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

Setpoint weighted PI-FOPD cascade controllers synthesis for unstable time-delayed processes satisfying prespecified safety margins

This article introduces a novel setpoint weighted PI-FOPD (SWPI-FOPD) cascade controller with a prefilter. It further describes a four-stage design strategy that sequentially enhances tracking responses, reduces overshoot, and ensures robustness for unstable time-delayed (UTD) processes. The controller applies to integrating and non-integrating UTD processes of any order and does not necessitate model order reduction or delay approximation. The strategy involves four stages, each targeting a specific aspect of performance improvement. The first stage designs the optimal and robust FOPD (ORFOPD) controller to accelerate tracking responses. In the second stage, the cascade optimal and robust PI (ORPI) controller ensures zero steady-state error. A gain and phase margin (GPM) tester determines the feasible specification-oriented regions (FSORs) on the KP1-KD1 and KP2-KI2 planes, aiding in selecting the ORFOPD and ORPI controllers to minimize the IAE or ISE index under ± 10% loop gain perturbations (LGPs). The third stage schedules setpoint weighting coefficients to reduce overshoot typically associated with UTD processes. The final stage uses a prefilter to refine the reference input signal and mitigate overshoot. A systematic design procedure is summarized to rapidly compute all controller gains in a step-by-step sequence. This SWPI-FOPD controller with a prefilter enhances robustness, provides rapid tracking response with zero steady-state error, and effectively reduces overshoot and IAE or ISE, even with ± 10% LGPs. Comparative simulations across three examples, along with a practical jacketed CSTR application, validate the feasibility and demonstrate the superior performance of the proposed controller.

IMC based modified Smith predictor for second order delay dominated processes with RHP

A modified Smith predictor (MSP) with IMC based tuning is proposed for second order delay dominated processes. These processes often exhibit unstable behaviour due to right half poles (RHP) with positive or negative zeros. The control scheme incorporates forward path PI/PID controller with a lead-lag filter and a PD controller in the feedback path. IMC technique having single tuning parameter is utilized to design the forward path controller, while the feedback path controller is tuned by Routh stability criterion. The proposed scheme ascertains quick set point following without overshoot and smooth disturbance rejection, resulting superior closed-loop performance compared to recent MSP schemes. Validation is made based on performance indices and stability margins.

Stabilization of Unstable Second-Order Delay Plants under PID Control: A Nyquist Curve Analysis

Time delays arise in various components of control systems, including actuators, sensors, control algorithms, and communication links. If not properly taken into consideration, time delays will degrade the closed-loop performance and may even result in instability. This paper studies the stabilization problem of the second-order delay plants with two unstable real poles. Stabilization conditions under PD and PID control are derived using the Nyquist stability criterion. Algorithms for computing feasible PD and PID parameter regions are proposed. In some special cases, the maximal range of delay for stabilization under PD control is also given.

The design of NMSS fractional-order predictive functional controller for unstable systems with time delay

Open-loop unstable systems are more difficult to control than stable processes. In presence of time delay and uncertainty, the complexity of problem increases. In this paper, non-minimal state space predictive functional control (NMSS-PFC) infrastructure has been generalized for control of unstable systems with time delay. At first, NMSS system representation has been extended for a so-called coprime-factorized equivalent model of the unstable processes. Then, the proposed NMSS-fractional-order PFC (NMSS-FOPFC) has been formulated via a fractional order cost function in terms of the output tracking error vector. In the developed formulation and via the NMSS structure, the constraints on inputs of the system could be easily formulated and employment of fractional order cost function led to improved performance even in case of disturbances, perturbations or uncertainties. Closed loop robust stability analysis was also performed based on small gain theorem and verified via simulations. Simulation examples show that the proposed NMSS-FOPFC results in improved nominal and perturbed responses compared to conventional methods. Comparison has been carried out by considering integral of absolute error (IAE) and integral of squared error (ISE) as well as step response transient and steady state properties and the control effort.

Optimized robust control for industrial unstable process via the mirror-mapping method

In this work, a novel optimized robust control algorithm, based on the mirror-mapping method, is proposed for a class of industrial unstable process with time delay. The optimizing criterion is to minimize the sensitivity function to enhance its robustness. The controllers are designed based on the Padé approximated mirror-mapping process with a stable form, other than the original unstable system. The developed algorithm could release the internal stability constraints to the unstable plant. By using the graphical stability criterion, a systematic methodology is derived to obtain the exact stabilizing region, where the sole design parameter is related to the stability degree of the closed-loop system. The proposed algorithm is with characteristics of concise and efficient design. Three experiments has been employed to illustrate that the control effects can achieve the satisfied performance in aspects of disturbance rejection and robustness.

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.