Order Plus Research Articles

Design of PIλDμ controller for global power control of Pressurized Heavy Water Reactor

In this paper, a robust stabilizing controller design method is presented for global power control of a Pressurized Heavy Water Reactor (PHWR) under step-back condition scheme using a Fractional Order Proportional Integral Derivative (PIλDμ) controller resulting into robust performance. The method is applicable to design a controller for One Non Integer Order Plus Time Delay (NIOPTD-I) plant which satisfies design specifications such as phase margin and gain crossover frequency. Stability boundary locus method is used in (Kp, Ki, Kd) parameter space for NIOPTD-I plants to obtain stability region. The robust performance is obtained by satisfying flat phase condition at gain crossover frequency where phase is almost constant for large span of frequencies. The simulation result of the proposed PIλDμ controller shows active step-back control to the insertion of the rod with no undershoot and with the robust performance, hence safe to the plant for gain variations from 500% lower side to 1000% upper side. The PIλDμ controller with a plant shows that 30% and 50% global power drop from initial 100% is achieved in a reasonable time without undershoot.

Design of FOPID controller for fractional-order plants with experimental verification

In this paper, a design method is proposed for a robust stabilizing fractional order proportional integral derivative (FOPID) controller for One Non-Integer Order Plus Time Delay plant (NIOPTD-I). The NIOPTD-I model is obtained after reducing the higher order continuous time process model. The FOPID controller is designed by using stability boundary locus method, which satisfies user defined frequency domain specifications phase margin and the gain crossover frequency. A robust control system is designed against gain variations by achieving flat phase condition which is due to zero slope at the gain crossover frequency of the phase plot. Thus robust stabilizing FOPID controller for NIOPTD-I fractional order plant is designed. The applicability of the proposed method is illustrated with simulation example and experimental validation with the liquid level control system.

Move Suppression Calculations for Well-Conditioned MPC

Several popular tuning strategies applicable to Model Predictive Control (MPC) schemes such as GPC and DMC have previously been developed. Many of these tuning strategies require an approximate model of the controlled process to be obtained, typically of the First Order Plus Dead Time type. One popular method uses such a model to analytically calculate an approximate value of the move suppression coefficient to achieve a desired condition number for the regularized system dynamic matrix; however it is not always accurate and tends to under-estimate the required value. In this paper an off-line method is presented to exactly calculate the move suppression coefficient required to achieve a desired condition number directly from the unregularized system dynamic matrix. This method involves an Eigendecomposition of the system dynamic matrix - which may be too unwieldy in some cases –and a simpler analytical expression is also derived. This analytical expression provides a guaranteed tight upper bound on the required move suppression coefficient yielding a tuning formula which is easy to apply, even in on-line situations. Both methods do not require the use of approximate or reduced order process models for their application. Simulation examples and perturbation studies illustrate the effectiveness of the methods in both off-line and on-line MPC configurations. It is shown that accurate conditioning and improved closed loop robustness can be achieved.

A Model Identification Method for Tuning of PID Controller in a Smith Predictor Structure

In this paper, a model identification method is presented for tuning of PID parameters in Smith predictor structure based on internal model control. The purposed method fits stability boundary locus (SBL) of a plant model with SBL of a FOPDT (First Order Plus Dead Time) or a SOPDT (Second Order Plus Dead Time) model to determine the controller parameters. Two examples are employed to illustrate the applicability and simplicity of the purposed method in both tuning of controller parameters and identification of model parameters for an integer order plant and a fractional order plant.

Design of PID Controllers for Unstable Second Order Plus Time Delay Systems by Equating Coefficient Method

Design of PID Controllers for Unstable Second Order Plus Time Delay Systems by Equating Coefficient Method

PID control of integrating systems using Multiple Dominant Poleplacement method

AbstractSimple tuning rules for proportional‐integral‐derivative (PID) controller are proposed for Pure Integrating Plus Time Delay systems (PIPTD), Double Integrating Plus Time Delay systems (DIPTD) and stable/unstable First Order Plus Time Delay Integrating systems (FOPTDI) based on Multiple Dominant Poleplacement (MDP) method. The main advantage of the method is that there is no time delay approximation for deriving PID settings. Tuning rules for PIPTD and DIPTD systems are given as a function of tuning parameter, and tuning parameter can be selected based on desired level of robustness (maximum magnitude of the sensitivity function, Ms). Tuning rules for FOPTDI system are given as a function of ratio of time delay to the process time constant for Ms = 2. Simulation on various transfer function models and on non‐linear model equations of CSTR carrying out an exothermic reaction shows the effectiveness of the proposed method in terms of Integral Absolute Error (IAE), Total Variation (TV), Overshoot (OS) and Ms. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.

Study on Control of First Order Plus Delay Using Smith Predictor

This paper presents the implementation of Smith predictor structure for the control of a first order plus delay time process. Water heater for vacuum distillation apparatus is studied, the open loop transfer function shows a first order plus delay time. The control system is analyzed using open loop Bode plot and root locus method through “sisotool” in MATLAB control tool box. The Smith predictor control design carried out using MATLAB (7.11.0) command windows. The controller gain is found to be 96.3 and the integral time 256.4

Experimental Validation of a Multi Model PI Controller for a Non Linear Hybrid System in LabVIEW

In this paper a real time Single Spherical Tank Liquid Level System (SSTLLS) has been chosen for investigation. This paper describes the design and development of a Multi Model PI Controller (MMPIC) using classical controller tuning techniques for a single spherical nonlinear tank system. System identification of these different regions of nonlinear process are done using black box modeling, which is identified to be nonlinear and approximated to be a First Order Plus Dead Time (FOPDT) model. A proportional and integral controller is designed using LabVIEW and Chen-Hrones-Reswick (CHR), Zhuang-Atherton (ZA), and Skogestad’s Internal Model Controller (SIMC) tuning methods are implemented in real time. The paper provides the details about the data acquisition unit, shows the implementation of the controller, and comparision of the results of PI tuning methods used for an MMPI Controller.

2DOF PID Controller Design for a Class of FOPTD Models–An Analysis with Heuristic Algorithms

Abstract In recent years, a number of controller design procedures are developed and implemented in process industries to enhance the performance of closed loop processes. In this paper, heuristic algorithm based Two Degrees Of Freedom (2DOF) PID controller design is proposed for a class of First Order Plus Time Delay (FOPTD) systems existing in the literature. Minimization of the weighted sum of multiple objective functions is considered to monitor the heuristic search towards the optimal controller parameters. A detailed comparative analysis between well known heuristic methods, such as Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO), Cuckoo Search (CS) and Firefly Algorithm (FA) are presented. The popular 2DOF PID structures, such as Feed Back Structure (FBS) and Feed Forward Structure (FFS) are considered in this work to enhance the performance of FOPTD systems. From the results, it is noted that, proposed controller provides enhanced results for the reference tracking and disturbance rejection operations.

Subspace Identification of Transfer Function Models for an Unstable Bioreactor

This work deals with the identification of transfer function model of an unstable bioreactor by a subspace-based identification method. The data set is generated from the simulated closed loop system by giving a random signal at the reference signal. The linear system matrices are estimated through the Multivariable Output Numerical algorithms for Subspace State Space System Identification (MON4SID) algorithm. The delay is estimated directly from the input–output data by the impulse response method. The identified First Order Plus Time Delay (FOPTD) model is compared with the locally linearized transfer function model derived around the unstable operating point. A Proportional Integral Derivative (PID) controller is designed for the identified model using the equating coefficient method. The closed loop servo and regulatory responses show that the model identified by MON4SID is similar to the linearized model and the optimization method.

Tuning rules for a quick start up in Dynamic Matrix Control

This paper pretends to offer design rules for the parameters adjustment of the Dynamic Matrix Control (DMC) to allow an easier starting up. The effect on the time response of each algorithm parameter that can be tuned by the user is studied in an unconstrained system. To this aim, the position of the closed loop poles of the equivalent system is calculated. To simplify the study and to obtain more direct conclusions the number of poles will be limited using a First Order Plus Death Time simplification of the real plant. Design rules proposed in this study are tested in some simulated benchmarks and in a real plant.

Robust controller design for First order Plus Time Delay systems using Kharitonov Theorem

In this paper, a new method using Kharitonov theorem and an algorithm in MATLAB for stability boundary locus is applied to compute all the stabilizing PI controller gains for a stable first order plus time delay system which satisfies both robust stability and robust performance criteria. The PI settings designed using SIMC rule is also shown in the common stability region. Similarly for an unstable FOPTD system all stabilizing PID controller is identified which satisfies both robust stability and P.M specification. The PI settings designed for unstable FOPTD system using Dominant Pole Placement and Equating Coefficient method is shown on k p – k i plane to compare robustness. It is also shown that to design robust controller for Unstable FOPTD, PID controller should be preferred to PI controller.

제약조건을 고려한 불안정 시스템의 RCGA 기반 PID 제어

PID control for unstable processes with time delay is not easy to apply because of unstability due to the poles existing on left-hand side in s-plane and the effect of time delay. In this paper, the authors consider the PID controller design technique in case of predefining overshoot or rising time by designer according to control environment. To deal with constraint problem like this, in this paper, the RCGA incorporating the penalty strategy is used. This is the method that if the RCGA violates given constraints, the defined penalty function is summed to the evaluation function depending on the severity and then the given constraint problem is converted to non-constraints optimization problem. The proposed method is applied to the unstable FOPTD(First Order Plus Time Delay) system and simulations are accomplished to illustrate the set-point tracking performance.

The nullity of [formula omitted]-cyclic graphs

A simple connected graph is called a k-cyclic graph provided that the number of edges equals its order plus (k-1). In this paper, we define a class of (k-1)-cyclic graph, denoted by Θk. The singularity of Θ-graph is studied. Also, the (k-1)-cyclic graphs that contain Θ-graph as an induced subgraph are paid much attention. We characterize those graphs that have extreme nullities. The results generalize the corresponding theorems on unicyclic and bicyclic graphs.

Blood glucose concentration regulation in Type 1 diabetics using multi model multi parametric model predictive control: An empirical approach

A Glucose- Insulin steady state static map is obtained from the Hovorka's 8th order virtual patient model. Three First Order Plus Time Delay (FOPTD) models are derived for the three piecewise linear regions in it. Through polyhedral vector space partitioning based on constraint violation, critical regions in state vector space are identified. A state feedback gain based controller is designed for each critical region. The controller design prevents constraint violations and ensures convexity while regulating the state vector to origin. The solution is also globally minimal. The state vector space of each empirical model is subjected to such analysis, resulting in three different set of critical regions and corresponding controllers. Gain Scheduling (GS) based on the Blood Glucose Concentration (BGC) measurement ensured proper profile selection. Through delay time compensation techniques, the multi model multi-parametric Model Predictive Control (mp-MPC) is designed for pure dynamics of each linear region. It is observed that the gain scheduled controller regulates the BGC within the acceptable range (80mg/dL to 160 mg/dL) during multiple meal disturbances. The explicit state feedback gain nature of the controller implies ease of deployment on memory constrained embedded devices.

Neuro-Fuzzy Modified Smith predictor for IPDT and FOPDT Processes Control

In this paper, intelligent control approaches are introduced to overcome the problems highlighted in the standard Smith predictor. First, in order to overcome the steady state error in the Integrator Plus Dead Time (IPDT) process control due to disturbance loading, a new fuzzy logic control based SP is developed by intentionally introducing a model mismatch to improve the system performance in terms of disturbance rejection and robustness to process modelling errors. In addition, for the First Order Plus Dead Time (FOPDT) process control, a SP based neural network control scheme is proposed to deal with the process modelling errors and proved to provide a significantly improved robustness. The neural network (NN) was designed to work with different types of modelling errors. Simulation results show that this NN approach provides excellent performance in terms of robustness to modelling errors and high adaptability to the control of both IPDT and FOPDT processes.

DESIGN AND REAL TIME IMPLEMENTATION OF FRACTIONAL ORDER PROPORTIONAL-INTEGRAL CONTROLLER ( PI ? ) IN A LIQUID LEVEL SYSTEM.

This research article deals with the design and real time implementation of a fractional order Proportional-Integral controller (PI?) for a Liquid Level System (LLS). The system is approximated as a First Order Plus Time Delay (FOPTD) model. The equivalent transfer function of this system in polynomial format is considered here for controller design. Expressions for controller parameters (KP and KI) in terms of frequency (?) and fractional order (?) are derived from the Fractional Order Characteristic Polynomial (FOCP) of the closed loop system. The global stability region based on K P and K I for each ? is constructed. Average values of KP and KI, for each ?, are taken. Among these values, the best fit of KP average and KI average and corresponding ? are identified by means of optimization techniques. The real time implementation of PI? controller with the identified controller settings in LLS is done. The PI? controller performances are analyzed in terms of ISE and IAE. A comparison of this control strategy with other conventional based controller techniques is made. PI? controller outperforms the conventional PI controllers. In addition the load disturbance studies are also carried out and it justifies the supremacy of PI? controller.

RELAY FEEDBACK-BASED CRITICAL PARAMETER ESTIMATION FOR FIRST ORDER PLUS DEAD TIME TYPE PLANT IN NETWORKED CONTROL SYSTEM CONFIGURATION

Most control strategies for networked control systems (NCS) assume that system model is known "a priori" which is, however, impractical in many industrial applications. To obtain the model of First Order Plus Dead Time type plant for networked control, this paper concentrates on model identification under the networked control environment. Ideal-relay feedback-based networked identification scheme is proposed here along with the new packet-based real-time queuing protocol to identify the plant's critical parameters, which takes into account the effect of nondeterministic factors such as network-induced delay, data packet disordering, and limited data packet loss between the sensor and controller as well as the controller and the actuator. Experimental results show that the proposed networked identification scheme can effectively overcome the impact of various network-induced nondeterministic factors for ideal-relay-based model identification in NCS.

Compensation Tuning of Analog and Digital Controllers for First Order Plus Time Delay Plants

Clanek je věnovan jednoduche kompenzacni metodě seřizeni analogových i cislicových regulatorů PI a PID pro proporcionalni regulovane soustavy se setrvacnosti prvniho řadu a dopravnim zpoţžěnim. Popisovana metoda umožňuje seřizeni regulatoru tak, aby regulacni proces byl nekmitavý a bez překmitu pro vsechny vstupni veliciny. Použiti je ukazano na přikladě.

On the model matching approach to PID design: Analytical perspective for robust Servo/Regulator tradeoff tuning

This communication addresses the robust tuning of a One-Degree-Of-Freedom (1DOF) PID controller for both acceptable load disturbance attenuation ( Regulator mode) and setpoint tracking ( Servo mode) of step signals based on a First Order Plus Time Delay (FOPTD) model. This problem arises naturally from the fact that sometimes a simple PID has to deal with setpoint changes and load disturbances in the same proportion. Hence, some kind of Servo/Regulator tradeoff tuning is necessary to minimize the overall performance degradation. Based on the well-established min–max model matching theory, two different analytical approaches are compared, determining when and why they outperform one another. First, a recent design which accomplishes the tradeoff tuning by means of considering the inherent behaviour of each operating mode is revisited. Second, an IMC-like design which looks at the Servo/Regulator tradeoff problem from a Robustness/Performance point of view is presented. Simulation examples clarify the discussion and confirm the effectiveness (and the limits) of the IMC-like design.