Robust Proportional Integral Controller Research Articles

Linear Quadratic Optimal Robust Multivariable Proportional-Integral Control Design for a Boiler-Turbine Unit

Abstract Boiler-turbine unit is a highly nonlinear, coupled, and ill-conditioned system. Moreover, the presence of physical constraints, such as actuator magnitude and rate limits, makes the system difficult to control. This paper employs a fixed multivariable proportional-integral (PI) controller of the I–P structure for robust linear quadratic (LQ) compensation of a nonlinear boiler-turbine benchmark. In order to ensure that a single PI controller works for the whole operating region of this nonlinear system, the linearized model of the system is represented as a norm-bounded, time-varying uncertain system. The ranges of the uncertain parameters of this linearized model are determined from different operating points of the nonlinear system. To design the PI controller for the uncertain system, first, it is transformed into a state feedback design for an augmented uncertain system and then the state feedback gains satisfying some LQ performance limit are computed by solving a linear matrix inequality (LMI) problem. As the uncertainty in the feedforward matrix of the linearized model cannot be considered in the above design process, an LMI-based method is developed to check if the designed PI controller performance in H∞ sense is close to the one if the neglected uncertainty is included. The performance of the controller is tested on the nonlinear boiler-turbine unit under several operating conditions and physical constraints. Comparisons are also made with some existing PI controllers, to show the superiority of the proposed robust PI controller.

Robust stability region analysis of time‐delayed load frequency control systems with EVs aggregator using Kharitonov theorem

AbstractThis study focuses on analyzing the robust stability regions and robustness margin of a time‐delayed load frequency control (LFC) system with Electric Vehicles (EVs) using the Kharitonov Theorem. Communication time delays in LFC systems can jeopardize stability and reliability, leading to suboptimal controller performance. Integrating EVs into LFC systems enhances dynamical stability but introduces additional complexity. Therefore, it is crucial to employ robust analysis and controller design techniques to ensure system stability. In this study, we utilize the Kharitonov Theorem to determine the robust stability regions and stability boundaries in the parameter plane of the Proportional‐Integral (PI) controller. By considering communication time delays and parametric uncertainties in the LFC system with EVs (LFC‐EVs), the robust PI controller gains using these methods are efficiently computed. To evaluate the performance of the theoretically computed robust controller parameters, time‐domain simulations are conducted.

Model-Independent Robust Consensus of Multiple Euler–Lagrange Systems

The robustness of multiple Euler–Lagrange systems (MELSs) measures the capability of maintaining coordination control performance when experiencing disturbance or faults. This article investigates a leader–follower robust consensus problem of MELSs, which experience time-varying input disturbance and uncertain communication link faults (CLFs). First of all, based on an adaptive control theory, we design fully distributed observers for estimating the dynamic and state of leader, which have robustness to CLFs. Then, an observer-based proportional–integral (PI) control protocol is designed to achieve consensus of MELSs with robustness to time-varying input disturbance. Different from the existing related results, this robust observer-based PI controller is fully distributed and model independent, which is irrelevant to any prior information (i.e., the structures and features) of agent dynamic or global network information. At last, the validity of the proposed theoretical results is confirmed by a simulation example.

Robust proportional–integral control of submersible autonomous robotized vehicles by backstepping-averaged sub-gradient sliding mode control

This study presents a novel robust controller strategy for submersible autonomous robotized vehicles (SARV). This controller applies the averaged sub-gradient (ASG) descendant method to optimize the tracking of well-posed reference trajectories. The motion control form of the SARV is done in three stages (cascade-like control design). The phases consist of using the translation velocities as pseudo controllers to adjust the SARV position, regulating the angular velocities to attain the requested translation velocities, and using the proposed ASG to control the thrusters to get the needed angular velocities. ASG implementation optimizes a convex cost function depending on the integral of the tracking error using the ASG method. The application of Barbalat’s lemma justifies the tracking error is converging the origin asymptotically. A class of integral sliding mode controllers with a variable state-dependent gain solves the tracking of the designed reference trajectories in each of the three stages. The sliding surface depends on the tracking error for each pseudo-controller, its integral, and the cost function average. The optimization of the cost function can be done without complete knowledge of the SARV dynamics. A numerical example is presented in this study to confirm the suggested control design’s effectiveness based on the cost function’s time evolution analysis. The forced motion by the proposed controller is compared with the movement obtained by a proportional–integral–derivative (PID) controller. The proposed controller exhibits a better tracking of the reference trajectory than the PID version.

Lyapunov stability analysis of a robust model reference adaptive PI controller for systems with matched and unmatched dynamics

In this paper, the discrete-time Lyapunov stability analysis of a Robust Model Reference Adaptive PI (Proportional-Integral) Controller is presented. The mathematical development of this controller is grounded on Robust Model Reference Adaptive Control philosophy, which provided boundedness of all closed-loop system signals and ensures its global stability. The resulting controller shows robustness characteristics to matched and unmatched dynamics, it guarantees the convergence of adaptive gains to a solution set and the convergence of tracking error to a residual set on steady state. Besides, to implement it, the only required information about the plant are its relative degree and the signal of its gain. Simulation results of the controller are provided, applying it on an unstable nonminimum-phase plant and in a practical plant. Besides, it was also compared with a Robust Model Reference Adaptive Controller and presented higher performance.

A Discrete-Time Robust Adaptive PI Controller for Grid-Connected Voltage Source Converter with LCL Filter

In this work, it is presented a new direct discrete-time robust adaptive PI (Proportional Integral) Controller for grid-injected current control loop of a voltage source converter with LCL filter. The mathematical background is based on Robust Model Reference Adaptive Control theory. However, the proposed controller is straightforward, it does not need a reference model and has capability to track directly currents reference. This approach simplifies significantly controller design, resulting in a reformulation of parameters vector used for adaptation of adjustable gains. It turns the controller robust to unmodelled dynamics, while avoid the complexity inherent to the conventional high order adaptive controllers for grid-connected power systems. Besides, it is highlighted that proposed controller does not need resonant controllers for grid disturbance rejection, or require any knowledge of grid parameters, lines impedance or load power demand. Also, due to its simple structure, it is easily implemented and does not require a high processing capacity. Furthermore, the effectiveness of the control strategy in terms of reference tracking, harmonics content and robustness to the grid impedance variation is corroborated through experiments.

Robustly stabilizing proportional integral controller for uncertain system under computational delay

In a feedback control loop, when there exists a delay in processing the control signal (often called computational delay), it is difficult to stabilize the system, particularly when the system exhibits uncertainty. To solve this problem, we proposed a new robust proportional integral control strategy for a class of uncertain systems exhibiting parametric uncertainty. A two-stage scheme is proposed in which the first stage identifies the worst plant that has the highest chance of facing instability; and in the second stage, based on the worst plant, the tuning parameters of the proportional integral controller are determined using the stability boundary locus approach under the desired closed-loop specifications of gain and phase margins. The efficiency of the proposed scheme is verified for servo and regulatory control problems.

Unstructured Uncertainty Based Modeling and Robust Stability Analysis of Textile-Reinforced Composites with Embedded Shape Memory Alloys

This paper develops the mathematical modeling and deflection control of a textile-reinforced composite integrated with shape memory actuators. The mathematical model of the system is derived using the identification method and an unstructured uncertainty approach. Based on this model and a robust stability analysis, a robust proportional–integral controller is designed for controlling the deflection of the composite. We showed that the robust controller depends significantly on the modeling of the uncertainty. The performance of the proposed controller is compared with a classical one through experimental analysis. Experimental results show that the proposed controller has a better performance as it reduces the overshoot and provide robustness to uncertainty. Due to the robust design, the controller also has a wide operating range, which is advantageous for practical applications.

Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

The paper is focused on robust Proportional-Integral (PI) control of interval plants with gain and phase margin specifications and on the application of this approach to a Continuous Stirred Tank Reactor (CSTR). More specifically, the work aims at the determination of PI controller parameter regions, for which not only robust stability but also some level of robust performance of the closed-loop control system is guaranteed, and this robust performance is represented by the required gain and phase margin that has to be ensured for all potential members of the interval family of controlled plants, even for the worst case. The applied technique is based on the combination of the previously published generalization of stability boundary locus method (for specified gain and phase margin under the assumption of fixed-parameter plants) with the sixteen plant theorem. This extension enables the direct application of the method to design the robustly performing PI controllers for interval plants. The effectiveness of the improved method is demonstrated on a CSTR, modeled as the interval plant, for which the robust stability and robust performance regions are obtained.

Linear active disturbance rejection control for a raceway photobioreactor

In this paper, the problem of pH regulation in photobioreactors has been addressed by using a robust Proportional–Integral controller in combination with a linear active disturbance rejection approach. This formulation is based on the Generalized Proportional–Integral (GPI) observers design to estimate online external disturbances and non-modeled dynamics. The methodology uses a model reference optimization procedure with tracking and regulatory target closed-loop transfer functions for first-order plus dead-time models. The proposed controller is validated on a full-scale Raceway photobioreactor, whose results show a significant improvement in the accuracy of pH regulation and, consequently, a positive influence on biomass production. Moreover, a classical feedforward approach has been used for comparison purposes. The performance of the robust technique is evaluated with different indexes, whose results confirm the good performance of the proposed active disturbance rejection control scheme.

Dynamic modeling and control of a 6-DOF micro-vibration simulator

A micro-vibration simulator with multiple degrees of freedom is required for performance testing of sensitive instruments in a micro-vibration environment on-board spacecraft before launch. In this study, a novel 6-DOF micro-vibration simulator (6-MVS) is proposed, which can reproduce a micro-vibration environment with a wide bandwidth of disturbance frequencies. The complete inverse dynamic equations of the proposed 6-MVS are derived using the Kane method, which is very suitable for processing by computer. The validity of the derived dynamic equations is then verified by co-simulation. The structural performance of the 6-MVS is investigated using the finite element method. Based on this dynamic model, a robust proportional-integral (PI) control scheme is then performed. The control performance of the proposed controller is evaluated by co-simulation. The analysis and simulation results show that the proposed robust PI controller has excellent robustness and stability and the 6-MVS can exactly produce the required micro-vibration spectrum.

Robust sampled-data PI controller design for networked control systems

This paper focuses on investigating the robust stabilization problem for a class of continuous-time networked control systems (NCS) with sampled-data strategy through uncertain time-varying sampling rate via the proportional-integral (PI) control design. The main objective of this paper is to design a state feedback sample-data PI controller with time varying input delay such that the resulting closed-loop system is robustly asymptotically stable for all admissible uncertainties. Based on the Lyapunov stability theory, a new set of delay-dependent conditions is obtained in terms of linear matrix inequalities to determine the system stability and achieve the sampled-data PI control design. Finally, simulation results based on electronic-circuit system and mass–spring damped system are provided to demonstrate the effectiveness and the merit of the proposed design technique.

Robust control of burst suppression for medical coma

Objective. Medical coma is an anesthetic-induced state of brain inactivation, manifest in the electroencephalogram by burst suppression. Feedback control can be used to regulate burst suppression, however, previous designs have not been robust. Robust control design is critical under real-world operating conditions, subject to substantial pharmacokinetic and pharmacodynamic parameter uncertainty and unpredictable external disturbances. We sought to develop a robust closed-loop anesthesia delivery (CLAD) system to control medical coma. Approach. We developed a robust CLAD system to control the burst suppression probability (BSP). We developed a novel BSP tracking algorithm based on realistic models of propofol pharmacokinetics and pharmacodynamics. We also developed a practical method for estimating patient-specific pharmacodynamics parameters. Finally, we synthesized a robust proportional integral controller. Using a factorial design spanning patient age, mass, height, and gender, we tested whether the system performed within clinically acceptable limits. Throughout all experiments we subjected the system to disturbances, simulating treatment of refractory status epilepticus in a real-world intensive care unit environment. Main results. In 5400 simulations, CLAD behavior remained within specifications. Transient behavior after a step in target BSP from 0.2 to 0.8 exhibited a rise time (the median (min, max)) of 1.4 [1.1, 1.9] min; settling time, 7.8 [4.2, 9.0] min; and percent overshoot of 9.6 [2.3, 10.8]%. Under steady state conditions the CLAD system exhibited a median error of 0.1 [−0.5, 0.9]%; inaccuracy of 1.8 [0.9, 3.4]%; oscillation index of 1.8 [0.9, 3.4]%; and maximum instantaneous propofol dose of 4.3 [2.1, 10.5] mg kg−1. The maximum hourly propofol dose was 4.3 [2.1, 10.3] mg kg−1 h−1. Performance fell within clinically acceptable limits for all measures. Significance. A CLAD system designed using robust control theory achieves clinically acceptable performance in the presence of realistic unmodeled disturbances and in spite of realistic model uncertainty, while maintaining infusion rates within acceptable safety limits.

MRFT-based design of robust and adaptive controllers for gas loop of oil–gas separator

AbstractThe modified relay feedback test (MRFT), which was recently proposed as a continuous oscillation method for identification of the process parameters and controller tuning, is used for the design of a robust and an adaptive Proportional-Integral (PI) controller for a gas loop in the oil–gas separator. The gas normally found in the separator is the natural gas (mostly methane) which is contained in crude oil coming from the reservoir. The robust and adaptive PI controllers are developed from analysis of 64 operating modes corresponding to certain ranges of the gas inflow and liquid-level values. It is shown through the developed model and simulations that these operating modes have significant effect on the dynamics of the gas loop. Dynamic properties of the process in each mode are studied through MRFT. The controllers are designed in order to maintain the pressure during the change of the operating conditions. Performance of the designed control system is studied by simulations.

Robust Fractional Order Proportional Integral Control for Large Time-Delay System

In this paper, a new control method for large time delay system is proposed. Firstly, the decreasing time delay controller is used to remodel large delay time plant into small delay time plant. Then, a fractional robust proportional-integral controller (FOPI) is designed, using the phase margin and cut-off frequency at a specified point in the Bode plot of flat robust conditions, to guarantee the desired control performance and the robustness of the high order system to the gain order system. For comparison between the fractional order proportional integral controller and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. The simulation results indicates that the both designed controllers work efficiently. Furthermore, the FOPI controller makes the large time-delay system get better control effect, the system has high robustness, adaptive ability and anti-jamming ability.

Emotional Learning Based Position Control of Pneumatic Actuators

This paper presents a new scheme for position tracking of pneumatic actuators. The controller is built upon the Brain Emotional Learning Based Intelligent Control (BELBIC) concept proposed by Caro Lucas [Lucas, C., Shahmirzadi, D., & Sheikholeslami, N. (2004). Introducing BELBIC: Brain emotional learning based intelligent controller. International Journal of Intelligent Automation and Soft Computing, 10, 11–21]. First the structure of BELBIC is analyzed to further understand its features. Next, different types of emotional signals, required by BELBIC, are experimentally evaluated to meet the challenges in position tracking of pneumatic actuators. The best performing BELBIC structure is then experimentally compared with a previously developed robust proportional integral controller. It is also successfully applied to a force reflecting tele-operated application of pneumatic actuator.

All stabilizing sets for proportional–integral controller of high-order delay processes

This article considers the problem of determining the complete stabilizing set of proportional–integral controllers, which is applied in a class of high-order processes with time delay in complex-frequency domain. First, we give a necessary condition for a proportional–integral controller to stabilize the process with certain constant delay using Descartes’ rule of signs. Then by employing the generalization of the Hermite–Biehler theorem applicable to quasi-polynomials, a complete set for all stabilizing proportional–integral parameters is derived to stabilize the open-loop stable and unstable systems. In the case of uncertain time delay, we provide a design approach to stabilize the related plant with a robust proportional–integral controller, where the unknown but constant time delay lies inside a known interval. Three examples illustrate the effectiveness of the proposed results.

Biomolecular implementation of linear I/O systems

Linear I/O systems are a fundamental tool in systems theory, and have been used to design complex circuits and control systems in a variety of settings. Here we present a principled design method for implementing arbitrary linear I/O systems with biochemical reactions. This method relies on two levels of abstraction: first, an implementation of linear I/O systems using idealised chemical reactions, and second, an approximate implementation of the ideal chemical reactions with enzyme-free, entropy-driven DNA reactions. The ideal linear dynamics are shown to be closely approximated by the chemical reactions model and the DNA implementation. We illustrate the approach with integration, gain and summation as well as with the ubiquitous robust proportional-integral controller.

Design of Robust PI Controllers and their Application to a Nonlinear Electronic System

Design of Robust PI Controllers and their Application to a Nonlinear Electronic SystemThe principal aim of the paper is to present a possible approach to the design of simple Proportional-Integral (PI) robust controllers and subsequently to demonstrate their applicability during control of a laboratory model with uncertain parameters through the Programmable Logic Controller (PLC) SIMATIC S7-300 by Siemens Company. The proposed and utilized synthesis consists of two steps. The former one is determination of controller parameters area, which ensures the robustly stable control loop and is based on computing/plotting the stability boundary locus while the latter one lies in the final choice of the controller itself relying on algebraic techniques. The basic theoretical parts are followed by laboratory experiments in which the 3rd order nonlinear electronic model has been successfully controlled in various working points.

Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems

This work presents an adaptive fuzzy sliding mode controller (AFSMC) that combines a robust proportional integral control law for use in designing single-input single-output (SISO) nonlinear systems with uncertainties and external disturbances. The fuzzy logic system is used to approximate the unknown system function and the AFSMC algorithm is designed by used of sliding mode control techniques. Based on the Lyapunov theory, the proportional integral control law is designed to eliminate the chattering action of the control signal. The simplicity of the proposed scheme facilitates its implementation and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense if all the signals involved are uniformly bounded. Simulation studies have shown that the proposed controller shows superior tracking performance.