect is mainly depended on the corresponding control mode or system. However, PID control mode, one typical representative of some traditional control ones, usually results in the undesirable effect of indoor temperature [12,14]. Thus, considering air-conditioning technology, FOPID theory and BACOA thoroughly, this paper presents an indoor temperature hybrid control design scheme for an air-conditioning room equipped with FCU, namely IT-FOPIDC for controlling indoor temperature and SAV-TPC for regulating the flow rate of supply air. In our strategy, on the basis of dividing the error between the measured value and the setting value of indoor temperature into three ranges, a SAV-TPC is used to regulate the speed of fan in FCU, and then the flow rate of SA discharged from FCU is dynamically variational in order to adapt the dynamic requirements of indoor air-conditioning cooling or heating load caused by solar radiation heat, heat transfer from indoor-outdoor temperature difference, heat dissipation of human body and electrical equipments, and so on. An IT-FOPIDC is adopted to keep indoor temperature steady and overcome the main disturbance to indoor temperature, whose parameters are composed of [Kp, Ki,Kd, λ, μ]. As stated above, it is known that how to continuously tune five parameters of IT-FOPIDC is closely related to the quality of this indoor temperature hybrid control system [[17], [18], [19]]. To obviously reduce the corresponding time-consuming to tune five parameters of IT-FOPIDC and to make full use of the advantages of easy execution, extensive adaptability, and strong parallel processing, based on the framework of BACOA [30], so an MACOA is reconstructed by decreasing the pheromone evaporation factor of BACOA exponentially during the corresponding iteration. The feasibility of this MACOA is verified through an example of the classical Rastrigin function and its performance of convergence and diversity is superior to that of BACOA. Accordingly, an algorithm using MACOA is developed for tackling such problem of tuning parameters of IT-FOPIDC. Thus, IT-FOPIDC and SAV-TPC work together for achieving the desired indoor temperature of an air-conditioning room equipped with FCU. By means of Matlab software tool, the simulation model of a hybrid control system including IT-FOPIDC and SAV-TPC for indoor temperature is configured and the proposed algorithm using MACOA for tuning five parameters of IT-FOPIDC is programmed as an independent producer named Tuning parameters.m. The simulation model and the proposed algorithm are implemented simultaneously until the control indexes of the desired indoor temperature are satisfied. The simulation results indicate that control performance of this hybrid control system for indoor temperature are met with the comfortable air-conditioning design criteria besides the optimal values of [Kp, Ki,Kd, λ, μ] are effectively found. To further verify the effectiveness of this MACOA and the proposed algorithm using MACOA, other intelligent algorithms such as DEA [25], PSOA [28] and GA [1,17] are applied to the classical Rastrigin function and the same IT-FOPIDC, respectively, the corresponding results show that both the best solution of Rastrigin function solved by this MACOA and the control effect hosted by IT-FOPIDC whose parameters tuned by the proposed algorithm using MACOA are superior to those obtained and tuned by PSOA, DEA and GA, respectively. All these results may offer the corresponding reference guides for regulating the key performance parameters in the problems belonged to an interdisciplinary associated with HVAC& R engineering and control theory and applications.

The paper is organized as follows. Section 2 briefly reviews some necessary knowledge of fractional order calculus, FOPID controller and air-conditioning system adopting FCUs. In addition, an indoor temperature hybrid control system including IT-FOPIDC and SAV-TPC is developed in the same section. An MACOA is reconstructed and its effectiveness is verified in Section 3. Accordingly, an algorithm using MACOA is designed to deal with the problem of tuning parameters of IT-FOPIDC. The simulations to demonstrate this indoor temperature hybrid control system and to slove the optimal values of five parameters of IT-FOPIDC are carried out in Section 4. Conclusion is provided in Section 5.

Section snippets

Fractional order calculus and fractional order PID controller

There are several definitions of fractional differ-integral in the existing literature [15], Riemann − Liouville (RL) is one of the most commonly used definition, which is given as the following form:Datαf(t)=1Γ(nα)dndtnαtf(τ)(tτ)αn+1dτ,n1<α<nwhere Γ(⋅) is the Euler's gamma function. The Laplace transform of the RL fractional derivative/integral (2) under zero initial conditions for order α (0 < α < 1) is expressed as follows:αteastDtαf(t)dt=e±αF(s)

From the perspective of time domains,

A modified ant colony optimization algorithm

On the basis of the cooperative behavior of real ant colonies, ant colony system and ant colony algorithms are set up to find the shortest paths from a food source to their nest [30]. Each ant deposits a chemical substance called pheromone on the ground while walking. Ants tend to choose these paths marked by strong pheromone concentrations in a probabilistic way. Since ants visit the shortest paths more frequently and pheromone on them can accumulate so rapidly, which in turn causes more ants

Experimental results

On the basis of the proposed hybrid system including IT-FOPIDC and SAV-TPC shown in Fig. 3, the corresponding simulation model are properly configured in Matlab Simulink environment, depicted in Fig. 9.

In the following simulation, the related parameters’ values of transfer functions of actuator to regulate the flow rate of chilled and hot water flowing through cooling\heating coil in FCU and the controlled plant of air-conditioning room equipped with FCU are set as K1 = 1, L1 = 1, K2 = 8, L2

Conclusion

Aiming at manipulating indoor temperature of an air-conditioning room equipped with FCU, a practical problem of an interdisciplinary associated with HVAC& R engineering and control theory and applications, this research presents a hybrid control system including IT-FOPIDC and SAV-TPC for dealing with it. Besides reconstructing an MACOA to improve the corresponding convergence and diversity of BACOA, an algorithm using this MACOA and Min ITAE is designed to tackle the key problem of tuning

Credit roles statement

  • Shaoyong Li, the corresponding author, is responsible for ensuring that the descriptions are accurate and agreed by all authors.

  • Shaoyong Li: Conceptualization, Methodology, Formal analysis, Validation, Writing Original Draft, Supervision.

  • Mingsong Wei: Writing Review and Editing.

  • Yeru Wei: Software.

  • Zongli Wu: Investigation.

  • Xilian Han: Data Curation.

  • Rongxia Yang: Project administration.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC, grants no. 61364004), Chinese Scholars to Study Overseas sponsored by China Scholarship Council Foundation (grant no. 201408625045), the Doctoral Research funds of Lanzhou University of Technology (grant no. 04-237), and Alumni Foundation Civil Engineering 77, Lanzhou University of Technology (grant no. TM-QK 1301). The authors would also like to thank the editor and anonymous reviewers whose comments and

References (30)

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