Integral Of Time-weighted Absolute Error Research Articles

Performance evaluation of material and comparison of different temperature control strategies of a Guarded Hot Box U-value Test Facility

The overall energy consumption in a building could be minimized by controlling the heat gain or loss through its building components like walls, floors, roofs, window glazing etc. and for doing this, the thermal performance of the building materials should be evaluated. The U-value is one of the key measures of evaluating the thermal performance of any building material. The lesser the U-value, the less energy is required to maintain comfortable conditions inside the building. The U-value is measured using the Guarded Hot Box Test Facility. In the present work, two control strategies, one with a simple on–off and another with a Proportional-Integral-Derivative (PID) logic driven Pulse Width Modulation (PWM) technique, have been implemented, once with AC circulating fans and again with DC circulating fans inside the Guard box. Performance evaluation and comparison of them has been made in terms of three error indices viz. per unit time of Integral of Square Error (ISE); Integral of Absolute Error (IAE) and Integral of Time weighted Absolute Error (ITAE). From the experimental data obtained, it is found that the PID logic driven pulse width modulation technique with DC circulating fans installed inside the guard box shows the best temperature control profile.

Comparative Study of Fuzzy PID Control Algorithms for Enhanced Position Control in Laparoscopic Surgery Robot

This paper proposes intelligent fuzzy proportional–integral–derivative (PID) controllers for the position control of a master–slave configuration laparoscopic surgery robot system. For the slave robot controller, two fuzzy PID control algorithms are implemented: a rule-based fuzzy control algorithm for online PID gain tuning and a learning fuzzy controller to tune the rules in the rule buffer automatically online. The two fuzzy controllers are tested using sinusoidal reference motions with various periods and the test results are compared with those of a conventional PID controller in terms of position control performance. Various performance indices are used for the comparison, including root mean square error, steady-state error, integral of average error, integral squared error, integral time-weighted absolute error, and integral of time multiplied by the squared error. The evaluation shows that the learning fuzzy controller yields the best performance among the three algorithms. Furthermore, the relationship between the scaling gains and the performance can be deduced to construct a comparative tuning algorithm, which enables the scaling gains to be optimally tuned with less trial and error. Further refinement of the algorithm for enhancing control performance is under way.

Design of Fractional Order PID Controller Based Particle Swarm

Fractional order PID (FOPID) controller is a special kind of PID controller whose derivative and integral order are fractional rather than integer which has five parameters to be tuned. This paper presents study of the implementation of tuning method and performance enhancement of the closed loop system by use of the fractional order PID (PIλDμ) controller utilizing a MATLAB/Simulink. The tuning methods for these type controllers have many mixed tools of the available optimization methods and update artificial optimization methods in the design. In this paper particle swarm optimization has been implemented to design FOPID controller in which the unknown parameters are determined minimizing a given integral of time weighted absolute error (ITAE). The main specification of this paper is that the all five parameters of (PIλDμ) have been found directly without spreading the steps. It has been shown that the response and performance of the closed loop system with FOPID controller is much better than integer order PID controller for the same system and with better robustness.

Model based temperature controller development for water cooled PEM fuel cell systems

PEM (proton exchange membrane) fuel cell operation necessitates thermal management to satisfy the requirements of safe and efficient operation by keeping the temperature within a certain range independent of varying load conditions. Heat generation within the fuel cell changes according to the power delivered from the stack, requiring a dynamic control system to remove this excess heat and maintain the desired stack temperature. In this study, a closed loop water circulation strategy is considered and evaluated for cooling a 3 kW PEM fuel cell. The cooling system consists of a water circulation pump and a radiator coupled to a fan, integrated with the fuel cell stack. A first principles based model is developed for the integrated cooling system through an energy balance containing the relevant terms. A sequence of dynamic tests is performed on the cooling system to identify the parameters appearing in the model developed. The resulting semi-empirical model is used to evaluate possible control strategies managing the cooling loop. Three specific strategies are analyzed and the performances of these controllers are evaluated in terms of stack temperature, integral time weighted absolute error (ITAE) and the parasitic energy requirements. Minimizing fan usage with an on/off controller while keeping the pump voltage as a continuously manipulated variable through a feedback PI (proportional–integral) controller delivers the best results. The MATLAB-SIMULINK® platform is used in the development and implementation of the models and controllers. In our strategy, the characterization of the cooling loop is physically de-coupled from the development of the fuel cell stack – allowing for the evaluation of candidate equipment and algorithms prior to the fuel cell stack being available, which is often the case during prototype development.

Parameters tuning of model free adaptive control based on minimum entropy

Dynamic linearization based model free adaptive control (MFAC) algorithm has been widely used in practical systems, in which some parameters should be tuned before it is successfully applied to process industries. Considering the random noise existing in real processes, a parameter tuning method based on minimum entropy optimization is proposed, and the feature of entropy is used to accurately describe the system uncertainty. For cases of Gaussian stochastic noise and non-Gaussian stochastic noise, an entropy recursive optimization algorithm is derived based on approximate model or identified model. The extensive simulation results show the effectiveness of the minimum entropy optimization for the partial form dynamic linearization based MFAC. The parameters tuned by the minimum entropy optimization index shows stronger stability and more robustness than these tuned by other traditional index, such as integral of the squared error (ISE) or integral of time-weighted absolute error (ITAE), when the system stochastic noise exists.

Design of Optimal PID Controllers for Integrating Systems

The optimum tuning rules for various integrating systems with time delay in terms of the process model parameters using Differential Evolution (DE) algorithm are proposed. The objective function is integral performance index (integral time-weighted absolute error, ITAE) for both servo and regulatory problems. The performance and robustness of the proposed optimal controllers are compared with the controllers designed by recently reported methods. Simulation results on various transfer function models are given to show the efficiency of the proposed optimal controllers.

Binary-coded extremal optimization for the design of PID controllers

Design of an effective and efficient PID controller to obtain high-quality performances such as high stability and satisfied transient response is of great theoretical and practical significance. This paper presents a novel design method for PID controllers based on the binary-coded extremal optimization algorithm (BCEO). The basic idea behind the proposed method is encoding the PID parameters into a binary string, evaluating the control performance by a more reasonable index than the integral of absolute error (IAE) and the integral of time weighted absolute error (ITAE), updating the solution by the selection based on power-law probability distribution and binary mutation for the selected bad elements. The experimental results on some benchmark instances have shown that the proposed BCEO-based PID design method is simpler, more efficient and effective than the existing popular evolutionary algorithms, such as the adaptive genetic algorithm (AGA), the self-organizing genetic algorithm (SOGA) and probability based binary particle swarm optimization (PBPSO) for single-variable plants. Moreover, the superiority of the BCEO method to AGA and PBPSO is demonstrated by the experimental results on the multivariable benchmark plant.

Multivariable Fuzzy Control Strategy for an Experimental Chiller System

AbstractA multivariable fuzzy controller was developed and implemented for the regulation of the secondary fluid temperature in a chiller using both the rotation frequencies of the pump and the compressor as manipulated variables. Its performance was measured using the integral of time‐weighted absolute error (ITAE) index and the energy consumption. The proposed control strategy proved able to adequately control the chiller in all experiments. For comparison purposes, similar experiments were carried out with fuzzy control strategies in which only one variable was manipulated at a time. Comparing the performance of the proposed controllers with the fuzzy single input–single output controllers for regulatory control, a mean percentage reduction of at least 88.5% was observed in the ITAE. Good results were also observed in control effort and energy consumption. Besides, the implementation of the control strategy was quite simple.Practical ApplicationsRefrigeration systems are of fundamental importance for food conservation. Besides, to maintain the temperature into a narrow range needs an efficient control system and implies energy consumption and equipment wear. The use of a fuzzy controller with two manipulated variables to regulate the secondary fluid temperature has proved to be an efficient control configuration. Desirable characteristics like small or no overshoot, reduced control effort were achieved by the proposed multivariable fuzzy controller. Therefore, this proposed strategy is a valuable alternative to control processes that require strict variability or long periods of operation without stopping.

A new PI tuning method for an industrial process: A case study from a micro-cogeneration system

Micro-cogeneration systems are efficient and clean energy sources. For this reason, reliable control of the overall system itself and its sub-components is of great importance. This paper presents a proportional–integral (PI) controller tuning method for cooling of the hydrogen production unit within the polymer electrolyte membrane (PEM) fuel cell based micro-cogeneration system having 5kW electrical and 30kW thermal capacity. The flow rate control of the coolant water was implemented by means of the modeled temperature control system. Modeling and control system design were implemented in both MATLAB/Simulink and industrial programmable logic controller (PLC) software. The novel analytical tuning rules proposed in this paper, which were developed with the help of the digital control theory and experiences in industrial control problems, are based totally on the model parameters. The output response attained by the proposed controller is a critically damped response (a non-oscillatory system response with damping ratio: ζ=1) and the control signal is a slowly varying safe control signal. Slowly varying control signal denotes that there is no sudden or fast change in the control effort which causes a wear and tear effect in the actuators and shortens the life cycle of the relevant hardware. Besides, an evolutionary multi-objective optimization (EMO) procedure, namely non-dominated sorting genetic algorithm (NSGA-II), was used in order to simultaneously minimize the integral time-weighted absolute error (ITAE) and the integral time-weighted absolute derivative (ITAD) objectives. This results in multiple trade-off solutions that enable user to observe the overall range of possible controller parameters and to choose any option between diverse solutions. Finally, a brief post-optimality study was manually performed to find out the common relations in the PI controller parameter sets of these multiple Pareto-optimal solutions. The proposed controller was applied to the hydrogen production process model. The simulation results indicate that the proposed tuning rules are as effective as NSGA-II and eliminates the need for an iterative optimization run to get the optimal PI controller parameters.

Decoupling and levitation control of a six-degree-of-freedom magnetically levitated stage with moving coils based on commutation of coil array

The research in the present paper focuses on decoupling the six-degrees-of-freedom motions of a magnetically levitated stage with moving coils and controlling the levitation motion. The decoupling is based on commutation of coil array, which is obtained reversely from the electromagnetic force/torque model of the stage. The control of levitation motion is carried out by a phase lead-lag controller designed on the criterion of minimum integral of time-weighted absolute error after gravity compensation modeling of the plant dynamics. Comprehensive simulations of the control system in MATLAB/Simulink and real levitation experiments on a digital signal processor-centered test platform are made to verify the six-degrees-of-freedom decoupling effect and the closed-loop control performances of the levitation degree of freedom. The results indicate that the six-degrees-of-freedom motions of the stage can be decoupled through coil array commutation and the levitation motion can be controlled by the phase lead-lag controller based on the gravity compensation model and designed on the criterion of minimum integral of time-weighted absolute error.

I-PD Controller Tuning for Unstable System Using Bacterial Foraging Algorithm: A Study Based on Various Error Criterion

This paper proposes a novel method to tune the I-PD controller structure for the time-delayed unstable process (TDUP) using Bacterial Foraging Optimization (BFO) algorithm. The tuning process is focussed to search the optimal controller parameters (, , ) by minimising the multiple objective performance criterion. A comparative study on various cost functions like Integral of Squared Error (ISE), Integral of Absolute Error (IAE), Integral of Time-weighted Squared Error (ITSE), and Integral of Time weighted Absolute Error (ITAE) have been attempted for a class of TDUP. A simulation study for BFO-based I-PD tuning has been done to validate the performance of the proposed method. The results show that the tuning approach is a model independent approach and provides enhanced performance for the setpoint tracking with improved time domain specifications.

Performance and gain and phase margins of well-known PID tuning formulas

The performance and robustness of well-known PID formulas for process with deadtime to time constant ratio between 0.1 and 1 are discussed in this paper. The Ziegler-Nichols, Cohen-Coon, and tuning formulas that optimize for load disturbance response (integral absolute error, integral squared error, and integral time-weighted absolute error) give gain margins of about 1.5. The phase margins increase from about 30 to 60/spl deg/ as the process deadtime to time constant ratio increases from 0.1 to 1. Tuning formulas that optimize setpoint response give gain margins of about two and phase margins of about 65/spl deg/. These formulas mostly make use of the proportional-integral derivative (PID) controller zeros to cancel the process poles. Approximate analytical formulas to compute gain and phase margins of PID control systems are also derived in this paper to facilitate online computation which would be particularly useful for implementing adaptive control.