Closed-loop Response Research Articles

PID control design for first-order delay systems via MID pole placement: Performance vs. robustness

The PID control is favored in controlling industrial processes for its ease of implementation. In this paper we present an analytical study, with an aim at stability robustness, tracking performance, and pole placement of first-order unstable plants under PID control. We employ a multiplicity-induced dominancy (MID) strategy to design and tune PID controller gains, which is shown to possess desirable properties that ensure specified decay rate of the closed-loop response and the stability robustness of the closed-loop system in spite of variations in the delay parameter. We also study the tradeoff between delay robustness and tracking performance of PID controllers. We show that under the constraint of steady-state tracking, the maximal delay robustness range can be computed by solving a unimodal pseudo-concave optimization problem.

Yaw-Rate-Tracking-Based Automated Vehicle Path Following: An MRAC Methodology With a Closed-Loop Reference Model

Abstract Concerning automated vehicles, various path-following controllers have been designed by the model reference adaptive control (MRAC) approach. Through appropriate Lyapunov redesigns, asymptotical stability and signal boundedness are ensured for the path-tracking control loops. However, transient behaviors of the closed-loop responses are seldom considered in the context of MRAC synthesis. To bridge the foregoing gap, a closed-loop-reference-model-based MRAC, which yields an improved transient performance compared with a traditional MRAC, is exploited to synthesize a vehicular path-following control law. Besides, an infinitely differentiable projection operator is complemented to the control parameters’ adaptation schemes for estimation speed-up and robustness enhancement. Hardware-in-the-loop experiments are used to evaluate the proposed method and to demonstrate its improvement over some conventional MRAC designs.

Model-free discrete-time fractional fuzzy control of robotic manipulators

Robots are commonly used to perform repetitive or dangerous tasks, and these systems integrate different components that increase the complexity of their dynamic model. Thus, in order to ensure an acceptable tracking performance, the implementation of robust control strategies should be considered. This paper proposes a discrete-time model-free-implementation controller, which relies on the well-known structural properties of mechanical systems, but it does not consider any knowledge on the values of the system parameters. Besides, a fuzzy logic formulation is considered to compensate external disturbances. The outputs of the fuzzy inference system are adapted online to improve the closed-loop response. Finally, representatives simulation and experiments are analyzed to demonstrated the feasibility of the proposed approach.

Intracorporeal Cortical Telemetry as a Step to Automatic Closed-Loop EEG-Based CI Fitting: A Proof of Concept.

Electrically evoked auditory potentials have been used to predict auditory thresholds in patients with a cochlear implant (CI). However, with exception of electrically evoked compound action potentials (eCAP), conventional extracorporeal EEG recording devices are still needed. Until now, built-in (intracorporeal) back-telemetry options are limited to eCAPs. Intracorporeal recording of auditory responses beyond the cochlea is still lacking. This study describes the feasibility of obtaining longer latency cortical responses by concatenating interleaved short recording time windows used for eCAP recordings. Extracochlear reference electrodes were dedicated to record cortical responses, while intracochlear electrodes were used for stimulation, enabling intracorporeal telemetry (i.e., without an EEG device) to assess higher cortical processing in CI recipients. Simultaneous extra- and intra-corporeal recordings showed that it is feasible to obtain intracorporeal slow vertex potentials with a CI similar to those obtained by conventional extracorporeal EEG recordings. Our data demonstrate a proof of concept of closed-loop intracorporeal auditory cortical response telemetry (ICT) with a cochlear implant device. This research breaks new ground for next generation CI devices to assess higher cortical neural processing based on acute or continuous EEG telemetry to enable individualized automatic and/or adaptive CI fitting with only a CI.

Active disturbance rejection control for nanopositioning: A robust U-model approach

Hysteresis severely reduces positioning performance of a piezoelectric nanopositioning stage. Linear active disturbance rejection control (LADRC) is a practical solution to improve the positioning accuracy. However, the PD controller utilized in the LADRC is not effective enough to suppress the uncancelled total disturbance, and high-order pure integrators are difficult to be stabilized just by a PD controller. In this work, a robust U-model active disturbance rejection control (RUADRC) is proposed by incorporating the core idea of the U-model control and the Glover–McFarlane control. Then, the controlled plant can be dynamically transformed to a unit. Difficulties in stabilizing high-order pure integrators are decreased, the phase lag between the input and output of a controlled plant is reduced, and the closed-loop responses is sped up. In addition, the influence of both inaccurate total disturbance estimation and imperfect approximation is also minimized by the Glover–McFarlane control Closed-loop stability, steady-state tracking error, and the phase advantage of the RUADRC have been analysed. Theoretical results show that the RUADRC promises a timelier and more accurate positioning. Experimental results still confirm the advantages of the RUADRC over the LADRC on both reference tracking speed, accuracy and disturbance rejection ability.

Development of tuning free SISO PID controllers for First Order Plus Time Delay (FOPTD) and First Order Lag Plus Integral Plus Time Delay model (FOLIPD) systems based on partial model matching and experimental verification

This work aims to introduce a tuning-free PID controller for stable FOPTD and FOLIPD systems. The objective was achieved using a partial model-matching strategy; matching the coefficients of corresponding powers of s of the closed loop response of the model to the desired closed loop transfer function. Closed-loop performance is evaluated by considering a unit step change in the process model and compared the results with other methods reported earlier in the literature. Input and output performances were evaluated using error analyses and total variation. The robustness of the proposed method was assessed via incorporation of uncertainties in the process model parameters. The proposed method was also experimentally validated for FOPTD model using a temperature controlled lab. It was concluded that the method was analytically derived and model based with a key advantage that the resultant PID required no tuning parameter.

Data-Driven Model-Free Adaptive Control of Z-Source Inverters.

The universal paradigm shift towards green energy has accelerated the development of modern algorithms and technologies, among them converters such as Z-Source Inverters (ZSI) are playing an important role. ZSIs are single-stage inverters which are capable of performing both buck and boost operations through an impedance network that enables the shoot-through state. Despite all advantages, these inverters are associated with the non-minimum phase feature imposing heavy restrictions on their closed-loop response. Moreover, uncertainties such as parameter perturbation, unmodeled dynamics, and load disturbances may degrade their performance or even lead to instability, especially when model-based controllers are applied. To tackle these issues, a data-driven model-free adaptive controller is proposed in this paper which guarantees stability and the desired performance of the inverter in the presence of uncertainties. It performs the control action in two steps: First, a model of the system is updated using the current input and output signals of the system. Based on this updated model, the control action is re-tuned to achieve the desired performance. The convergence and stability of the proposed control system are proved in the Lyapunov sense. Experiments corroborate the effectiveness and superiority of the presented method over model-based controllers including PI, state feedback, and optimal robust linear quadratic integral controllers in terms of various metrics.

Comparison of closed loop performance of consistency process dynamics for various PID controller algorithms

In this work, various algorithms of PID (Proportional-Integral-Derivative) controllers such as series, parallel, series together with derivative filter and parallel together with derivative filter form are implemented for the comparative analysis of the closed loop responses of an important parameter in head box of a paper machine in a paper making process industry called consistency, which has FOPDT (First Order Plus Dead Time) dynamics. Also the comparison is made between the closed loop responses achieved from different values of derivative filter factor for non-ideal situations. The steady state and dynamic characteristics are analyzed and compared and important inferences are derived.

Modified Smith predictor‐based P‐PD control for pure integrating delay dominated processes

AbstractModified Smith predictor (MSP) with P (proportional)‐PD (proportional‐derivative) control methodology is designed for pure integrating processes with time delay (IPTD). Industrial processes such as liquid supply to the large storage, fractional distillation, and superheated steam flow to turbine are found to be integrating in nature with dominant time delay. The proposed P‐PD control strategy ascertains the desired closed loop response. The closed loop time constant () is considered to be the sole tuning parameter for reducing the tuning intricacies of the proposed MSP‐based design. P controller in the forward path is tuned by the internal model control (IMC) technique towards enhanced servo tracking. In the feedback path, PD controller parameters are obtained from Routh's stability analysis for improving regulatory responses. Overshoot free set point response is observed and smooth as well as reasonably faster recovery is also found during load fluctuations. Effectiveness of the proposed MSP is validated during closed loop performance and stability analyses in comparison to others' reported dead time compensating methodologies.

Wind turbine load reduction based on 2DoF robust individual pitch control

The individual pitch controller can mitigate asymmetric loads in wind turbines. However, wind turbine dynamics have strong nonlinearity and high uncertainty. In addition to target value tracking, suppression of wind disturbance is also a performance requirement of the individual pitch controller, while the traditional PI controller cannot take into account the tracking and disturbance rejection performance simultaneously. Therefore, the two-degree-of-freedom (2DoF) robust individual pitch controller is proposed to reduce loads in the above-rated region. Besides, parameter tuning is complicated in the design of the robust individual pitch controller. So the reference model method is proposed to preset the closed-loop system response. Firstly, the state-space model is established to describe the dynamics of the wind turbine. The multi-blade coordinate transformation is applied to transform the model into the fixed coordinate system. Subsequently, the μ-synthesis problem is solved by the D-K iterative algorithm to get the controller parameter. Finally, the control method is verified in GH Bladed. It is shown that rotor loads are suppressed without affecting the output power. Tower loads are also mitigated. Moreover, the relationship between the pitch actuator action and the load reduction capability is discussed by designing different bandwidths of the proposed method.

Modeling and flapping vibration suppression of a novel tailless flapping wing micro air vehicle

This paper establishes and analyzes a high-fidelity nonlinear time-periodic dynamic model and the corresponding state observer for flapping vibration suppression of a novel tailless Flapping Wing Micro Air Vehicle (FWMAV), named NPU-Tinybird. Firstly, a complete modeling of NPU-Tinybird is determined, including the aerodynamic model based on the quasi-steady method, the kinematic and dynamic model about the mechanism of flapping and attitude control, combined with the single rigid body dynamic model. Based on this, a linearized longitudinal pitch dynamic cycle-averaged model is obtained and analyzed through the methods of neural network fitting and system identification, preparing for the design of flapping vibration suppression observer. Flapping vibration is an inherent property of the tailless FWMAV, which arises from the influence of time-periodic aerodynamic forces and moments. It can be captured by attitude and position sensors on the plane, which impairs the flight performance and efficiency of flight controller and actuators. To deal with this problem, a novel state observer for flapping vibration suppression is designed. A robust optimal controller based on the linear quadratic theory is also designed to stabilize the closed-loop system. Simulation results are given to verify the performance of the observer, including the closed loop responses combined with robust optimal controller, the comparison of different parameters of observer and the comparison with several classic methods, such as Kalman filter, H-infinity filter and low-pass filter, which prove that the novel observer owns a fairly good suppression effect on flapping vibration and benefits for the improvement of flight performance and control efficiency.

Design of an Optimized GMV Controller Based on Data-Driven Approach

This paper presents a data-driven scheme that can obtain the optimized Generalized Minimum Variance (GMV) control parameters by applying the Nelder—Mead (NM) method based on Proportional-Integral Derivative (PID) controller for linear system. An adjustable λ is included in the GMV-PID controller. In the existing GMV-PID controller, the PID parameters are calculated by simply changing λ manually. Therefore, it is hard to get desirable control performance. The NM method is introduced to improve the control performance. The application of NM method can optimize the calculation of λ. However, the objective function in NM method needs the output calculation. In other words, the model information is inevitably to obtain output. To achieve model-free design scheme, the estimation of closed-loop response method is introduced in database-driven approach. Using obtained closed-loop data can predict the output and then substitute it into the objective function without any model information of the process. The effectiveness is verified by experiment.

Design and simulation of a novel FOIMC-PD/P double-loop control structure for CSTRs and bioreactors

Abstract The design of control methods for unstable plants is somewhat complex than that of stable plants. This is because unstable process models contain one or more poles lying on the right of the s-plane which yields unbounded closed-loop response. Further, the presence of the dead-time induces more complexity as it decreases the gain and phase margins which in turn deteriorates the closed-loop performance. The design of control strategies become more challenging for plants of unstable nature with positive zeros because they exhibit a phenomenon called inverse response. This paper suggests a method to design a double-loop scheme for unstable plants with/without inverse response. Accordingly, a proportional-derivative (PD)/proportional (P) controllers are used in the inner-loop for stabilizing the plant. A fractional order internal model controller (FOIMC) scheme is used to obtain the outer-loop controller using the stabilized plant model. The P/PD controller settings have been obtained by using the Routh-stability criteria and the maximum sensitivity approach. Procedure for selecting the outer-loop tuning parameter and fractional order is also given. Linear and nonlinear models of unstable plants including bioreactors and isothermal chemical reactors are used to demonstrate the merits of the suggested strategy. Robustness of the design and effect of measurement noise are also studied. Integrated absolute/squared error measures are also calculated. The suggested design is found to be more effective in controlling unstable processes than some reported works.

A Simple Analytical Method for Estimation of the Five-Parameter Model: Second-Order with Zero Plus Time Delay

Process models play an important role in the process industry. They are used for simulation purposes, quality control, fault detection, and control design. Many researchers have been engaged in model identification. However, it is difficult to find an analytical identification method that provides a good model and requires a relatively simple experiment. This is the advantage of the method of moments. In this paper, an analytical method based on the measurement of the process moments (characteristic areas) is proposed, to identify the five-parameter model (second-order process with zero plus time delay) from either the closed-loop or open-loop time responses of the process (in the time-domain), or the general-order transfer function with time delay (in the frequency-domain). The only parameter required by the user is the type of process (minimum phase or non-minimum phase process), which in practice can be easily determined from the time response of the process. The method can also be used to reduce the higher-order process model. The proposed identification method was tested on several illustrative examples, and compared to other identification methods. The comparison with existing methods showed the superiority of the proposed method. Moreover, the tests confirmed that the algorithm of the proposed method works properly for a wide family of process models, even in the presence of moderate process noise.

Design and Control of Pneumatic Systems for Soft Robotics: A Simulation Approach

Pressure control plays a major role in the overall performance of fluid-driven soft robots. Due to the increasing demand for higher speed actuation and precision, a need exists for a practical design methodology that converts actuator performance specifications to a set of minimum pneumatic specifications, such as receiver volume and pressure, and valve conductance. This article presents a systematic parameter selection approach for pneumatic soft robotic systems by taking into consideration the desired closed-loop pressure responses. The two controllers under evaluation here are the PI controller with anti-windup and the on-off controller with hysteresis. Simulations are developed within Simscape Fluids to evaluate the effect of physical components and controller parameters on the actuator performance. The proposed parameter selection procedures are then applied on three soft actuators and their closed-loop pressure responses are experimentally evaluated. The measured pressure responses are in close agreement with the simulations and satisfy the rise time specifications.

Design an Optimal Fractional Order PID Controller Based on New Algorithms and a Fuzzy Logic Controller to Regulate Type 1 Diabetes Patients

Diabetes is one of the most important diseases that researchers have focused on in scientific research since the time, because of the seriousness of this disease if it is not properly dealt with, especially with the emergence of some global epidemics such as Corona Virus (COVID 19), as the pancreas is the organ responsible for regulating sugar in the blood by secreting the insulin enzyme, insulin is widely used to control blood sugar. Therefore, it is important that the required insulin value is constant and controlled. The aim of this study is to control the blood glucose value that is achieved as a desired value and to maintain it as a constant value using a proportional, integral, and derivative control unit (FOPID) fractional order of the control parameters. In this research, the new control unit is applied to Bergman's mathematical model as a non-linear and simple model that simulates the mechanism of the interaction of glucose and insulin in the blood, and based on this, a closed control loop was designed to regulate the level of blood sugar to be an automatic control of blood glucose using the measured data from Special sensor. The contribution in this scientific paper is to define the (FOPID) parameters according to the closed loop responses of the system, and these parameters were adjusted using new meta-heuristic algorithms including the Invasive Weed Optimization (IWO), the PSO Particle Swarm optimization, the Genetic Algorithm (GA), The bat optimization algorithm (BA) and (ACO). As a result, the results of the five modern algorithms were compared based on several criteria to find out which one was better using MATLAB / SIMULINK simulation. It was found that the IWO algorithm performs better than PSO. The simulation results of the closed-loop system of this controller at the time of settling, overshoot and control inputs indicate very positive results compared to previous results. In addition, a new method has been proposed which is to design a pump in the form of a valve to control insulin pumping by controlling it with the fuzzy logic control unit, which in turn, we obtained better results, compared to the results of other previous studies.

System Identification and Design of Inverted Decoupling IMC PID Controller for Non-Minimum Phase Quadruple Tank Process

A systematic analytical and experimental method of identification of Two Input Two Output (TITO) Quadruple-Tank Process (QTP), operated at non-minimum phase condition has been presented. Parameters of the process transfer function matrix have been validated on an experimental laboratory-scale physical setup of the process. Appropriate input-output pairing and interaction among control loops have been studied based on the Relative Gain Array (RGA) analysis. Inverted Decoupling Internal Model Control (IMC) based Proportional Integral Derivative (PID) controller has been designed for the TITO process. The effect of changes in controller tuning parameters on the closed-loop response for servo problem has been reported in terms of quantitative performance indices such as Integral of Square of Error (ISE), Integral of Absolute Error (IAE), percentage overshoot and offset. The simulation results have been compared with the literature.

Parallel P-PD controller to achieve vibration and position control of a flexible beam

Robotic arms are considered as a cantilever beam fixed at one end and due to the length-to-weight ratio, it has a significant vibration-induced that needs to be controlled to achieve accurate position, speed control and to increase its efficiency. In this project, a discretized Timoshenko beam model is used to discuss the dynamics of the system. Further, to implement the control on the hardware an experimental setup is fabricated to observe the open-loop and closed-loop responses of the beam made of low-density polyethylene. An accelerometer as a feedback sensor is attached at one end of the flexible beam while another end is fixed at the moving cart having DC motor as an actuator. Simulink is used as the programming tool to perform all of the experimentation. Proportional-integral-derivative (PID) tuning is performed. Following that open-loop responses of the deflection of the beam parallel to the motion are observed with different input waveforms. By applying a proportional control scheme, another experiment is performed to demonstrate the disturbance rejection with an accelerometer as a feedback sensor, while ignoring position control. Finally, a PD and P based parallel control scheme is proposed to obtain simultaneously both position control and vibration reduction.

Fractional-Order Approximation of PID Controller for Buck-Boost Converters.

Viability of a fractional-order proportional–integral–derivative (PID) approximation to regulate voltage in buck–boost converters is investigated. The converter applications range not only to high-power ones but also in micro/nano-scale systems from biomedicine for energy management/harvesting. Using a classic closed-loop control diagram the controller effectiveness is determined. Fractional calculus is considered due to its ability at modeling different types of systems accurately. The non-integer approach is integrated into the control strategy through a Laplacian operator biquadratic approximation to generate a flat phase curve in the system closed-loop frequency response. The controller synthesis considers both robustness and closed-loop performance to ensure a fast and stable regulation characteristic. A simple tuning method provides the appropriate gains to meet design requirements. The superiority of proposed approach, determined by comparing the obtained time constants with those from typical PID controllers, confirms it as alternative to controller non-minimum phases systems. Experimental realization of the resulting controller, implemented through resistor–capacitor (RC) circuits and operational amplifiers (OPAMPs) in adder configuration, confirms its effectiveness and viability.

A novel optimal PIλDND2N2 controller using coyote optimization algorithm for an AVR system

In this paper, a novel PIλDND2N2 controller is designed for an Automatic Voltage Regulator (AVR) in a power system and is studied in this paper. AVR is responsible for keeping the terminal voltage of a synchronous generator at a specified interval. The proposed control design is achieved by deploying for the first-time the coyote optimization algorithm (COA) in an AVR system by optimizing a novel objective function. A comparison is made among the proposed controller and FOPID, PID, PIDA and PIDD2 controllers optimized by others metaheuristic algorithms in the literature. The comparison is deducted in terms of transient response and disturbance rejection. From the simulations it is concluded that the proposed method outperforms other methods in the literature. Furthermore, the stability of the proposed design is examined via the location of the closed-loop poles and frequency response. Moreover, the robustness of the controller is tested under model uncertainties. In both tests the proposed method displays an outstanding performance.