Integral Of The Time Weighted Absolute Error Research Articles

PID auto-tuning using new model reduction method and explicit PID tuning rule for a fractional order plus time delay model

In this paper, a new model reduction method and an explicit PID tuning rule for the purpose of PID auto-tuning on the basis of a fractional order plus time delay model are proposed. The model reduction method directly fits the fractional order plus time delay model to frequency response data by solving a simple single-variable optimization problem. In addition, the optimal tuning parameters of the PID controller are obtained by solving the Integral of the Time weighted Absolute Error (ITAE) minimization problem and then, the proposed PID tuning rule in the form of an explicit formula is developed by fitting the parameters of the formula to the obtained optimal tuning parameters. The proposed tuning method provides almost the same performance as the optimal tuning parameters. Simulation study confirms that the auto-tuning strategy based on the proposed model reduction method and the PID tuning rule can successfully incorporate various types of process dynamics.

Design and tuning of feedback controllers: effects on proteins ultrafiltration process modeled by a hybrid system

The focus of the paper was the description of a feedback control system that, based on the predictions of a previously formulated hybrid neural model, allowed improving the performance of proteins UF, carried out in pulsating conditions. The behavior of three classical feedback controllers, i.e., proportional (P), proportional integral (PI) and proportional-integral-derivative (PID), were compared and analyzed in different situations. The characteristic equation defining each type of controller was added to the already developed hybrid model in order to obtain the true closed-loop responses, thus allowing achieving a proper design and an accurate tuning of the controllers. It was observed that when no control action occurred, the permeate flux tended to progressively decay and that a proportional control was capable to reduce this decay only to a limited extent. The differences between the actual permeate flux and the desired set-point tended, instead, to nil when a properly tuned PI or PID controller was utilized. The selection of the best values for the adjustable parameters of the controller was eventually attained by a time-integral performance criterion, i.e., the minimization of the integral of the time-weighted absolute error (ITAE), using, as a starting point, the values provided by the application of the Ziegler-Nichols tuning method.

Saving energy using fuzzy control applied to a chiller: an experimental study

In this study the energy consumption of a chiller system, under different configurations and control strategies, was investigated. Two control strategies (Proportional integral—PI and fuzzy-PI) were applied to regulate the temperature of propylene glycol solution and the evaporating temperature using compressor motor supply frequency and pump rotation frequency as manipulated variables. The experiments were initiated with the system in open loop. When the steady-state condition was reached the system was submitted to a positive disturbance in its heat load and the feedback control was activated. Hence, the results were analyzed by means of integral of the time-weighted absolute error (ITAE) criterion and total energy consumption. The analysis of experimental results showed that both controllers were able to regulate the controlled variables appropriately. Also, it was verified that the use of the compressor motor supply frequency as manipulated variable can smooth out process variable oscillations. Besides, comparing the energy demands of both controllers, it was observed that the fuzzy-PI controller required 3.4% less electric energy (0.81 kWh). Considering the propylene glycol solution temperature (secondary fluid) as controlled variable and compressor motor supply frequency as manipulated variable, fuzzy-PI control achieves smaller ITAE index value, and energy consumption than the PI counterpart, consuming 0.25 kWh less energy. Thus, energy savings could be attained for control configurations that exhibit higher ITAE values. It was demonstrated that is desirable to include the energy consumption as a control performance parameter in order to increase the energetic efficiency of process.