Effective Open-loop Transfer Function Research Articles

ETF dead-time compensation based multiloop control approach for multivariable processes

Due to significant interaction dynamics and time delays in multivariable processes, designing a well-tuned PI controller is always challenging. When tuning multi-loop PI controllers, effective open-loop transfer function should be used instead of the diagonal transfer function element. The complexity of the effective open-loop transfer function (EOTF) increase rapidly for high-dimensional multivariable processes. Therefore, in this manuscript, it is proposed to use equivalent transfer functions (ETFs) under perfect control approximation. Subsequently, a dead-time compensation (DTC) scheme is used for ETFs and PI controllers are tuned. DTC can facilitate eliminating the impact due to time delay from the multivariable process, making the task of tuning PI controllers relatively less complex. The proposed multi-loop control topology minimizes the controller effort, and a good controller design for a multivariable process can be achieved. The PI controller parameters for dead-time compensated ETFs are calculated using simple IMC PI tuning rules, where the filter factor is taken based on the paired element relative gain value. To examine the effectiveness of the proposed controller tuning approach, the proposed control strategy was applied to a wide range of multivariable processes. Compared to state-of-the-art control strategies, the proposed control strategy provides superior closed-loop performance indices, even when there is a significant plant-model mismatch.

Voltage and active power local PI control of distributed energy resources based on the effective transfer function method

This paper presents the design of local PI regulators to control voltage and active power of the Distributed Energy Resources (DERs) in grid-connected Active Distribution Networks (ADNs). The design is developed based on the proposed Multiple-Input Multiple-Output (MIMO) model of ADN. Firstly, the Relative Gain Array (RGA) matrix is used to address the problem of input–output pairing and to show that the voltage control loops are coupled whereas the active power control loops are decoupled. Subsequently the method of the Effective Open-Loop Transfer Function (EOTF) is used to decompose the multi-loop voltage control system into a set of equivalent Single-Input Single-Output (SISO) loops. Then, each PI regulator is independently designed to fulfill some control objectives dictated by the designer. The proposed design procedure is simple and straightforward. The fixed-parameters PI regulators facilitate the integration of DERs into traditional distribution networks which are usually operated without or with limited communication infrastructure. The simulation results presented for various scenarios of two different ADN confirm that performance objectives and regulation at the desired set-points are achieved in a robust sense.

IMC‐PID tuning method based on maximum sensitivity for uncertain multivariable systems

SummaryA controller design method based on effective open‐loop transfer function (EOTF) and internal model control (IMC) is proposed for square multivariable systems with uncertain parameters. In this paper, two equivalent substitutions are used to deal with the multivariable system with uncertain parameters. In the first equivalent substitution, the EOTF method is used to solve the coupling problem of the system. In order to prevent the interval explosion problem of parameters, the affine algorithm is adopted in the decoupling process to determine the value region of system parameters. Then, the multivariable system with uncertain parameters is transformed into a set of single‐variable system with uncertain parameters. The second equivalent substitution is based on Kharitonov's theorem to process every single variable system with uncertain parameters and replace it by a set of boundary models. Meanwhile, in order to ensure that the tuning controller can not only make the system stable but also meet a certain degree of robustness, based on the idea of IMC, the maximum sensitivity is introduced to design the PID controller. Finally, numerical simulation results are given to verify the effectiveness of the proposed method.

Integral-Square-Error Based Normalized Relative Gain Array for the Input-Output Pairing and Equivalent Transfer Function Design of MIMO Processes

Input-output pairing effectively minimizes the loop interaction in MIMO processes and avoids integral instability. In this article, a modified Relative Normalized Gain Array is proposed for the Input-Output Pairing and design of the First-order and Second-order Equivalent Transfer function. The proposed modified Relative Gain Array (mRNGA) matrix is derived by Normalizing the Relative Gain Array matrix with a normalization factor, which is calculated by minimizing the Integral Square Error of the given MIMO process. After that, the first order and second order Equivalent Transfer function is design by the derived mRNGA matrix, which offers an improved estimation of the Effective open-loop transfer function of the given MIMO process. The proposed method is corroborated with the help of the Input-Output pairing examples up to the 5 × 5 MIMO processes and three ETF design example.

Energy-efficient decentralized control method with enhanced robustness for multi-evaporator air conditioning systems

Multi-evaporator air conditioning system has found increasing applications in buildings. Energy-efficient control for this kind of system presents significant challenge because of strong coupling effects and various operation modes. Existing control methods are most likely to encounter uncontrollable problems and lack robustness under uncertain operation conditions. This paper proposes an energy-efficient decentralized control method with enhanced robustness for multi-evaporator air conditioning system. The proposed method is featured by a self-optimizing control strategy and a decentralized proportional-integral (PI) control algorithm based on the effective open-loop transfer function (EOTF). Different from most of previous studies that regulated compressor speed to control the evaporating pressure by using a supervisory optimizer, the proposed self-optimizing control strategy regulates compressor speed to maintain constant suction superheat and achieves energy-efficient operation in a simple and robust manner. Meanwhile, the EOTF-based decentralized PI algorithm overcomes the weakness of decentralized controllers in dealing with coupling effects, while retaining robustness against model errors and component faults. Control performance of the proposed method is tested using a validated system dynamic model. Through extensive controllability tests, it is found that the proposed control method significantly improves temperature control performance of the conventional strategy. Up to 8.6% energy savings are achieved with the proposed control strategy. Moreover, the proposed EOTF-based PI controller demonstrates enhanced robustness in comparison with an advanced model predictive controller.

Load Frequency Control of Power Systems Based on ADRC

Load frequency stability is an important power quality index in power system, any sudden load disturbance will cause the system load frequency deviation, and as the power system becomes more complex, the difficulty of control is also increasing, it is necessary to find a more appropriate control method. Considering that the load frequency control system model has the characteristics of multi-variable and strong coupling, combines the superior anti-interference and anti-coupling ability of the active disturbance rejection control, a novel scheme for power system load frequency control was presented based on the principle of active disturbance rejection control and effective open-loop transfer function. The simulation results show that the proposed method is simple tuning and strong decoupling ability, and provides a successful control of load frequency.

Design of a Decentralized PID Controller for Poultry House System using Genetic Algorithm

Climate control for livestock building is of considerable significance but it is additionally a difficult and convoluted task. The chickens are mainly affected by the variation of temperature and relative humidity. The arrangement of these parameters is accomplished by selecting proper control techniques. In this paper, an optimized controller for the stabilization of the poultry house system has been designed in order to reduce the heat stress of broilers and to achieve the preservation of chickens’ health and comfort. A hygro-thermal model describing the behavior of the poultry house is decomposed into two single loops based on the theory of the effective open-loop transfer function. Adopting a model reduction technique, the equivalent transfer function of each loop is then designed by developing an independent multi-loop PID controller. The initial stability of the reduced model is assured via the Hermite-Biehler theorem. Then, the Genetic Algorithm is adopted to search the optimal gain values that contribute to the desired indoor climate monitoring. An extensive numerical simulation is tested with original experiments measures to show the effectiveness of the design control and the results are compared to those of the ant colony optimization and Ziegler-Nichols methods.

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.

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.

Fractional order IMC based PID controller design using Novel Bat optimization algorithm for TITO Process

An independent design of adaptive multiloop fractional order internal model control based PID (FOIMC-PID) controller for a two input two output process (TITO) is presented. The multivariable system is decomposed by ideal decoupler to develop effective open loop transfer function (EOTF) and then it is approximated into first order plus dead time (FOPDT) model. The multiloop FOIMC-PID controller is designed for TITO model and controller parameters are optimally tuned using Novel Bat Optimization Algorithm (NBOA). The simulation results are demonstrated to show the effectiveness of proposed controller and also some tuning procedure is suggested to get better FOIMC-PID controller performance.

The design of an IMC-PID controller based on MEOTF and its application to non-square processes with time delay

It is difficult to design a controller directly for non-square multi-variable systems with time delay. In the current paper, we propose a new design method for an Internal Model Control PID controller based on a modified effective open-loop transfer function (MEOTF) for non-square processes with time delay. The MEOTF method is used to decompose the complex non-square process into several equivalent independent single-input/single-output processes. Using the Taylor Particle Swarm Optimisation (Taylor-PSO) model reduction method, the MEOTF of the non-square process is approximated by a reduced order form. The reduced form of the MEOTF is then used to design the Internal Model Control PID controller, which is then used for the original non-square process. To improve the robust stability, a first-order filter is added in the feedback loop. Finally, we present simulation results showing the validity and reliability of this method. In particular, our method has a strong anti-interference characteristic and retains its good control performance in the presence of model perturbation and interference.

A multivariable IMC-PID method for non-square large time delay systems using NPSO algorithm

Multiple time delays and strong interactions among different loops are the main problems in the design of multivariable controller for non-square systems. In this paper, the concept of effective open-loop transfer function (EOTF) is extended to non-square systems. By applying the internal model control (IMC) method, the controllers with equivalent models are designed. For practical applications, the NPSO algorithm is used to obtain the parameters of the incremental PID with first-order lag filter. This new method does not only avoid the complex computation caused by the procedure of decoupling first and then designing controllers but also employs the advantages of IMC-PID's suitable for large time delay systems and strong robustness. Simulation is carried out to demonstrate the effectiveness of the proposed method; also significant performance improvement has been achieved with the proposed method compared with other methods.

Controller Design for MIMO Processes Based on Simple Decoupled Equivalent Transfer Functions and Simplified Decoupler

A method for the independent design of proportional-integral/proportional-integral derivative (PI/PID) controllers is proposed based on the equivalent transfer function (ETF) model of the individual loops and the simplified decoupler matrix. It is shown that the conventional effective open-loop transfer function (EOTF, derived from the dynamic relative gain array (DRGA)) is equivalent to the ETF (derived from the relative normalized gain array (RNGA) and relative average residence time array (RARTA)). This relation is used to approximate the decoupled process models as ETF models. The simplified decoupler is shown to decompose the multiloop systems into independent loops (multi-single loop systems) with the ETFs as the resulting decoupled process model. The concept of the ETF (perfect control approximation) is validated by introducing the decoupler. Based on the corresponding ETFs, the decentralized PI controllers are designed using the simplified internal model control (SIMC) method. Three simulation examples of multi-input multi-output (MIMO) process models are considered to demonstrate the simplicity and effectiveness of the proposed method. The performance of the proposed control system is compared with the ideal, normalized, inverted decoupling, and centralized control systems.

Independent design of multi-loop PI/PID controllers for interacting multivariable processes

The interactions between input/output variables are a common phenomenon and the main obstacle encountered in the design of multi-loop controllers for interacting multivariable processes. In this study, a novel method for the independent design of multi-loop PI/PID controllers is proposed. The idea of an effective open-loop transfer function (EOTF) is first introduced to decompose a multi-loop control system into a set of equivalent independent single loops. Using a model reduction technique, the EOTF is further approximated to the reduced-order form. Based on the corresponding EOTF model, the individual controller of each single loop is then independently designed by applying the internal model control (IMC)-based PID tuning approach for single-input/single-output (SISO) systems, while the main effects of the dynamic interactions are properly taken into account. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.