An effective frequency domain approach to tuning non-PID controllers for high performance

In this paper, a new tuning method is proposed for the design of non-PID controllers for complex processes to achieve high performance. Compared with the existing PID tuning methods, the proposed non-PID controller design method can yield better performance for a wide range of complex processes. A suitable objective transfer function for the closed-loop system is chosen according to process characteristics. The corresponding ideal controller is derived. Model reduction is applied to fit the ideal controller into a much simpler and realizable form. Stability analysis is given and simulation examples are provided to demonstrate the effectiveness of the proposed method.     

基于遗传算法的多PID控制器参数整定

为了解决多入多出系统和采用状态控制的单入单出系统的多PID控制器参数整定困难的问题，本文提出了基于遗传算法的多PID控制器参数整定方法，该方法只需给出大概的PID参数范围即可得到控制性能最优的PID参数，本文结合实例证实了该方法的有效性。     

Disturbance-rejection-based tuning of proportional–integral–derivative controllers by exploiting closed-loop plant data

A systematic data-based design method for tuning proportional–integral–derivative (PID) controllers for disturbance attenuation is proposed. In this method, a set of closed-loop plant data are directly exploited without using a process model. PID controller parameters for a control system that behaves as closely as possible to the reference model for disturbance rejection are derived. Two algorithms are developed to calculate the PID parameters. One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas. Because plant data integrals are used in the regression equations for calculating PID parameters, the two proposed algorithms are robust against measurement noises. Moreover, the controller tuning involves an adjustable design parameter that enables the user to achieve a trade-off between performance and robustness. Because of its closed-loop tuning capability, the proposed method can be applied online to improve (retune) existing underperforming controllers for stable, integrating, and unstable plants. Simulation examples covering a wide variety of process dynamics, including two examples related to reactor systems, are presented to demonstrate the effectiveness of the proposed tuning method.     

PID tuning rules for SOPDT systems: review and some new results

PID controllers are widely used in industries and so many tuning rules have been proposed over the past 50 years that users are often lost in the jungle of tuning formulas. Moreover, unlike PI control, different control laws and structures of implementation further complicate the use of the PID controller. In this work, five different tuning rules are taken for study to control second-order plus dead time systems with wide ranges of damping coefficients and dead time to time constant ratios (D/tau). Four of them are based on IMC design with different types of approximations on dead time and the other on desired closed-loop specifications (i.e., specified forward transfer function). The method of handling dead time in the IMC type of design is important especially for systems with large D/tau ratios. A systematic approach was followed to evaluate the performance of controllers. The regions of applicability of suitable tuning rules are highlighted and recommendations are also given. It turns out that IMC designed with the Maclaurin series expansion type PID is a better choice for both set point and load changes for systems with D/tau greater than 1. For systems with D/tau less than 1, the desired closed-loop specification approach is favored.     

Extension of IMC tuning correlations for non-self regulating (integrating) processes

The filter term of a PID with Filter controller reduces the impact of measurement noise on the derivative action of the controller. This impact is quantified by the controller output travel defined as the total movement of the controller output per unit time. Decreasing controller output travel is important to reduce wear in the final control element. Internal Model Control (IMC) tuning correlations are widely published for PI, PID, and PID with Filter controllers for self regulating processes. For non-self regulating (or integrating) processes, IMC tuning correlations are published for PI and PID controllers but not for PID with Filter controllers. The important contribution of this work is that it completes the set of IMC tuning correlations with an extension to the PID with Filter controller for non-self regulating processes. Other published correlations (not based upon the IMC framework) for PID with Filter controllers fix the filter time constant at one-tenth the derivative time regardless of the model of the process. In contrast, the novel IMC correlations presented in this paper calculate a filter time constant based upon the model of the process and the user's choice for the closed-loop time constant. The set point tracking and disturbance rejection performance of the proposed IMC tunings is demonstrated using simulation studies and a bench-scale experimental system. The proposed IMC tunings are shown to perform as well as various PID correlations (with and without a filter term) while requiring considerably less controller action.     

Simple PID parameter tuning method based on outputs of the closed loop system

Most of the existing PID parameters tuning methods are only effective with pre-known accurate system models, which often require some strict identification experiments and thus infeasible for many complicated systems. Actually, in most practical engineering applications, it is desirable for the PID tuning scheme to be directly based on the input-output response of the closed-loop system. Thus, a new parameter tuning scheme for PID controllers without explicit mathematical model is developed in this paper. The paper begins with a new frequency domain properties analysis of the PID controller. After that, the definition of characteristic frequency for the PID controller is given in order to study the mathematical relationship between the PID parameters and the open-loop frequency properties of the controlled system. Then, the concepts of M-field and θ-field are introduced, which are then used to explain how the PID control parameters influence the closed-loop frequency-magnitude property and its time responses. Subsequently, the new PID parameter tuning scheme, i.e., a group of tuning rules, is proposed based on the preceding analysis. Finally, both simulations and experiments are conducted, and the results verify the feasibility and validity of the proposed methods. This research proposes a PID parameter tuning method based on outputs of the closed loop system.     

MIMO extended predictive control-implementation and robust stability analysis

The objective of this work is to develop a new tuning strategy for multivariable extended predictive control (EPC). A natural concern is the problem of ill conditionality in controlling multi-input multi-output (MIMO) systems. The main advantage of EPC is that it has a simple and effective tuning strategy that results in a well-conditioned system which can achieve tight closed-loop response. Moreover, unlike most existing model predictive control tuning strategies, the proposed strategy establishes a direct relationship between one main tuning parameter for each subprocess of the MIMO system. This tuning method has been derived based on the assumption of an infinite control horizon resulting in powerful stability for the nominal case and in the presence of model uncertainty. This tuning method is applicable to unconstrained multivariable processes, and was proven to have good control on nonsquare systems. The main features of the new tuning strategy are practically illustrated on a MIMO temperature system with improved control performance as compared to move suppressed predictive control.     

CONVEX CONTROLLER DESIGN APPLIED TO AC INDUCTION MOTOR TO SATISFY MULTIPLE SIMULTANEOUS SPECIFICATIONS

The application of a closed-loop specification oriented feedback control design method, which addresses the design of controllers to satisfy multiple simultaneous conflicting closed-loop performance specifications is presented. The proposed approach is well suited to the design of controllers which must meet a set of conflicting performance specifications. Gain tuning is central to the design process, however, the tuning process is greatly simplified over that presented by the problem of tuning a PID controller for example. The proposed control method is applied to an AC induction motor, with an inner-loop flux vector controller applied to design a position control system. Experimental results verify the effectiveness of this method.     

Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload

The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers.     

Multivariable design of improved linear quadratic regulation control for MIMO industrial processes

In this study, a multivariable linear quadratic control system using a new state space structure was developed for the chamber pressure in the industrial coke furnace. Such processes typically have complex and nonlinear dynamic behavior, which causes the performance of controllers using conventional design and tuning to be poor or to require significant effort in practice. The process model is first treated into a new state space form and the implementation of linear quadratic control is designed using this new model structure. Performance in terms of regulatory/servo, disturbance rejection and measurement noise problems were all compared with the recent model predictive control strategy. Results revealed that the control system showed more robustness and improved the closed-loop process performance under model/process mismatches.     

On the selection of tuning methodology of FOPID controllers for the control of higher order processes

In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modelling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is also presented. The time domain optimal tuning of FOPID controllers have also been carried out to handle these higher order processes by performing optimization with various integral performance indices. The paper highlights on the practical control system implementation issues like flexibility of online autotuning, reduced control signal and actuator size, capability of measurement noise filtration, load disturbance suppression, robustness against parameter uncertainties etc. in light of the above tuning methodologies.     

Iterative tuning of modified uncertainty and disturbance estimator for time-delay processes: A data-driven approach

Uncertainty and disturbance widely exist in the process industry, which may deteriorate control performance if not well handled. The uncertainty and disturbance estimator (UDE) emerges as a promising solution by treating the external disturbances and internal uncertainties simultaneously as a lumped term. To overcome its limitation caused by time delay, a modified UDE (MUDE) has been proposed recently. However, its parameter tuning relies heavily on trial-and-error, thus being time-consuming in balancing the robustness and performance. To this end, this paper aims to develop an automatic tuning procedure for the MUDE-based control system. The quantitative relationship between system performance and the scaled parameters is empirically built. Iterative Feedback Tuning (IFT) is utilized to approximate the nominal model towards actual process. Through the empirical formula and optimized model, an automatic design procedure is proposed after taking into account the system robustness and output performance simultaneously. Simulation results show the superiority of the closed-loop performance over the original MUDE controllers. The experimental results validate the feasibility of the method proposed in this paper, depicting a promising prospect in the practical application.     

Stabilization and PID tuning algorithms for second-order unstable processes with time-delays

Open-loop unstable systems with time-delays are often encountered in process industry, which are often more difficult to control than stable processes. In this paper, the stabilization by PID controller of second-order unstable processes, which can be represented as second-order deadtime with an unstable pole (SODUP) and second-order deadtime with two unstable poles (SODTUP), is performed via the necessary and sufficient criteria of Routh-Hurwitz stability analysis. The stability analysis provides improved understanding on the existence of a stabilizing range of each PID parameter. Three simple PID tuning algorithms are proposed to provide desired closed-loop performance-robustness within the stable regions of controller parameters obtained via the stability analysis. The proposed PID controllers show improved performance over those derived via some existing methods.     

Auto-tuning of PID controller parameters with supervised receding horizon optimization

In this paper, a novel two-layer online auto-tuning algorithm is presented for a nonlinear time-varying system. The lower layer consists of a conventional proportional-integral-derivative (PID) controller and a plant process, while the upper layer is composed of identification and tuning modules. The purpose of the upper layer is to find a set of optimal PID parameters for the lower layer via an online receding horizon optimization approach, which result in a time-varying PID controller. Through mathematical analysis, the proposed system performance is equivalent to that of a standard generalized predictive control. Simulation and experiment demonstrate that the new method has a better control system performance compared with conventional PID controllers.     

A novel interval type-2 fractional order fuzzy PID controller: Design,performance evaluation,and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.     

Using MV overshoot as a tuning metric in choosing DMC move suppression values

Traditionally the tuning of dynamic matrix control (DMC) type multivariable controllers is done by trial and error. The APC engineer chooses arbitrary starting values and tests the performance on a simulated controller. The engineer then either increases the values to suppress movement more, or decreases them to have the manipulated variables move faster. When the controller performs acceptably in simulation, then the tuning is improved during the commissioning of the controller on the plant. This is a time consuming and unscientific exercise and therefore often does not get the required attention. This leads to unacceptable controller behaviour during commissioning and sub-optimal control once commissioning is completed. This paper presents a new method to obtain move suppression factors for DMC type multivariable controllers by using a Nelder Mead search algorithm to find move suppressions that will provide acceptable control behaviour. Acceptable behaviour is described by characterising the dynamic move plan calculated by the controller for each of the manipulated variables.     

Robust on-line relay automatic tuning of PID control systems

In this paper, a robust on-line relay automatic tuning method for PID control systems is developed which expand on the application domain of Astrom's renowned relay autotuning method. In the proposed configuration, a relay is applied to an inner loop of a controller-stabilised process in the usual manner. Using the induced limit cycle oscillations from the closed-loop system, the controller settings may be re-tuned non-iteratively to achieve enhanced performance without disrupting closed-loop control. Two control tuning methodologies are developed -- a direct and an indirect method based on an explicit process model. Simulation examples and a real-time experiment are provided to illustrate the practical appeal and potential advantages of the proposed method over the basic one.     

Fractional order model reduction approach based on retention of the dominant dynamics: application in IMC based tuning of FOPI and FOPID controllers

Fractional order PI and PID controllers are the most common fractional order controllers used in practice. In this paper, a simple analytical method is proposed for tuning the parameters of these controllers. The proposed method is useful in designing fractional order PI and PID controllers for control of complicated fractional order systems. To achieve the goal, at first a reduction technique is presented for approximating complicated fractional order models. Then, based on the obtained reduced models some analytical rules are suggested to determine the parameters of fractional order PI and PID controllers. Finally, numerical results are given to show the efficiency of the proposed tuning algorithm.     

New tuning method for PID controller

In this paper, a tuning method for proportional-integral-derivative (PID) controller and the performance assessment formulas for this method are proposed. This tuning method is based on a genetic algorithm based PID controller design method. For deriving the tuning formula, the genetic algorithm based design method is applied to design PID controllers for a variety of processes. The relationship between the controller parameters and the parameters that characterize the process dynamics are determined and the tuning formula is then derived. Using simulation studies, the rules for assessing the performance of a PID controller tuned by the proposed method are also given. This makes it possible to incorporate the capability to determine if the PID controller is well tuned or not into an autotuner. An autotuner based on this new tuning method and the corresponding performance assessment rules is also established. Simulations and real-time experimental results are given to demonstrate the effectiveness and usefulness of these formulas.     

Development of characteristic equations and robust stability analysis for MIMO move suppressed and shifted DMC

Discrete-time controller and closed-loop transfer functions were developed for move suppressed λ and the recently formulated m-shifted multiple-input-multiple-output (MIMO) dynamic matrix control (DMC). Using these transfer functions, robust analyses were conducted for MIMO plants by varying corresponding delay and gain ratios of the system. In all instances, robust plots indicate that the shifted DMC is less sensitive and hence more robust to variations in the plant parameters than move suppressed DMC. It was shown that the design of these MIMO DMC controllers depends on the plant closed-loop performance and overall stability, since the selection of λ and m directly influences the plant robustness and closed-loop dynamics.