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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.

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.

This paper proposes a control structure suitable for high-order non-minimum phase (NMP) processes. In general, dead-time compensators (DTCs) firstly predict the process output with zero error at a steady-state and then a primary controller with an integrator is designed based on the delay-free model. The main advantage of the proposed structure is that the primary controller is only a state feedback gain with no integrators. This leads to fewer parameters to tune and lower order filters, while a robustness filter is used to reject disturbances and guarantee zero error at a steady state. Simulation results show better or equivalent performance compared to other recently published works, even kept the controller design simplicity.

In this paper, control of stable, unstable and integrating processes with large time delay in the presence of uncertainty, external disturbances and measurement noise is investigated. For this purpose, fractional order controllers in the parallel cascade scheme based on smith predictor are designed. The applied parallel cascade control strategy consists of a set point tracking controller, a disturbance rejection and a stabilizing controller. Set point tracking and disturbance rejection controllers are fractional order controllers and stabilizing controller is designed based on Routh–Hurwitz stability criterion. Also, the robust stability and the performance of the proposed strategy are studied in some details. The numerical simulation results are used to make comparisons with the other researchers’ works to show superiority of the designed controllers.

PID controllers are still widely practiced in the industrial systems. In the literature, many publications can be found considering PID controller design for unstable processes. However, owing to the structural limitations of PID controllers, generally, good closed loop performance cannot be achieved with a PID for controlling unstable processes and usually a step response with a high overshoot and oscillation is obtained. On the other hand, PI-PD controllers are proved to give very satisfactory closed loop performances for unstable processes. The paper presents a simple design method to tune parameters of a PI-PD controller for the control of the unstable processes with time delay. The proposed method is based on plotting the stability boundary locus, which is a locus dependent on the parameters of the controller and frequency, in the parameter plane. The method uses a new concept named centroid of the convex stability region. Simulation examples and an experimental application are given to illustrate the superiority of the proposed method over some existing ones.

First-order plus dead-time (FOPDT) models are broadly used in process control to represent damped dynamic processes with time delays. An explicit condition for parameter- and delay-dependent robust stability of FOPDT systems with varying uncertain parameters and delay is derived in this paper. An internal model control (IMC) approach is proposed to parameterize stabilizing controllers that satisfy the output tracking objective in time-varying FOPDT systems represented by an uncertain first-order dynamic model with a time-varying delay in the control input. The small-gain theorem is used to derive an explicit necessary and sufficient parameter-dependent robust stability condition as a function of the nominal system gain, nominal varying delay, nominal time constant, and the bounds of the parameter uncertainties. An equivalent proportional-integral-derivative (PID) controller is then extracted to facilitate the implementation of the proposed IMC-based robust control. The application of the proposed explicit robust stability condition is studied in the context of air-fuel ratio (AFR) control in lean-burn spark ignition (SI) engines with a large time-varying transport delay in the control loop due to the placement of the universal exhaust gas oxygen (UEGO) sensor downstream the catalytic converter.

This paper presents a decentralized PID controller design method for two input two output (TITO) systems with time delay using characteristic ratio assignment (CRA) method. The ability of CRA method to design controller for desired transient response has been explored for TITO systems. The design methodology uses an ideal decoupler to reduce the interaction. Each decoupled subsystem is reduced to first order plus dead time (FOPDT) model to design independent diagonal controllers. Based on specified overshoot and settling time, the controller parameters are computed using CRA method. To verify performance of the proposed controller, two benchmark simulation examples are presented. To demonstrate applicability of the proposed controller, experimentation is performed on real life interacting coupled tank level system.

This paper aims to find a practical solution to reduce oscillation on the Smith Predictor (SP) based design with the dead time (DT) uncertainty, making it less sensitive to DT change and more effective in disturbance rejection. First, a conditional feedback mechanism is introduced in SP to reduce the amount of oscillation caused by the model inaccuracies in the DT parameter. Then, to address the oscillation caused by the phase lag in traditional PI controller and uncertain dynamics, this conditional SP is combined with active disturbance rejection control (ADRC), assisted by the knowledge of process dynamics. A practical tuning method is provided for the practicing engineers. The proposed approach is validated in extensive simulation studies with different types of plants and in frequency domain analysis. The simulation results show significant improvements in performance robustness and transient response.

In this paper, a PID controller design method for the integrating processes based on frequency response matching is presented. Two approaches are proposed for the controller design. In the first approach, a double feedback loop configuration is considered where the inner loop is designed with a stabilizing gain. In the outer loop, the parameters of the PID controller are obtained by frequency response matching between the closed-loop system with the PID controller and a reference model with desired specifications. In the second approach, the design is directly carried out considering a desired load-disturbance rejection model of the system. In both the approaches, two low frequency points are considered for matching the frequency response, which yield linear algebraic equations, solution of which gives the controller parameters. Several examples are taken from the literature to demonstrate the effectiveness and to compare with some well known design methods.

Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes., Comment: 31 pages, 20 figures

This paper presents a dead-time compensation structure able to deal with stable and unstable multiple delay single input single output (SISO) systems. The proposed method aims to simplify the primary controller by replacing it for FIR filters placed at the feedback path. Such modification reduces the total number of parameters to be tuned which facilitates the overall design in comparison with other primary controllers normally considered. Simulation results show a better performance for the proposed control approach compared with other dead-time compensator (DTC) recently proposed in the literature.

Recently, fractional order (FO) processes with dead-time have attracted more and more attention of many researchers in control field, but FO-PID controllers design techniques available for the FO processes with dead-time suffer from lack of direct systematic approaches. In this paper, a simple design and parameters tuning approach of two-degree-of-freedom (2-DOF) FO-PID controller based on internal model control (IMC) is proposed for FO processes with dead-time, conventional one-degree-of-freedom control exhibited the shortcoming of coupling of robustness and dynamic response performance. 2-DOF control can overcome the above weakness which means it realizes decoupling of robustness and dynamic performance from each other. The adjustable parameter η2 of FO-PID controller is directly related to the robustness of closed-loop system, and the analytical expression is given between the maximum sensitivity specification Ms and parameters η2. In addition, according to the dynamic performance requirement of the practical system, the parameters η1 can also be selected easily. By approximating the dead-time term of the process model with the first-order Pade or Taylor series, the expressions for 2-DOF FO-PID controller parameters are derived for three classes of FO processes with dead-time. Moreover, compared with other methods, the proposed method is simple and easy to implement. Finally, the simulation results are given to illustrate the effectiveness of this method.

In industrial practice, controller designs are performed based on an approximate model of the actual process. It is essential to design a control system which will exhibit a robust performance because the physical systems can vary with operating conditions and time. Gain and phase margins are well known parameters for evaluating the robustness of a control system. This paper presents a tuning algorithm to design and tune PI controllers for stable processes with a small dead time while meeting specified gain and phase margins. Simulation examples are given to demonstrate that the proposed design method can result, in a closed-loop system, in better performances than existing design methods which are also based on user-specified gain and phase margins.

This paper presents the results of a heuristic approach for developing model predictive control (MPC) tuning rules. The tuning has been applied and tested in easy-to-use MPC. Process modeling in this MPC uses normalized input/ output range. As a result there is no need for tuning outputs, a procedure known as adjusting equal concern error. Penalties on moves are set as a function of process dead time as the primary factor, with some correction from process gain. The default calculation delivers robust control, which tolerates up to triple increase in process static gain. If control is too aggressive, further on-line adjustment can be done by set point reference trajectory. Test results show that this tuning is robust for process gain change, however, it is much less efficient in compensating for process dead-time changes. It was found that dead-time mismatch is much better compensated with the model correction filter. Combining the three handles, i.e., penalties on moves, reference trajectory, and model filter, easy and intuitively understandable MPC tuning was achieved. The findings are illustrated by numerous MPC simulated tests.

In this paper, a new design for Smith Predictor systems is presented. It employs a deliberately mismatched model to enhance performance over a perfectly matched system while using a simple primary controller. The design methodology is formulated in the frequency domain as an optimization problem and it turns out that an approximate solution can be obtained using the linear least squares method. To improve the performance further, a modified Smith Predictor system structure is also proposed, and it reduces the system into one involving second-order dynamics for the primary controller design. Illustrative simulation of several typical processes are included.

A PID type algorithm called Q-PID was developed to improve online quality control of continuous processes. It has adjustable parameters to improve the controlled variable response or to decrease the manipulated variable movements, hence decrease the cost of control. Q-PID has PID type terms, a lead/lag term and dead time compensation. All previously published work using this algorithm considered continuous systems. Discrete implementation must be analyzed so that it can be used practically. This paper presents a sound development and simulation of the three possible dead time implementation schemes, Smith predictor, analytical predictor, and generalized analytical predictor that could be used for discrete implementation. It was discovered that either the Smith predictor or analytical predictor techniques could be used in the Q-PID with satisfactory results. The generalized analytical predictor results in drastic cost increases and instability in the presence of modeling error. The Smith predictor is the suggested method as it performs the best in the presence of modeling error and is simple and easy to implement.

Due to recent requirements by the U.S.E.P.A. towards the standards on chlorine residuals for chlorination and dechlorination processes, together with the commitment to optimize the process operating conditions for chemical cost savings and to let the plant operator have more time working on other important projects, the City of Houston has been utilizing automatic control systems (Programmable Logic Controllers) at over twenty WWTPs to meet the above tasks. This paper will present one of the City's WWTPs which implemented the auto-control system. It also discusses how to solve the problems of noises in instrumentation signals and dead time which are common in auto-control systems. Finally, it will show how much success the system has complied with the U.S.E.P.A.'s requirements and effectively reduced the chemical costs.

In this paper, a decentralized PI/PID controller design method based on gain and phase margin specifications for two-input-two-output (TITO) interactive processes is proposed. The decouplers are designed for systems to minimize the interaction between the loops, and the first order plus dead time (FOPDT) model is achieved for each decoupled subsystem based on the frequency response fitting. An independent PI/PID controller is designed for each reduced order decoupled subsystem to obtain the desired gain and phase margins, and the performance is verified on the original interactive system to show the effectiveness of the proposed design method for the general class of TITO systems. Simulation examples are incorporated to validate the usefulness of the presented algorithm. An experimentation is performed on the Level-Temperature reactor process to show the practical applicability of the proposed method for the interactive system.

Several tuning methods, including Ziegler-Nichols, have been used for decades in the process industries. These methods have the important advantage of ease of use and provide relatively good tuning for the majority of loops. The methods all use a “first-order plus dead time” (FOPDT) model of the process. However, processes do not always fit the FOPDT model; most have multiple lags. The degree to which the process fits the FOPDT model determines how well the traditional tuning methods will work with the process. This paper examines several tuning methods and presents some comparisons and evaluations based on experiments using computer simulations of loops with various combinations of multiple-lag and dead time dynamics. Guidelines for the applicability of the tuning methods are presented, and several aspects of the methods, including the training requirements, are discussed.

This paper presents an effective design and robust tuning method for the control structure based on a series PD controller and a simple Disturbance Observer. All elements of the proposed controller are directly obtained from the low-order Integrating First-Order Plus Dead-Time (IFOPDT) model, used to approximate essential dynamic characteristics of lag-dominant stable, integrating and unstable plants. The structure of the proposed controller is an effective, easy to implement and tune, extension of the series PID controller. For the same robustness, a better disturbance rejection response is obtained by the proposed controller than that of the PID, by adjusting only two parameters with a clear meaning. A comparison with well-tuned PIDs, done by simulations, and the experimental results, obtained on a real thermal power plant, confirm that high performance and robustness are obtained, for dynamic characteristics common to industrial processes.

Many tuning strategies for model predictive control algorithms have been proposed in the literature depending on the conditionality of the system matrix and the choice of its cost function. In this paper, the properties of a new predictive controller termed extended predictive control (EPC) are investigated and presented. These properties are important to the understanding of the unique tuning strategy of EPC. EPC is based on the assumption of infinite horizon which is preferable to guarantee stability. The EPC properties are derived using a second order plant with relatively large dead time and is applicable to any open-loop stable system. The tuning strategy of EPC was applied to generalized predictive control with good results.

This paper discusses PID stabilization of a first-order-plus-dead-time (FOPDT) process model using the stability framework of the Hermite-Biehler theorem. The FOPDT model approximates many processes in the chemical and petroleum industries. Using a PID controller and first-order Pade approximation for the transport delay, the Hermite-Biehler theorem allows one to analytically study the stability of the closed-loop system. We derive necessary and sufficient conditions for stability and develop an algorithm for selection of stabilizing feedback gains. The results are given in terms of stability bounds that are functions of plant parameters. Sensitivity and disturbance rejection characteristics of the proposed PID controller are studied. The results are compared with established tuning methods such as Ziegler-Nichols, Cohen-Coon, and internal model control.

Good control of processes with long dead time is often achieved using a Smith predictor configuration. Typically a PI or PID controller is used; however, it is shown in this paper that for some situations improved set point and disturbance responses can be obtained if a PI-PD controller is used. Several methods are possible for selecting the parameters of the PI-PD controller but when the plant transfer function has no zeros, the use of the standard forms provides a simple algebraic approach, and also reveals why difficulties may be encountered if a PID controller is used. Some examples are given to show the value of the approach presented.

In this paper, a two-degree-of-freedom level control scheme for delay free processes is analyzed. The nominal performance and robustness are examined. And sufficient and necessary conditions for robust stability are derived. An alternative level control scheme is developed for processes with dead time and suboptimal controllers that can produce smooth response are derived analytically based on the internal model control. The scheme has an important feature in that it is simple and transparent in design and in the corporation of performance and robust stability issues. Numerical examples are provided to compare the proposed scheme with those developed.