Open-loop Unstable Processes Research Articles

An Internal Model Based—Sliding Mode Control for Open-Loop Unstable Chemical Processes with Time Delay

This paper presents a dynamic sliding mode control (DSMC) for open-loop unstable chemical or biochemical processes with a time delay. The controller is based on the sliding mode and internal model control concepts. The proposed DSMC has an internal P/PD controller to provide systems with disturbance rejection. An identification method approximates the open-loop unstable nonlinear process to a first-order delayed unstable process (FODUP). The reduced-order model(FODUP) is used to synthesize the new controller. The performance of the controller is stable and satisfactory despite nonlinearities in the operating conditions due to set-point and process disturbance changes. In addition, the performance analysis of the control schemes was evaluated based on various indices and transient characteristics, including the integral of squared error (ISE), the total variation of control effort (TVu), the maximum overshoot (Mp), and the settling time (ts). Finally, the process output and the control action for all controllers are compared using the nonlinear process as the real plant.

Grey Wolf Optimizer-Based Optimal Controller Tuning Method for Unstable Cascade Processes with Time Delay

This paper presents a controller design technique for cascade control systems based on the grey wolf optimization (GWO) algorithm. In the proposed control scheme, the proportional-integral-proportional-derivative (PI-PD) controller structure is used to control both the open-loop unstable process in the primary loop and the stable process in the secondary loop. To determine the optimal controller parameters, a new optimization algorithm is used in which the Euclidean distance function is used as a multi-objective function. A symmetry property of the Euclidean distance function is that its distance does not depend on the starting point and destination. The multi-objective function is designed according to system time response specifications such as settling time, overshoot, and steady-state error. Thus, the optimization algorithm allows the simultaneous determination of all controller parameters according to the desired output response. Three simulation studies are presented in the paper and the results are compared with studies using various methods based on internal model control, a modified Smith predictor, and a genetic algorithm. The simulation results reveal that the proposed method improves the performances of the systems in the control of cascade processes.

A Generalised Dynamic Matrix Control for unstable processes based on filtered predictions

This paper presents a Generalised Dynamic Matrix Control (GDMC) algorithm that can be used to control open-loop unstable processes. In contrast to the Dynamic Matrix Control (DMC), the GDMC is able to provide internally stable predictions due to a generalised filtered approach. The conditions to achieve internal stability are shown and a new data-driven filter design procedure is proposed. Two simulation case studies are presented to illustrate the usefulness of the GDMC.

Reinforcement learning based adaptive PID controller design for control of linear/nonlinear unstable processes

Control of unstable process is challenging owing to its dynamic nature, output multiplicities and stability issues. This research work focuses to develop a generic data driven modified Proximal Policy Optimization (m-PPO) reinforcement learning based adaptive PID controller (RL-PID) for the control of open loop unstable processes. The RL agent acting as the supervisor explores and identifies optimal gains for the PID controller to ensure desired servo and regulatory performance. Adaptive modifications in terms of inclusion of action repeat, modified reward function and early stopping criterion are incorporated to the m-PPO algorithm to handle the unbounded output nature of unstable processes. Effect of m-PPO algorithm is proven in terms of reward earned by the RL agent. Servo and regulatory performance of the proposed RL-PID controller is compared with that of classical PID controller, Deep Discriminant Policy Gradient based PID controller and Advantage Actor Critic based PID controller on various linear, non linear, multivariable unstable systems including unstable jacketed CSTR process and Unmanned Aerial Vehicle in simulation environment. Validation of the proposed controller is also done in real time level control process station, a laboratory level experimental test rig. It is observed that the proposed RL-PID performs satisfactorily better than the other controllers in both qualitative and quantitative metrics. The striking feature of this control scheme is that it eliminates the need of process modeling and pre-requisite knowledge on process dynamics and controller tuning. The proposed controller is a data driven generic approach that can be directly applied to any industrial process.

Optimal PI–PD Controller Design for Pure Integrating Processes with Time Delay

Though Proportional-Integral-Derivative (PID) controllers are commonly being used for process control applications, it has been proven that they may give unacceptable closed loop responses for open loop unstable processes including integrating ones. Hence, this paper addresses to tuning of PI–PD controllers which is an extension of PID controllers and uses PD part in an inner feedback loop to convert the open loop unstable processes to a stable one so that PI controller in the forward path can be used to achieve a better closed loop response. PI–PD tuning parameters are determined from simple analytical rules which were obtained from minimization of the control system error based on IST3E criterion which is an integral performance index and has been proven to be resulting in very satisfactory closed loop responses. Derived tuning rules are in terms of the assumed process transfer function parameters, namely the gain and time delay. Effectiveness and superiority of obtained tuning rules have been shown by simulation examples.

Pre-stabilised Predictive Functional Control for Open-loop Unstable Dynamic Systems

Abstract Predictive functional control (PFC) is the simplest model-based algorithm, equipped with the attributes of a fully fledged predictive controller but at the cost and complexity threshold of a standard PID regulator. It has proven benefits in controlling stable SISO dynamic systems, but similarly to its competitor PID, it loses efficacy when a challenging application is introduced. In this paper, we present a modified PFC approach, especially tailored for open-loop unstable processes, using pre-stabilisation to efficiently control the undesirable dynamics at hand. This is essentially a two-stage design scheme with implications for PFC tuning and constraint handling. The proposal, nevertheless, is straightforward and intuitive, and provides improved closed-loop control in the presence of external perturbations against the standard PFC, and significantly better performance overall compared to the common PID algorithm, as demonstrated in a numerical case-study.

Enhanced control of unstable cascade systems using direct synthesis approach

This paper presents a controller design method for the open-loop unstable process in the primary loop and the open-loop unstable, integrating and stable processes in the secondary loop of the simple cascade control configuration. The controller of the secondary loop and the primary loop is designed through a direct synthesis (DS) approach in the frequency domain for load disturbance rejection and set-point tracking, respectively. Moreover, a set-point filter is used to reduce unnecessary overshoot in servo tracking. The proposed method is applicable to a wide range of processes having unstable, integrating and stable dynamics in a unified way. It avoids the complexity of order reduction and dead time approximation of the plant. The simulation study illustrates that the present approach provides enhanced closed-loop performance as compared to the approaches recently reported in the literature.

Predictor-based fractional disturbance rejection control for LTI fractional-order systems with input delay

In this paper, a predictor-based fractional disturbance rejection control (PFDRC) scheme is proposed for processes subject to input delay. The proposed scheme can be generally applied to open-loop stable, integrative, and unstable integer-order processes, but it can be particularly utilized for open-loop stable fractional-order systems. A closed-loop reference model is formulated based on Bode’s ideal transfer function. The primary control design objective is to enable the output of input-delay process to follow the closed-loop reference model. Towards this end, the closed-loop transfer function of the PFDRC must take the same structure as that of the reference model. Meanwhile, the adverse effects of the input delay must be mitigated. To meet the latter, a filtered Smith predictor (FSP) is employed to provide a prediction of delay-less output response. To address the former, process dynamics are treated as a common disturbance; then, a fractional-order extended state observer (FESO) is introduced to estimate the delay-less output response and also the total disturbance (i.e. external disturbance and system uncertainties). The PFDRC feedback controller is easily derived by the gain crossover frequency of Bode’s ideal transfer function which facilitates the tuning process. The convergence analysis of the FESO is carried out in terms of BIBO stability. The effectiveness of the proposed control scheme is verified through three illustrative examples from the literature.

Design and development of modified RTD-A controller for unstable bioreactor

Control of open loop unstable process is a challenging one owing to the presence of right hand plane pole(s). The spotlight of this paper is to develop modified Robustness set point Tracking Disturbance rejection and Aggressiveness controller(RTD-A) for an unstable process. The RTD-A controller formulation is modified accordingly to suit the unstable process. The proposed control scheme has two control loops. The unstable process is initially stabilized by an inner feedback loop consisting of a proportional controller. The RTD-A control strategy is then implemented on the stabilized plant. The developed control scheme is validated on an nonlinear unstable bioreactor plant model in a simulation environment. It is found that the proposed controller has better servo and regulatory performance when compared to the conventional IMC-PID controller. Effect of variation in the tuning parameters of the controllers on the process output is analysed in detail.

Importance of heat-transfer area in the controllability of openloop unstable reactors

Openloop unstable reactors present probably the most interesting and challenging control problem in chemical engineering. They can occur when the reactions are exothermic and irreversible and when reactant per-pass conversion is not high so that there is “fuel” available in the reactor to cause a temperature runaway. An openloop unstable process cannot be operated without a feedback controller on automatic. In a typical CSTR process the reactor temperature is controlled by manipulating the flowrate of the cooling medium. Closedloop stability may be achieved if the reactor is designed with sufficient heat-transfer area. The temperature control loop exhibits “conditional stability” since the controller gain must lie inside some range of values whose span depends on the heat-transfer area selected in the design. The purpose of this paper is to demonstrate the critical design trade-off between heat-transfer area and dynamic controllability in openloop unstable CSTRs.

Interactive Tuning Tool of Proportional-Integral Controllers for First Order Plus Time Delay Processes

Engineering education and, particularly, control engineering, has shown growth in research and development activities during last years. Currently, proportional–integral (PI) and proportional–integral–derivative (PID) controllers are the most commonly used in industrial process applications. Nonetheless, it is reported that many of them are badly tuned. From an educational perspective, it is crucial for the student to understand the importance of tuning a control loop correctly. This paper presents an interactive tool focused on the study of PI controllers. The tool provides a set of tuning rules for both open-loop stable and unstable first order plus time delay processes. The different tuning rules can be compared interactively by the user, allowing a critical analysis of basic concepts about stability, robustness, and performance in PI control loops. In addition to educational purposes, the tool has been developed, taking into account practical considerations, such as simulation with a controller discrete implementation, process input saturations, and windup effect. We evaluated students’ achievement in the final examination in the Automatic Control course of the Electronics Engineering degree. Students showed significant improvement in their understanding of PI controller design. A survey and a practical case study were performed to evaluate the effectiveness of the proposed tool.

Implementations of the Tennessee Eastman Process in Modelica

The Tennessee Eastman process is a typical industrial process that consists of five main process units: a two-phase reactor where an exothermic reaction occurs, a separator, a stripper, a compressor, and a mixer. This is a nonlinear open-loop unstable process that has been used in many studies as a case study for plant-wide control, statistical process monitoring, sensor fault detection, and identification of data-driven network models. There are many implementations of this process with different levels of detail, but there is no implementation developed in an object-oriented modeling language such as Modelica.This paper presents the development of two different Modelica libraries, TEprocess and TESimplified, that facilitate the implementation of the Tennesse Eastman process. These two libraries have been validated using data available in the literature.

Analytical design of an industrial two-term controller for optimal regulatory control of open-loop unstable processes under operational constraints

This paper proposes a novel optimization-based approach for the design of an industrial two-term proportional-integral (PI) controller for the optimal regulatory control of unstable processes subjected to three common operational constraints related to the process variable, manipulated variable and its rate of change. To derive analytical design relations, the constrained optimal control problem in the time domain was transformed into an unconstrained optimization problem in a new parameter space via an effective parameterization. The resulting optimal PI controller has been verified to yield optimal performance and stability of an open-loop unstable first-order process under operational constraints. The proposed analytical design method explicitly takes into account the operational constraints in the controller design stage and also provides useful insights into the optimal controller design. Practical procedures for designing optimal PI parameters and a feasible constraint set exclusive of complex optimization steps are also proposed. The proposed controller was compared with several other PI controllers to illustrate its performance. The robustness of the proposed controller against plant-model mismatch has also been investigated.

Constraint handling optimal PI control of open-loop unstable process: Analytical approach

This paper proposes the closed-form analytical design of proportional-integral (PI) controller parameters for the optimal control of an open-loop unstable first order process subject to operational constraints. The main idea of the design process is not only to minimize the control performance index, but also to cope with the constraints in the process variable, controller output, and its rate of change. To derive an analytical design formula, the constrained optimal control problem in the time domain was transformed to an unconstrained optimization in a parameter space associated with closed-loop dynamics. By taking advantage of the proposed analytical approach, a convenient shortcut algorithm was also provided for finding the optimal PI parameters quickly, based on the graphical analysis for the optimal solution of the corresponding optimization problem in the parameter space. The resulting optimal PI controller guarantees the globally optimal closed-loop response and handles the operational constraints precisely.

A simple method of tuning parallel cascade controllers for unstable FOPTD systems

A simple method is proposed to design parallel cascade controllers for open loop unstable processes. A proportional (P)controller is considered for the secondary loop and a proportional integral (PI) controller is considered for the primary loop (P/PI control configuration). Coefficients of the corresponding powers of s (Laplace variable), in the numerator is matched with the coefficients of the corresponding powers of s in the denominator of a closed loop transfer function for a servo problem. Three simulation case studies are considered in this paper. The first case involves a stable secondary loop process and an unstable primary process, the second case involves both unstable primary and secondary processes and the third one, a simulation application to a nonlinear bioreactor model equations. For comparison purposes, P/PI controller design is also carried out by improved simultaneous relay autotuning method, synthesis method and minimizing ISE criterion method. It is found that the proposed method gives a better performance. Robust stability analysis using the complimentary sensitivity function is carried out. The present method is found to be more robust.

On the filtered Smith predictor with feedforward compensation

This paper discusses about a general implementation structure of the filtered Smith predictor for single-input single-output processes with a measurable disturbance. Dead-time free models are used to feed-forward the measurable disturbance into the feedback controller. It is demonstrated that the proposed controller can be applied to control open-loop unstable processes with different time delays associated with control and disturbance signals. Different simulated industrial processes are used to illustrate the proposed strategy properties and advantages over other time-delay compensators.

Recycle Compensator Facilitates Rapid Parameterization of Proportional Integral/Derivative (PI/D) Controllers for Open-Loop Unstable Recycle Processes

Processes with recycle are quite common in the process industries. It has been pointed out that such processes often exhibit unusual dynamics, such as open-loop instability, which makes the task of designing a model-based controller for them challenging. In this work, a design procedure for rapid parametrization of simple internal model control (IMC)-based proportional integral/derivative (PI/D) controller for open-loop unstable recycle processes is proposed. In the proposed strategy, first, the recycle process model is decomposed into the forward and recycle path. Thereafter, a perfect/approximate compensator is designed for the global process. The final controllers for the global process are then parametrized using the compensated system model and implemented on the system. It was observed that the compensator was able to restore stability to the open-loop unstable recycle process model and simplifies its model order considerably. Simulation results obtained revealed that the recycle compensated system ...

On the filtered Smith predictor for MIMO processes with multiple time delays

This paper discusses about a unified implementation structure of the filtered Smith predictor (FSP) for MIMO processes with multiple time delays. Two kinds of dead-time free models are analyzed in order to extend the original properties of the SISO Smith predictor to MIMO processes with multiple time delays. It is demonstrated that FSP strategy can be applied to control open-loop unstable processes with multiple time delays by considering a model without any input, output or internal coupling delays. Moreover, for open-loop stable processes, it is shown that the FSP scheme can be used to speed-up disturbance rejection of processes with multiple time delays by using a nominal model without delay. Different simulation examples are used to illustrate the proposed strategy properties and advantages over other MIMO time-delay compensators. The results may be considered to control either square or non-square processes.

Determination of all feasible robust PID controllers for open-loop unstable plus time delay processes with gain margin and phase margin specifications

This paper proposes a novel alternative method to graphically compute all feasible gain and phase margin specifications-oriented robust PID controllers for open-loop unstable plus time delay (OLUPTD) processes. This method is applicable to general OLUPTD processes without constraint on system order. To retain robustness for OLUPTD processes subject to positive or negative gain variations, the downward gain margin (GMdown), upward gain margin (GMup), and phase margin (PM) are considered. A virtual gain-phase margin tester compensator is incorporated to guarantee the concerned system satisfies certain robust safety margins. In addition, the stability equation method and the parameter plane method are exploited to portray the stability boundary and the constant gain margin (GM) boundary as well as the constant PM boundary. The overlapping region of these boundaries is graphically determined and denotes the GM and PM specifications-oriented region (GPMSOR). Alternatively, the GPMSOR characterizes all feasible robust PID controllers which achieve the pre-specified safety margins. In particular, to achieve optimal gain tuning, the controller gains are searched within the GPMSOR to minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Thus, an optimal PID controller gain set is successfully found within the GPMSOR and guarantees the OLUPTD processes with a pre-specified GM and PM as well as a minimum IAE or ISE. Consequently, both robustness and performance can be simultaneously assured. Further, the design procedures are summarized as an algorithm to help rapidly locate the GPMSOR and search an optimal PID gain set. Finally, three highly cited examples are provided to illustrate the design process and to demonstrate the effectiveness of the proposed method.

Improved PID controller design for unstable time delay processes based on direct synthesis method and maximum sensitivity

In this paper, a proportional-integral-derivative controller in series with a lead-lag filter is designed for control of the open-loop unstable processes with time delay based on direct synthesis method. Study of the performance of the designed controllers has been carried out on various unstable processes. Set-point weighting is considered to reduce the undesirable overshoot. The proposed scheme consists of only one tuning parameter, and systematic guidelines are provided for selection of the tuning parameter based on the peak value of the sensitivity function (Ms). Robustness analysis has been carried out based on sensitivity and complementary sensitivity functions. Nominal and robust control performances are achieved with the proposed method and improved closed-loop performances are obtained when compared to the recently reported methods in the literature.