Robust Proportional-integral-derivative Research Articles

Robust adaptive PID control of functional electrical stimulation for drop-foot correction

A robust, adaptive proportional–integral–derivative (PID) control strategy is presented for controlling ankle movement using a functional electrical stimulation (FES) neuroprosthesis. The presented control strategy leverages the structurally simple PID controller. Moreover, the proposed PID controller automatically tunes its gains without requiring prior knowledge of the musculoskeletal system. Thus, in contrast to previously proposed control strategies for FES, the proposed controller does not necessitate time-consuming model identification for each patient. Additionally, the computational cost of the controller is minimized by linking the PID gains and updating only the common gain. As a result, a model-free, structurally simple, and computationally inexpensive controller is achieved, making it suitable for wearable FES-based neuroprostheses. A Lyapunov stability analysis proves uniformly ultimately bounded (UUB) tracking of the joint angle. Results from the simulated and experimental trials indicate that the proposed PID controller demonstrates high tracking accuracy and fast convergence.

Robust PID controller design for positioning systems with hysteresis and time-varying delay

This paper presents Linear Matrix Inequalities (LMIs) conditions for designing Proportional-Integral-Derivative (PID) controllers that guarantee asymptotic stability with exponential convergence rate for positioning systems affected by hysteresis nonlinearity and time-varying delay. The hysteresis is modelled using the Prandtl-Ishlinskii operator, and the effects of both the time-varying delay and hysteresis are encapsulated into a bounded uncertain parameter confined within a known convex polytope. Numerical results support the theoretical developments, confirming that the controller effectively mitigates the effects of disturbances while suppressing both the hysteresis and time-varying delay influences.

Robust fractional-order PID controller assisted by active disturbance rejection control for the first-order plus time-delay systems

Time-delay characteristics of various industrial processes may degrade the stability and dynamic performance of the control systems. Aiming at the problems of the existing methods in dealing with the time delay plant, a modified fractional-order proportional–integral–derivative (FOPID) controller for the first-order plus time-delay (FOPTD) system is developed. Assisted by a modified active disturbance rejection control (ADRC) scheme with increased observer bandwidth, the proposed FOPID controller inherently obtains good robustness to time-delay uncertainties and external disturbances. In addition, taking advantage of the fractional-order operator, the proposed controller can provide larger stability margin over the proportional–integral–derivative (PID) controller. By suitably establishing the relation between ADRC and FOPID controller parameters, the proposed controller can be analytically tuned based on the common design indices. A practical tuning guideline is developed according to frequency-domain characteristic analysis, making the proposed controller more acceptable to industrial application. The performance of the ADRC-based FOPID controller is tested by the control simulation of some typical FOPTD systems and a diesel engine speed regulation system. The efficiency of the ADRC-based FOPID controller is demonstrated by the comparisons with some existing controllers.

A robust PID and RLS controller for TCP/AQM system

Transmission Control Protocol (TCP) controlling congestion by peer-to-peer is challenging to handle communication with numerous concurrent TCP flows and heavy traffic loads. Therefore, TCP requires the active queue management (AQM) to assist in avoiding buffer bloat in intermediate devices. Thus, Some AQM controllers, such as Red, Codel, and Pie, have been proposed to control congestion better. However, these controllers are unable to overcome the drawbacks, including micro-burst streams, unfair competition of flows with different workloads, as well as sluggishly responding to congestion in heavy traffic, which degrade the performance of data transmission. To address these problems, in this paper, we proposed a queueing-delay-based AQM controller for TCP/AQM systems, namely PID-R. PID-R adopts two-level control components, i.e., the Proportional-Integral-Derivative (PID) algorithm and the recursive least squares (RLS) filter, and combines the advantages of the two parts. Meanwhile, we also constructed a new TCP/PID-R fluid model derived from TCP/AQM classical model. According to the model, PID-R parameters are determined to keep the TCP/PID-R system steady. The comprehensive simulation reveals that PID-R outperforms the state-of-the-art AQM controllers.

Robust PID control of a tuned mass damper system and its stability analysis validation by Kharitonov and Edge theorems

ABSTRACT A robust control and stability analysis of a tuned mass damper attached to benchmark the model of mass-spring-damper system via different Kharitonov-related approaches, including the post-Kharitonov Edge Theorem, is presented in this paper. The control of uncertain parameters of the given system is demonstrated via robust Proportional-Integral-Derivative (PID) system tuning techniques in MATLAB. Usually, the Kharitonov theorem is sufficient to check the stability analysis of a controlled interval system. A detailed stability analysis of the given system by forming the Kharitonov rectangular parameter boxes and testing the positivity of Hurwitz determinants of the enclosed segments connecting opposite corners of the box is explained here. Stability checking is validated by the analysis based on the Hurwitz matrices of two Kharitonov polynomials. The multi-linear affine system model in the overall system plant is controlled and analysed via Edge theorem.

Multiobjective Robust PI Synthesis in Plants with Uncertain Poles

The use of multiobjective optimization procedures for control tuning has been constantly explored, presenting satisfactory results, and generating significant contributions to control engineering. In this way, the field of robust control can benefit significantly from the integration of multiobjective optimization design procedures for robust Proportional-Integral-Derivative (RPID) controller synthesis, enabling innovative solutions to complex control challenges. Due to this fact, this paper explores an approach to utilize multiobjective optimization algorithms in a simplified procedure, considering uncertain systems in the form of interval plants with uncertain poles, the Kharitonov theorem is used to obtain a region of stability as search space for the multiobjective algorithm, being the optimization process performed over a nominal system model. Two numerical cases and a flexible actuator model were used to demonstrate the procedure for RPI synthesis, resulting in robustly stable controllers with optimized performance over error and control signal effort measures.

Evaluating the Impact of Drivetrain Vibrations on MPPT Control Performance in Horizontal Axis Wind Turbines

This study investigates the impact of drivetrain shift vibrations on the control performance of Horizontal Axis Wind Turbines (HAWTs) using a Proportional-Integral-Derivative (PID) controller for Maximum Power Point Tracking (MPPT). Traditionally, PID controllers are tested on simplified rigid models, which do not account for the complex mechanical vibrations encountered in real-world applications. These vibrations, particularly those caused by drivetrain shifts, can significantly affect the stability and efficiency of the control system. Through detailed simulations involving both rigid and flexible drivetrain models, this paper evaluates how drivetrain vibrations influence the performance of the PID-based MPPT control algorithm. The results indicate that the flexible model, which incorporates drivetrain dynamics, experiences pronounced overshoot, oscillations, and significant drops in power coefficient (Cp) compared to the rigid model. These findings highlight the challenges of maintaining control stability and efficiency under varying vibration conditions, with the flexible model showing compromised stability and reduced power conversion efficiency during certain key intervals. This study emphasizes the importance of considering drivetrain dynamics in wind turbine control system design and provides insights into developing more robust and resilient PID control strategies.

Performance Comparison of Robust PID and FOPID for an Inverse Response Process Model

This paper provides a quantitative comparison between the performance provided by the use of Proportional-Integral-Derivative (PID) and Fractional-Order Proportional-Integral-Derivative (FOPID) controllers for the control of second-order processes with inverse response based on the integrated absolute value of the error (IAE index). These controllers are designed in order to achieve an optimal performance in both, set-point tracking task and regulatory control operation, while robustness considerations are taken into account, and, therefore, also the trade-of between robustness and performance of the control system is considered. The performance comparison and example, show that FOPID controllers achieve higher performance that PID controllers mainly for processes with larger normalized dead times as well when more robustness should be considered in the closed-loop system. These advantages are due to the use of the fractional parameter µ associated to the derivative part of the FOPID controller.

Neuromechanical Model-Based Corrective Torque Estimation During Weight Shifting in Lower Limb Amputees

As a consequence of limb loss, unilateral lower limb amputees (LLAs) exert additional flexion torque in the intact limb during postural balance, leading to other secondary complications. A prosthetic device with torque delivery is required to avoid such complications. However, estimating desired torque is an acknowledged challenge in this domain. Motivated by the above, this paper focuses on estimating the corrective torque required from an assistive device to balance the individual while performing weight-shifting exercises. Further, a healthy individual’s inverted pendulum (IP) model is explored to model LLA’s dynamics during weight-shifting. The model and the control strategy are validated using forward and backward body lean angles recorded from healthy and LLA individuals. Finally, a robust Proportional Integral Derivative controller is designed to estimate the corrective torque for maintaining the postural balance during weight-shifting. Along with the IP dynamics, a suitable control law based on Coefficient Diagram Method achieves the experimentally recorded body lean angle. The proposed control scheme is validated through simulation studies to evaluate the tracking performance in two different biomechanically relevant IP postural models. The findings assist in determining the external torque required to maintain the postural balance during gait initiation and compensatory measures for pathologically reduced torque. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Gait initiation is a transition between vertical posture and gait. Since vertical stance is inherently unstable, a postural adjustment occurs before gait initiates, propelling the center of mass forward and towards the first stance leg. The absence of flexor torque in the amputated limb causes a loss of postural stability during weight shifting activities. In the case of powered exoskeletons and prosthetic devices, a prior estimation of corrective torque through a computational approach helps to select a suitable actuator that provides an appropriate joint torque while maintaining the postural balance. As a result, an efficient computational model of gait initiation that accounts for neuromuscular system components before designing assistive devices is necessary. The controllers further provide corrective action to the assistive device to obtain robust and optimal coordination between the prosthetic element and gait. Therefore, this study demonstrates the significance of neuromuscular controller and assists in determining how much corrective torque from an external device is required to maintain postural stability and adaptability during weight shifting exercises. The effectiveness of the neural controller is also tested for real-time data to compensate for the effect of external disturbance and noise, thereby achieving a proper and controlled degree of movement in amputee users. These findings could provide one of the fundamental aspects of gait initiation model paradigms of compensatory measures for pathologically diminished torque and contribute to developing low-cost prosthetic solutions for the benefit of the rehabilitation society in developing countries.

A new MOPSO algorithm for solving mathematical test functions and control engineering problems

In this article, a new multiobjective particle swarm optimization (MOPSO) algorithm is introduced to improve the performance of a sliding mode based robust fuzzy proportional–integral–derivative (PID) controller. In this regard, the non-dominated solution having minimum number of neighbors is considered as the global best position, while the sigma values of the members are employed to determine the personal best position. A modified multiple-crossover operator is combined with the operators of the particle swarm optimization to significantly increase the convergence speed of the algorithm. To limit the size of the archive, a dynamical elimination scheme defined in the Euclidean space is introduced. Besides, iteration-based linear relations are implemented to adaptively compute the inertia weight and learning coefficients. To evaluate the effectiveness of the introduced MOPSO algorithm, the requirements are conducted by means of three benchmark functions with regard to generational distance, spacing, and maximum spread metrics. This analysis demonstrates that the proposed algorithm operates better through comparison with well-known elitist multiobjective evolutionary algorithms. Moreover, the MOPSO algorithm is applied for optimal design of a hybrid robust fuzzy PID controller for a pneumatic system with two bellows. Conflicting objective functions are considered as the normalized values of overshoot and settling time of the displacement between the bellows that should be simultaneously minimized. The feasibility and efficiency of the strategy are assessed in comparison with the conventional controllers.

Design and implementation of a robust ANN-PID corrector to improve high penetrations photovoltaic solar energy connected to the grid

The best quality of PV energy into the grid is now problematic that is why this paper focuses on the design and implementation of a robust Proportional Integral Derivative based on Artificial Neural Network (ANN-PID). This technique used to ensure the regulation of the Boost Converter (BC) output voltage and the Three Phase Inverter (3 PI) output currents of a photovoltaic solar system (PVS) connected to the grid. The mathematical model of the DC bus and the 3-PI is presented. Applications under Matlab/Simulink justify the efficiency of the neural regulator. In comparison with the conventional one, the proposed method presents the best follow-up of the DC link voltage reference and a maximum overshoot of 3.16 %. In addition, despite the long time put in transient mode, the proposed method keeps better robustness and ensures an injection of current of a total harmonic distortion (THD) of 0.96 % against 2.18 % of the classical PID regulator.

Robust PID controllers tuning based on the beetle antennae search algorithm

The core components of both traditional and contemporary control systems are the proportional–integral–derivative (PID) control systems, which have established themselves as standards for technical and industrial applications. Therefore, the tuning of the PID controllers is of high importance. Utilizing optimization algorithms to reduce the mean square error of the controller’s output is one approach of tuning PID controllers. In this paper, an appropriately modified metaheuristic optimization algorithm dubbed beetle antennae search (BAS) is employed for robust tuning of PID controllers. The findings of three simulated experiments on stabilizing feedback control systems show that BAS produces comparable or higher performance than three other well-known optimization algorithms while only consuming a tenth of their time.

LQ optimal robust multivariable PID control for dynamic positioning of ships with norm-bounded parametric uncertainties

The design of a suitable controller for dynamic positioning (DP) of ships is a challenging task keeping the hydrodynamic uncertainties in mind. The magnitude and rate constraints on the actuators make the problem more difficult. The present work employs a two-degree-of-freedom (2-DOF), multivariable, proportional–integral–derivative (PID) control for DP of a ship. To design the controller, first, the ship dynamics with hydrodynamic parameter uncertainties is represented in an uncertain state-space descriptor form. Then, the design of feedback gains of 2-DOF PID controller for the uncertain descriptor plant is converted into a state feedback design for an augmented uncertain descriptor plant. Next, a linear matrix inequality-based condition is obtained to solve this state feedback problem in order to ensure a desired linear quadratic (LQ) performance, even in presence of uncertainties. Finally, to further improve the tracking performance, the feedforward gain of the 2-DOF PID controller is designed using H∞ approach. The DP performance of the proposed controller is tested for the considered ship model along with uncertainties, actuator constraints, and environmental disturbances. A comparison with the existing PID controllers is also carried out to show superiority of the proposed controller.

Robust feedback compensation and PID Tuning under actuator rate limit effect based on Bode’s integrals

The actuator rate limit is a common phenomenon in control systems while its underlying mechanism remains elusive. Magnitude reduction and phase delay generated by the rate limiter degrade the control performance, but this adverse effect has always been omitted in practical engineering. This study proposes a robust controller design method and controller update rules for general minimum-phase systems to compensate for the rate limit effect and improve control performance. Firstly, a simplified implementation method of “flat phase” constraint is carried out based on the Bode’s integrals for proportional–integral–derivative (PID) and fractional-order proportional–integral (FOPI) controllers. Secondly, the update rules of the controller design specifications are proposed based on Bode’s integrals to mitigate the actuator rate limit effect. The proposed method maintains the original controller structure without extra compensation filters, thereby can be easily applied to engineering practice. The outperformance of FOPI controllers compared to PID controllers is qualitatively analyzed and has been indicated to have lower probability of infinity loops under actuator rate limit. Illustrative examples and experimental results have demonstrated the effectiveness, robustness under gain variation and disturbance rejection capability of the proposed rate limit compensation strategies.

A Moth-Flame Optimized Robust PID controller for a SEPIC in Photovoltaic Applications

The paper presents a robust proportional integral derivative (PID) controller improved by the metaheuristic moth-flame optimization (MFO) technique for a DC-DC single-ended primary inductor converter (SEPIC) to achieve aimed user output performance in photovoltaic systems. Having non-linear dynamics, SEPIC with the conventional linear PID controllers possessing constant tuning gains cannot exhibit robust performance under the input and load variations. To confront the problem, a process-adaptive PID controller, whose tuning gains are adjusted by the MFO algorithm to ensure the continuity and stability of output voltage and the power, is designed and simulated. Comparative performance analysis of MFO tuned PID controller compared with the classic PID controller is conducted. The simulation results reveal a substantial performance improvement of the MFO-PID controller over the traditional PID controller in terms of maintaining constant regulated output voltage and having excellent setpoint tracking capability with minimal settling times and overshoot under considerable input and load disturbances.

Robust PID consensus-based formation control of nonholonomic mobile robots affected by disturbances

In this work, we report a novel controller to solve (globally) the position and orientation consensus-based formation problem of multiple nonholonomic vehicles modelled as differential drive robots affected by external disturbances. The controller has the structure of a simple to implement Proportional Integral Derivative (PID) scheme. In order to satisfy the well-known Brocket stabilisation theorem for nonholonomic systems, we also incorporate a time-varying persistency of excitation term in the angular velocity dynamics. Our proposal reports the first solution to the robust formation problem using a smooth time-varying controller. Simulations are shown to evidence the theoretical findings of this work.

H ∞-PID distributed control for output leader-tracking and containment of heterogeneous MASs with external disturbances

This paper addresses both the output leader-tracking and output containment control problems for heterogeneous linear high-order Multi-Agent Systems (MASs) sharing information over a directed communication topology and subject to external unknown disturbances. To solve these control problems, we propose a robust fully distributed Proportional-Integral-Derivative (PID) control strategy, equipped with a filter on the derivative action that allows obtaining both a simpler closed-loop formulation, without the need of the descriptor transformation, and good tracking performances in the case of fast reference signal behaviours. The stability analysis is analytically proven via the Lyapunov theory and the approach. The derived robust stability conditions are expressed as a set Linear Matrix Inequalities (LMIs) whose solution provides the proper tuning of the robust PID control gains. Numerical simulations confirm the effectiveness and robustness of the proposed approach in solving both the output leader-tracking and output containment control problems.

Coordinated control of a 3DOF cartesian robot and a shape memory alloy-actuated flexible needle for surgical interventions: a non-model-based control method

SummarySuccess of any needle-based medical procedures depends on accurate placement of the needle at the target location. However, accurate targeting and control of flexible self-actuating (active) needle are challenging. We have developed a shape memory alloy-actuated flexible needle steered by a 3D Cartesian robot and performed a comparative study of four, non-model-based, coordinated control methodologies for the combined robot steering and flexible-needle insertion process for surgical interventions. Investigated four controllers are: proportional–integral–derivative (PID), PID with the cubic of positional error term (PID-P3), static PID sliding mode controller, and robust adaptive PID sliding mode controller (RAPID-SMC). Relative efficacies of these controllers are demonstrated by performing experiements using a tissue-mimicking soft material phantom. Results from experiments have reavealed that RAPID-SMC is superior to other three controllers.

On-Line Auto-Tuning Robust Nonlinear Neural PID Controller Design for Double-Pipe Heat Exchanger Based on Particle Swarm Optimization

The heat exchanger systems have highly nonlinear features between its variables and time delay. In addition, the parameters of them change constantly during operation. Therefore, the heat exchangers need nonlinear robust controller for obtaining required outlet temperature under all operating conditions.In this paper, a robust nonlinear neural PID (NLNPID) controller is proposed for temperature control of double-pipe heat exchanger. Particle swarm optimization (PSO) technique is used to determine on line auto tuning the optimal parameters of proportional-integral-derivative (PID) controller. Mathematical model of heat exchanger takes into account the changes in the density, thermal conductivity, viscosity, specific heat and convection heat transfer coefficient of the fluid which are resulting from changing in temperatures and the velocities with classical PID control. Simulations results show that the performance of the NLNPID controller produces good responses features and give desired outlet temperature under all operating conditions without over shoot and fluctuating.

Control of high-order processes: near-optimal robust tuning of PID regulators for repeated-pole plus dead-time models

This paper aims to present an analysis of the performance and robustness characteristics of repeated-pole plus dead-time (RPPDT) model PID (Proportional Integral Derivative) regulatory control system. Their performances are evaluated with the integrated absolute error index (IAE) and their robustnesses with the maximum sensitivity ( M S ). Normalised controlled process models and controllers are used for control system design. Optimal – robustness free – and optimal robust PID regulators parameters are found. A Near-Optimal Robust tuning rule (NORpid) for PID controllers based on high-order RPPDT models is obtained and applied to the control system of an eighth-order process. Examples include the control of the superheated steam temperature system (SHSTS) of a 500-MW boiler.