## 6 Conclusions  
The design of Proportional, Integral, and Derivative controllers (PID) using a technique based on the particle swarm optimization algorithm is presented in this work. Classical PID tuning rules are dependent of the system dynamics and PID controller structure. Moreover, the PID settings in most methods differ according to the specific control design objective (e.g., set-point tracking or load disturbance rejection). The proposed PSO-based PID controller optimization technique holds the following characteristics which are of great practical interest: (a) To be easily implemented in digital industrial computers/microcontrollers; (b) to cope simultaneously with several control design criteria; (c) can be applied to control systems independently of system dynamics; and (d) rely in a reduced number of heuristic parameters, which can be easily adjusted for control purposes.  
The merits of the proposed design technique lie within:  
* The use of an additive compromise cost function involving the minimization of two performance criteria: The Integral Absolute Error (IAE) and the Total Variation (TV). By using a simple compromise cost function, the proposed PID controller design technique simultaneously considers the following major control design criteria: Set-point tracking, load disturbance rejection, and control signal variation.
* By using the proposed cost function, it was shown that it is quite simple to select the PSO heuristic parameters with a special emphasis on the inertia weight decay.  
Figure 17: TCLab responses overlapping the responses for Cohen-Coon (CC), AMIGO, and PSO, case IV (J = IAE + 100 TV).  
Figure 18: TCLab responses using PSO (J = IAE + 60 TV). Output disturbance considered at t \(\cong\) 600 s.  
* The PSO was used to both perform the TCLab system identification as well as PID controller tuning. In both optimization problems, the proposed technique blends quite well with classical design techniques. One of the problems with the use of optimization algorithms in practical problems is to define appropriate decision variable search intervals. The identification of a first-order plus time delay model with the PSO technique uses the two-point step response method [39; 40] to define the model parameter search space. The Cohen-Coon PID controller tuning rules were used to define the controller gain search space.
* The PSO results for the specific TCLab control case performs as well as a much more recently introduced metaheuristic: The grey wolf optimization.
* The proposed technique was tested with an Arduino Temperature Control Laboratory (TCLab) and compared with well-established PID tuning methods. Both the simulation as well as physical TCLab results were presented to provide evidence of improved control performance. The results show a good agreement between the simulation and measured results to validate the dynamic model identified with PSO.
* The TCLab Arduino kit was introduced as a simple to use portable laboratory to test simulation results obtained with the proposed PSO-based technique. The same device has great potential to test other optimization and artificial intelligence-based techniques.  
[PERSON] was involved in the proposed technique conceptualization, validation, TCLab software, and physical experiments; [PERSON] was involved in the TCLab Arduino kit experiment methodology, software, and prosed technique results analysis; [PERSON] was involved in the proposed technique validation. All authors were involved in the writing of the original draft preparation, review, and editing. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.