Time Domain Performance Indices Research Articles

Centralized model matching integer/fractional-order controller design for multivariable processes with real-time validation

This paper proposes a novel approach to design a centralized model matching integer/fractional-order (FO) controller for multivariable processes. As a first step, for a linear time-delay process, a desired closed-loop reference model is formulated with the inclusion of a linear quadratic regulator with integral controller. The reference model is formulated with the objective of embodying the desired closed-loop specifications. The second step involves equating the closed-loop system with the reference model, leading to a synthesis equation that yields a higher-order controller. In the third step, the lower-order approximant of the controller is obtained by matching a set of approximate generalized time moments/approximate generalized Markov parameters of the higher-order controller to that of its lower-order approximate at a few expansion points in the s-plane. The selection of an optimal set of expansion points is formulated in an optimization problem frame with the aim of minimizing the area between responses of the desired and designed closed-loop systems, keeping the stability of the designed closed-loop system as a constraint. The efficacy of the proposed approach is illustrated by the design of different controllers for time-delay-dominated nonsquare process and FO square process. Comparative analysis is carried out using time-domain performance indices by introducing parameter uncertainty and disturbance signals. To demonstrate the applicability of the proposed method, a real-time investigation is carried out with the design and implementation of a controller for interacting hybrid (conical and spherical) tank process setup.

Fractional-order PID controller design via optimal selection strategy of frequency domain specifications

In this paper, a novel fractional-order Proportional-Integral Derivative (PID) controller design depending on optimal selection of frequency domain specifications is proposed for time delay systems. The frequency domain specification sets, namely, (i) phase margin and gain crossover frequency and (ii) phase margin and gain margin are determined so that the reference model is optimal according to three time domain performance indices, i.e. Integral Square Error (ISE), Integral Time Square Error (ITSE) and Integral Absolute Error (IAE). Here, the delayed Bode's ideal transfer function is employed in the reference model. Moreover, the stability region of the reference model is given via a theorem. In simulation studies, the proposed methodology is compared with other two different methods using the same frequency domain specifications. It is observed that the proposed optimal fractional-order PID controllers outperform according to the mentioned performance indices, and they also possess considerably acceptable performance in terms of other time domain specifications such as overshoot, settling time, etc.

Power System Stabilizers Design Using BAT Algorithm

A new metaheuristic method, the BAT algorithm based on the echolocation behaviour of bats is proposed in this paper for optimal design of Power System Stabilizers (PSSs) in a multimachine environment. The PSSs parameter tuning problem is converted to an optimization problem which is solved by the BAT search Algorithm. An eigenvalues based objective function involving the damping factor, and the damping ratio of the lightly damped electromechanical modes is considered for the PSSs design problem. The performance of the proposed BAT based PSSs (BATPSS) has been compared with Genetic Algorithm (GA) based PSSs (GAPSS) and the Conventional PSSs (CPSS) under various operating conditions and disturbances. The results of the proposed BATPSS are demonstrated through time domain analysis, eigenvalues and performance indices. Moreover, the results are presented to demonstrate the robustness of the proposed algorithm over the GA and conventional one.

A Novel Generalized Predictive Control Strategy With Improved Time Domain Performance

Abstract Due to the ability of handling the coupling property of multivariable control system, generalized predictive control (GPC) has been widely employed in process industry. However, the existing GPC method normally utilizes the frequency domain indices in the design procedure, which is not intuitive to the industrial end users. Therefore, a new GPC method with improved time domain performance is proposed for multiple-input-multiple-output system. First, the slope and rate of change of the slope of the system outputs are considered as two new weighting terms in the cost function of GPC such that the dynamic characteristics of the system can be better considered in the optimal control problem of the controller. Second, given the modified cost function, the resultant GPC algorithm is developed to improve the time domain performance of the system. Third, the convergence and stability of the closed-loop system under the proposed method are theoretically proved. Finally, the experimental results based on the variable air volume (VAV) air conditioning system show that the time domain performance indices, including overshoot and settling time, of the proposed method, have been improved by 68.75% and 66.67%, compared with the traditional GPC, showing the advantages of the new GPC method.

Observer-based interval type-2 fuzzy PID controller for PEMFC air feeding system using novel hybrid neural network algorithm-differential evolution optimizer

In this paper, a novel hybrid Neural Network Algorithm-Differential Evolution (NNA-DE) optimizer which integrates both NNA and DE is proposed. The proposed hybrid NNA-DE optimizer demonstrates better performance compared to the standard NNA and the other state-of-the-art optimization algorithms. The proposed hybrid NNA-DE algorithm is then employed for optimizing an observer-based interval type-2 fuzzy PID (OB-IT2FPID) controller applied to the proton exchange membrane fuel cell (PEMFC) air feeding system. The whole design parameters of the OB-IT2FPID controller including the scaling factors, interval type-2 membership function parameters and the footprint-of-uncertainty (FOU) are optimized using the proposed hybrid NNA-DE algorithm. The results show that the proposed NNA-DE optimized OB-IT2FPID controller achieves better performance in terms of set-point tracking, disturbance rejection and the time-domain performance indices. The robustness of the proposed NNA-DE optimized OB-IT2FPID controller against parametric uncertainty in the PEMFC air-feeding system is tested. The proposed controller demonstrated better robustness against parameter uncertainty in the system. Processor-in-the-Loop (PIL) approach is adopted to validate the performance of the proposed controller on embedded control hardware.

Design of fractional order PID controller for load frequency control system with communication delay

This work explores a frequency-domain approach to design a fractional order proportional–integral–derivative (FO-PID) controller cascaded with a first-order filter for the load frequency control (LFC) system with communication delay. The proposed method is based on suitable reference model development in the direct synthesis (DS) approach, followed by frequency response matching technique. The reference model is developed for robust control-loop performance using the stability-margin and time-domain specifications. The values of the fractional orders of the integral and derivative terms are obtained according to the dynamics of the nominal system. The proposed controllers have been designed for some LFC systems taken from the literature that have different dynamics with reheat, non-reheat and hydraulic turbines and performances with non-linearity like generation rate constraint (GRC), generation dead band (GDB) along with noise have been compared favorably with that of some controllers prevalent in the literature. The proposed controllers have been shown to work efficaciously for the decentralized multi-area IEEE 39-bus New England test system along with variable communication delay. To show the efficacy of the proposed controllers the load-disturbance responses along with the frequency and time domain performance indices have been evaluated for comparison.

Optimal Fractional-Order Active Disturbance Rejection Controller Design for PMSM Speed Servo System.

In this paper, a fractional-order active disturbance rejection controller (FOADRC), combining a fractional-order proportional derivative (FOPD) controller and an extended state observer (ESO), is proposed for a permanent magnet synchronous motor (PMSM) speed servo system. The global stable region in the parameter (Kp, Kd, μ)-space corresponding to the observer bandwidth ωo can be obtained by D-decomposition method. To achieve a satisfied tracking and anti-load disturbance performance, an optimal ADRC tuning strategy is proposed. This tuning strategy is applicable to both FOADRC and integer-order active disturbance rejection controller (IOADRC). The tuning method not only meets user-specified frequency-domain indicators but also achieves a time-domain performance index. Simulation and experimental results demonstrate that the proposed FOADRC achieves better speed tracking, and more robustness to external disturbance performances than traditional IOADRC and typical Proportional-Integral-Derivative (PID) controller. For example, the JITAE for speed tracking of the designed FOADRC are less than 52.59% and 55.36% of the JITAE of IOADRC and PID controller, respectively. Besides, the JITAE for anti-load disturbance of the designed FOADRC are less than 17.11% and 52.50% of the JITAE of IOADRC and PID controller, respectively.

Tuepras upgrades Izmit refinery to expand diesel production

In this paper, various optimization techniques for the parameter tuning of a P.D controller to control the water level in a boiler drum have been applied. The optimization techniques utilized and compared in this paper are 1) Particle Swarm Optimization (PSO) 2) Bacterial Foraging – Particle Swarm Optimization hybrid (BFPSO) 3) Gravitational Search Algorithm – Particle Swarm Optimization hybrid (GSAPSO). A comparative study of the above-mentioned optimization techniques was done based on the time domain characteristics and performance indices namely, Integral Square Error (ISE), Integral Absolute Error (IAE), and Integral Time Absolute Error (ITAE).

WITHDRAWN: Comparison and analysis of hybrid optimization algorithms for water level control of drum boiler system

In this paper, various optimization techniques for the parameter tuning of a P.D controller to control the water level in a boiler drum have been applied. The optimization techniques utilized and compared in this paper are 1) Particle Swarm Optimization (PSO) 2) Bacterial Foraging – Particle Swarm Optimization hybrid (BFPSO) 3) Gravitational Search Algorithm – Particle Swarm Optimization hybrid (GSAPSO). A comparative study of the above-mentioned optimization techniques was done based on the time domain characteristics and performance indices namely, Integral Square Error (ISE), Integral Absolute Error (IAE), and Integral Time Absolute Error (ITAE).

Optimal Reduced Order Model of Single- Shaft Heavy Duty Gas Turbine Power Plants

Design of controller and analyzing the response of higher order system in real time environment would be very complex and expensive. Therefore, an attempt has been made in this paper to obtain the reduced order model of single-shaft Heavy duty gas turbine plants ranging from 18.2 to 106.7 MW by using various model order reduction techniques. The step response of Heavy duty gas turbine model using the reduced order models are compared with that of the original MATLAB/ Simulink model. Various time domain specifications and performance index criteria have been considered for analyzing the responses. The simulation results show that the response obtained by Routh approximation-Pade approximation technique based reduced order model mimics the original, higher order Heavy Duty gas turbine response. It is also proposed in this paper to improve the response by optimizing the co-efficients of reduced order model using Particle Swarm Optimization technique. On comparing the simulation results, Particle Swarm Optimization technique based reduced order model yield better transient and steady state response as close to original higher order system and hence it is identified as an optimal reduced order model for all Heavy Duty gas turbine plants in grid connected operation

Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

This paper presents a study of optimal control design for a single-inverted pendulum (SIP) system with the multi-objective particle swarm optimization (MOPSO) algorithm. The proportional derivative (PD) control algorithm is utilized to control the system. Since the SIP system is nonlinear and the output (the pendulum angle) cannot be directly controlled (it is under-actuated), the PD control gains are not tuned with classical approaches. In this work, the MOPSO method is used to obtain the best PD gains. The use of multi-objective optimization algorithm allows the control design of the system without the need of linearization, which is not provided by using classical methods. The multi-objective optimal control design of the nonlinear system involves four design parameters (PD gains) and six objective functions (time-domain performance indices). The Hausdorff distances of consecutive Pareto sets, obtained in the MOPSO iterations, are computed to check the convergence of the MOPSO algorithm. The MOPSO algorithm finds the Pareto set and the Pareto front efficiently. Numerical simulations and experiments of the rotary inverted pendulum system are done to verify this design technique. Numerical and experimental results show that the multi-objective optimal controls offer a wide range of choices including the ones that have comparable performances to the linear quadratic regulator (LQR) control.

Time Domain Particle Swarm Optimization of PI Controllers for Bidirectional VSC HVDC Light System

This paper proposes a novel technique to tune the PI controllers of a bidirectional HVDC light system by embedding particle swarm optimization directly in the Simulink model in the design procedure. The HVDC light system comprises of a rectifier station, a DC link, and an inverter station. Each converter station requires four PI controllers to be tuned in the decoupled d-q vector control scheme, and with the bidirectional HVDC system, the required PI controllers are doubled. Tuning these many controllers using conventional methods is a challenging task, especially if the parameters of the converter stations are different. A novel approach to tune the PI controllers for a bidirectional HVDC system using the time-domain performance indices is presented in this paper. The time-domain performance indices are optimized using the particle swarm optimization (PSO) algorithm. The results of the proposed tuning method show that the proposed method not only gives superior results but also is less cumbersome to tune compared to conventional methods like modulus optimum (MO).

An empirical Study Investigation of Task Allocation Process Barriers in the Context of Offshore Software Development Outsourcing: An Organization Size Based Analysis

This research presented a holistic approach in determining the trade-off optimized Proportional-Integral-Derivative (PID) tunings for both servo and regulatory controls of the cascade control loop by using Genetic Algorithm (GA). Performance of GA-based PID tunings was significantly compared with the IMC-based single loop tunings and conventional cascade control tunings. GA-based PID tunings eliminated the complicated mathematic calculations in obtaining the correlation PID tuning values and also reduce the dependency on engineering knowledge, experience, and skills. The performance of transient and steady-state responses was compared through time domain specification, performance index, and process response curve. It is concluded that the GA-based PID tunings for the cascade control loop had produced the best result for both servo and regulatory control objectives, which is eventually determined.

Fractional Order Fuzzy PID Control of Automotive PEM Fuel Cell Air Feed System Using Neural Network Optimization Algorithm

The air feeding system is one of the most important systems in the proton exchange membrane fuel cell (PEMFC) stack, which has a great impact on the stack performance. The main control objective is to design an optimal controller for the air feeding system to regulate oxygen excess at the required level to prevent oxygen starvation and obtain the maximum net power output from the PEMFC stack at different disturbance conditions. This paper proposes a fractional order fuzzy PID controller as an efficient controller for the PEMFC air feed system. The proposed controller was then employed to achieve maximum power point tracking for the PEMFC stack. The proposed controller was optimized using the neural network algorithm (NNA), which is a new metaheuristic optimization algorithm inspired by the structure and operations of the artificial neural networks (ANNs). This paper is the first application of the fractional order fuzzy PID controller to the PEMFC air feed system. The NNA algorithm was also applied for the first time for the optimization of the controllers tested in this paper. Simulation results showed the effectiveness of the proposed controller by improving the transient response providing a better set point tracking and disturbance rejection with better time domain performance indices. Sensitivity analyses were carried-out to test the robustness of the proposed controller under different uncertainty conditions. Simulation results showed that the proposed controller had good robustness against parameter uncertainty in the system.

Adaptive multi-loop IMC-based PID controller tuning using bat optimisation algorithm for two interacting conical tank process

In this paper, multi-loop adaptive internal model controller (IMC)-based PID is designed for the two interacting conical tank level process (TICTLP). The nonlinear TICTLP is decomposed into linear transfer function matrix around the operating points and the effective open loop transfer function (EOTF) is developed using simplified decoupler. The IMC-based PID controller parameters are obtained for EOTF model using bat optimisation algorithm (BOA). A weighted sum of integral time absolute error is used as control design objective function for multi-loop IMC-PID design which yields faster settling time with minimum over shoot. The fuzzy-based adaptive gain scheduling is used to provide complete control to TICTLP and fuzzy-based adaptive decoupler is implemented to eliminate the dynamic interaction between control loops. The simulation results of proposed controller are compared with conventional ZN-PID, IMC controllers to show the superiority of proposed controller. The simulation response of proposed controller indicates the performance improvement control schemes interns of time domain performance indices, servo tracking, regulatory response and faster settling time.

Sine-cosine algorithm-based optimization for automatic voltage regulator system

A novel design method, sine-cosine algorithm (SCA) is presented in this paper to determine optimum proportional-integral-derivative (PID) controller parameters of an automatic voltage regulator (AVR) system. The proposed approach is a simple yet effective algorithm that has balanced exploration and exploitation capabilities to search the solutions space effectively to find the best result. The simplicity of the algorithm provides fast and high-quality tuning of optimum PID controller parameters. The proposed SCA-PID controller is validated by using a time domain performance index. The proposed method was found efficient and robust in improving the transient response of AVR system compared with the PID controllers based on Ziegler-Nichols (ZN), differential evolution (DE), artificial bee colony (ABC) and bio-geography-based optimization (BBO) tuning methods.

Tuning of a PID controller using evolutionary multi objective optimization methodologies and application to the pulp and paper industry

Proportional–Integral–Derivative controller technique continues to provide the easiest and effective solutions to most of the industrial applications in recent years. However PID controller is poorly tuned in practice compared to most other tuning methods and is complicated with poor performance. This research presents a multi objective optimization approach involving Genetic Algorithm, Evolutionary Programming, Particle Swarm Optimization and Bacterial foraging optimization. The proposed multi objective optimization algorithm is used to tune the PID controller parameters and their performances have been compared with the conventional methodologies like Ziegler Nichols method. The results proved that the use of multi objective optimization approach based controller tuning improves the performance of process in terms of time domain specifications and performance index, set point tracking and regulatory changes and also provides stability. This paper describes the various multi objective optimization algorithms and its implementation to tune the PID Controller used in paper machine DCS as real time processing of a Pulp and paper industry processes.

Adaptive Multi loop IMC Based PID controller tuning using Bat Optimization algorithm for Two Interacting Conical Tank Process

In this paper, multi-loop adaptive internal model controller (IMC)-based PID is designed for the two interacting conical tank level process (TICTLP). The nonlinear TICTLP is decomposed into linear transfer function matrix around the operating points and the effective open loop transfer function (EOTF) is developed using simplified decoupler. The IMC-based PID controller parameters are obtained for EOTF model using bat optimisation algorithm (BOA). A weighted sum of integral time absolute error is used as control design objective function for multi-loop IMC-PID design which yields faster settling time with minimum over shoot. The fuzzy-based adaptive gain scheduling is used to provide complete control to TICTLP and fuzzy-based adaptive decoupler is implemented to eliminate the dynamic interaction between control loops. The simulation results of proposed controller are compared with conventional ZN-PID, IMC controllers to show the superiority of proposed controller. The simulation response of proposed controller indicates the performance improvement control schemes interns of time domain performance indices, servo tracking, regulatory response and faster settling time.

Analytical phase‐lead controller design using pole placement: a pole‐zero ratio minimisation approach

Owing to their simple structure and considerable improvement to the transient response, phase-lead controllers are broadly used in industrial applications. They are designed using root locus or Bode diagrams to introduce extra phase shift at the crossover frequency. Traditional phase-lead design techniques are either graphical or based on trial-and-error. In design techniques using root locus diagrams, there is no direct control on the values of a given time-domain performance index. To make this criterion satisfactory, the designer has to try different locations of the controller's zero and pole. Based on minimisation of the controller's pole-zero ratio subject to pole placement requirements, a simple analytical design technique is developed in this Letter. The necessary and sufficient conditions to determine optimal controller parameters are provided. To evaluate the performance of the proposed method, it is applied to a single integrating plant with time delay.

Robust PI-PD Controller Design for Systems with Parametric Uncertainties

This paper presents a robust design of the four parameters PI-PD controller for systems with parametric uncertainties. The Particle swarm Optimization (PSO) method is applied to tune the controller parameters such that the robust specifications are satisfied. For the robust stability and performance to be guaranteed, the Kharitonov's theorem of interval polynomials is combined with the time domain performance index. The effectiveness of the proposed controller is illustrated by two examples of uncertain systems.