Simple Tuning Rules for Dead-Time Compensation of Stable, Integrative, and Unstable First-Order Dead-Time Processes

Twice-optimal control design with construction pruning for second order plus time delay systems

To effectively control a class of second-order plus time delay (SOPTD) systems, based on twice-optimal control (TOC) and construction pruning (CP) methods, an SOPTD-TOCCP controller is proposed, which can achieve strong robustness and excellent set-point tracking performance. The TOC controller of the SOPTD is designed based on a classical cascade controller and an extended state observer (ESO). A fast and accurate method is proposed to help engineers obtain the optimal time scale, which is the most critical parameter for regulating control performance. The influence of different parameter sensitivities on SOPTD is studied. In addition, a new robust enhancement method is proposed for SOPTD systems. A construction pruning method for SOPTD systems is proposed to further improve control performance, particularly robustness. Finally, a comparison with other control methods demonstrates that the SOPTD-TOCCP controller is simple, reliable, and versatile and can achieve better control performance.

A review from 1996 to 2021 of tuning methodologies and controller structures applied for an unstable/stable (bio)reactor with imperfect mixing and bypass

This paper presents a critical review of tuning methodologies and controller structures applied to the Cholette bioreactor. This (bio)reactor has been studied extensively by the automatic control community from the point of view of controller structures and tuning methodologies, from controllers with a single structure to nonlinear controllers, and from the synthesis method to the frequency response. Therefore, new trends and opportunities of study have been detected with regard to their operating points, controller structures and tuning methodologies which could be addressed for this system.

A comparative study of various Smith predictor configurations for industrial delay processes

Efficient control of industrial delay processes is a challenging problem in the field of process control. Time delays are generally experienced in industrial processes from distance velocity lags, composition analysis loops, recycle time, mass, and energy transportation time. A high time delay adds a large phase lag to the system, thereby affecting the closed-loop control system stability and thus not easily controlled with PID approach. Smith predictor (SP) is a prominent technique based on process model for processes with high time delay. Unfortunately, the performance of SP deteriorates when the plant model is inaccurate. To overcome the problems related to conventional SP, various modifications have been suggested over the years in terms of structure alterations and controller parameters tuning improvements. This paper focuses on a comparative study of various Smith predictor configurations available in the literature for controlling inverse, integrating, stable and unstable industrial processes with time delay.

Dead-Time Compensation for the First-Order Dead-Time Processes: Towards a Broader Overview

The article reviews the results of a number of recent papers dealing with the revision of the simplest approaches to the control of first-order time-delayed systems. The concise introductory review is extended by an analysis of two discrete-time approaches to dead-time compensation control of stable, integrating, and unstable first-order dead-time processes including simple diagnostics of the model used and focusing on the possibility of simplified but reliable plant modelling. The first approach, based on the first historically known dead-time compensator (DTC) with possible dead-beat performance, is based on the reconstruction of the actual process variables and the compensation of input disturbances by an extended state observer (ESO). Such solutions play an important role both in a disturbance observer (DOB) based control and in an active disturbance rejection control (ADRC). The second approach considered comes from the Smith predictor with two degrees of freedom, which combines feedforward control with output disturbance reconstruction and compensation by the parallel plant model. It is shown that these two approaches offer advantageous properties in the case of actuator limitations, in contrast to the commonly used PID controllers. However, when applied to integrating and unstable first-order systems, the unconstrained and possibly unobservable output disturbance signal of the second solution must be eliminated from the control loop, due to the hidden structural instability of the Smith predictor-like solutions. The modified solutions, usually referred to as filtered Smith predictor (FSP), then no longer provide a disturbance signal and thus no longer fully fit into the concept of Industry 4.0, which is focused on further optimization, predictive maintenance in dynamic systems, diagnosis, fault detection and fault identification of dynamic processes and forms the basis for the digitalization of smart production. Nevertheless, the detailed analysis of the elimination of the unstable disturbance response mode is also worth mentioning in terms of other possible solutions. The application of both approaches to the control of a thermal process shows almost equivalent quality, but with different dependencies on the tuning parameters used. It is confirmed that a more detailed identification of the controlled process and the resulting higher complexity of the control algorithms does not necessarily lead to an increase in the resulting quality of the transients, which underlines the importance of the simplified plant modelling for practice.

Novel control strategy for non-minimum-phase unstable second order systems: generalised predictor based approach

A control structure based on generalized predictor is proposed to control non-minimum phase unstable second order processes with time delay. The scheme contains a predictor structure and a direct synthesis method based primary controller for servo tracking. The predictor structure consists of two filters acting on input and current output which are designed to provide noise attenuation and disturbance rejection. A set-point filter minimises the overshoot caused by the introduction of additional zeros of the controller in the overall closed loop transfer function so as to smooth the tracking performance. Different second order unstable time delay systems are considered and Integral Absolute Error (IAE) and Total Variation (TV) measures are used for comparing the performances quantitatively. The method is implemented experimentally on an inverted pendulum. The proposed predictive strategy is found to provide enhanced control performances in comparison to the existing literature methods.

Simplified filtered Smith predictor for high-order dead-time processes

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.

Asymmetries in the Disturbance Compensation Methods for the Stable and Unstable First Order Plants

This paper analyzes the first-order and first-order time-delayed systems control approaches, focusing mainly on unstable systems. First, it discusses asymmetries between the disturbance observer-based (DOB) control with decoupled tracking and the disturbance rejection responses, stressing applications to stable and unstable plants. The paper analyzes some DOB-based control solutions for unstable systems which do not use internal closed-loop stabilization. The novelty of the paper is thorough study accompanied with a comprehensive explanation of the differences between two distinct approaches: the transfer-function- and the closed-loop-based feedforward control approach from the point of view of control constraints. It is clearly illustrated that the main cause of instability of DOB-based approaches, applied to unstable systems, is given by their effort to impose on the system the unstable dynamics of the chosen nominal process model. It is also shown that the closed-loop stability of the DOB-based control, applied to the unstable systems, can be restored by using the supervising reference model control (RMC). The main novelty of the proposed approach is that its eliminates the mentioned stability problems while maintaining the full functionality of the chosen control structures. RMC has so far only been implemented for generating a setpoint feedforward signal. However, by generalization of this approach for disturbance rejection, the methodology of DOB design, based on nominal models, can be extended to the control of unstable systems. Without the use of disturbance reference models, the interactions of the master stabilizer with disturbance compensation cannot be eliminated. Without the internal stabilization, the stable transients can only be achieved by designing controllers based on stable models, instead of unstable ones. The existing modifications of DOB-based schemes for unstable plants, proposed in some references, are shown to lead to traditional Proportional-Integrative (PI) control, thus losing all the advantages over the PI controllers. In all the considered structures, the role of integrating models is also emphasized.

New simple approach for enhanced rejection of unknown disturbances in LTI systems with input delay

This work proposes the extension of the simplified filtered Smith predictor (SFSP) for state-space systems to improve rejection of matched and unmatched unknown disturbances in LTI systems with input delay. The proposed structure is simpler than others recently proposed in the literature and can be applied to continuous-time or discrete-time systems. Furthermore, it allows improving rejection of both matched and unmatched disturbances, while also enhancing noise attenuation and robustness characteristics. Finite spectrum assignment (FSA) based implementation is used in order to guarantee the internal stability of the proposed controller. Simulation and experimental results are used to show the usefulness of the proposal.

Enhanced PID Controller for Non-Minimum Phase Second Order Plus Time Delay System

A tuning method is developed for the stabilization of the non-minimum phase second order plus time delay systems. It is well known that the presence of positive zeros pose fundamental limitations on the achievable control performance. In the present method, the coefficients of corresponding powers of s, s2 and s3 in the numerator are equated to α, β and γ times those of the denominator of the closed-loop system. The method gives three simple linear equations to get the PID parameter. The optimal tuning parameters α, β and γ are estimated by minimizing the Integral Time weighted Absolute Error (ITAE) for servo problem using fminsearch MATLAB solver aimed at providing lower maximum sensitivity function and keeping in check with the stability. The performance under model uncertainty is also analysed considering perturbation in one model parameter at a time using Kharitonov’s theorem. The closed loop performance of the proposed method is compared with the methods reported in the literature. It is observed that the proposed method successfully stabilizes and improves the performance of the uncertain system under consideration. The simulation results of three case studies show that the proposed method provides enhanced performance for the set-point tracking and disturbance rejection with improved time domain specifications.

Tuning of a dead-time compensator focusing on industrial processes

This paper proposes tuning rules for the Simplified Dead-Time Compensator (SDTC), which is intended to deal with stable, unstable and integrative dead-time processes. The main contribution is the proposal of new guidelines for the tuning of the robustness filter. The new set of rules allow for the use of lower order filters which are able to simultaneously account for closed-loop robustness and noise attenuation. Through illustrative examples, it is shown that the proposed approach provides enhanced disturbance rejection and noise attenuation in the control of industrial processes when compared with other recently published works. Furthermore, the internal temperature of an in-house thermal chamber is controlled to evaluate the applicability of the strategy on real processes.

Discrete-time domain two-degree-of-freedom control design for integrating and unstable processes with time delay

A discrete-time domain two-degree-of-freedom (2DOF) design method is proposed for integrating and unstable processes with time delay. Based on a 2DOF control structure recently developed, a controller is analytically designed in terms of the H2 optimal control performance specification for the set-point tracking, and another controller is derived by proposing the desired closed-loop transfer function for load disturbance rejection. Both controllers can be tuned relatively independent to realize control optimization. Analytical expression of the set-point response is given for quantitatively tuning the single adjustable parameter in the set-point tracking controller. At the meantime, sufficient and necessary conditions for holding robust stability of the closed-loop control system are established for tuning another adjustable parameter in the disturbance rejection controller, along with numerical tuning guidelines. Illustrative examples from the literature are used to demonstrate the effectiveness of the proposed method.