Automatic Controller Tuning Research Articles

Advances and Prospects of PID Controller in Mechanical Field: From Traditional Tuning to Intelligent Optimization

Abstract. The extensive use of PID controllers in the mechanical fieldparticularly in robots and other mechanical systemsis covered in this study. In these sectors, PID controllers have become the most popular control technology due to their straightforward design and simplicity of use. PID controller performance in nonlinear complex systems is explored, along with stability and adaptive adjustment, by comparing the conventional and intelligent PID tuning methods. According to the research, control performance can be greatly enhanced by merging PID controller with intelligent technologies like fuzzy logic and genetic algorithms. These results point to the possible use of PID-based control in numerical control systems in the future. PID controllers' automatic tuning capabilities have garnered significant attention in the industrial sector. Future research will focus on the automatic tuning of PID controller to further optimize its performance and broaden its application range.

A Novel Toolbox for Automatic Design of Fractional Order PI Controllers Based on Automatic System Identification from Step Response Data

This paper describes a novel automatic control toolbox, designed for non-experienced practitioners. Fractional order (FO) controllers are easily tuned with the main purpose of easy practical implementation. Experimental step data are required for the automatic FO controller tuning. An embedded system identification algorithm uses the step data to obtain a process model as a second order plus dead-time (SOPDT) system. Finally, the FO controller is computed based on the previously estimated SOPDT model in order to fulfil a set of user-imposed frequency domain performance specifications: phase margin, gain crossover frequency and gain margin maximization. Experimental step response data from a strongly nonlinear vertical take-off and landing unit have been used to design an FO controller using the toolbox. The experimental closed loop results validate the proposed toolbox. The end result is a user-friendly automatic fractional order controller tuning with endless possibilities of real-world applicability.

Settling Time Optimization in Wire Bonder Systems via Extremum-Seeking Control1

Adequate tuning of control laws is essential for high positioning accuracy, large system throughput, and reliability in high-end mechatronic and robotic systems. However, a population of such systems generally shows slight variations in dynamic responses due to, e.g., manufacturing tolerances, different disturbance situations, or position-dependent dynamics. Given the time-consuming nature of controller design, even by experienced control engineers, typically just one control law is designed for the whole system population based on worst-case bounds on variations in dynamic responses, resulting in a loss of individual system performance. The main contribution of this paper is the development of an automated controller tuning approach, based on extremum-seeking control, for settling time optimization via individual controller tuning. While other automated controller tuning methods exist, the developed approach allows inclusion of closed-loop stability and robustness constraints based solely on non-parametric frequency-response measurements of open-loop plant dynamics, and therewith directly optimizes transient system performance in a purely data-based manner. The proposed approach has been applied in simulation in an industrial case study for settling time optimization in point-to-point motions of a wire bonder system. In this case study, the effectiveness of the approach has been shown by achieving significant performance increases of 39.4% and 40.6% compared to controllers designed by experienced control engineers using manual loop-shaping techniques and a frequency-based auto-tuner, respectively, without needing manual tuning effort.

Automated controller tuning for Weighted Multiple Model Adaptive Control

Multiple model adaptive control (MMAC) uses models of different operating modes and optimizes a set of system controllers that can ensure stability over all modes. Traditionally, one controller is tuned for every operating mode but the number of operating modes and all their combinations increase exponentially. We present a novel convex-hull-based optimization algorithm that automatically generates a controller parameter set for a set of operating modes. The main contribution of the presented algorithm is that it can find a smaller controller set than the traditional one-controller per operating mode tuning approach, which we demonstrate empirically on a quadcopter trajectory tracking simulation using five different operating modes. The presented algorithm achieves this by constructing a convex hull in the controller parameter space to ensure the chosen parameters are affinely independent, which results in a set of only three controllers for five investigated operating modes without a significant loss in performance.

On-line automatic controller tuning using Bayesian optimisation - a bulk tailings treatment plant case study

The automatic tuning problem of multiple-input-multiple-output (MIMO) controllers is considered within the framework of Bayesian optimisation and applied in simulation to a bulk tailings treatment process. The aim is to develop a model free, on-line, automatic tuner which can optimise the performance of a given controller to the task at hand. The automatic tuning procedure can be conducted during commissioning, when poor controller performance is observed or when the process has changed. Simulations indicate that the method is able to locate the optimal tuning parameters for the bulk tailings treatment process as compared to a de-coupled controller developed from a model of the process. The parameters were obtained from an objective function which was balanced and weighted according to the response required.

Ziegler and Nichols meet Kermack and McKendrick: Parsimony in dynamic models for epidemiology

The COVID-19 crisis popularized the importance of mathematical modeling for managing epidemics. A celebrated pertinent model was developed by Kermack and McKendrick about a century ago. A simplified version of that model has long been used and became widely popular recently, even though it has limitations that its originators had clearly articulated and warned against. A basic limitation is that it unrealistically assumes zero time to recovery for most infected individuals, thus underpredicting the peak of infectious individuals in an epidemic by a factor of as much as about 2. One could avoid this limitation by returning to the original comprehensive model, at the cost of higher complexity. To remedy that, we blend Ziegler-Nichols modeling ideas, developed for automatic controller tuning, with Kermack-McKendrick ideas to develop novel model structures that predict infectious peaks accurately yet retain simplicity. We illustrate these model structures with computer simulations on real epidemiological data.

Data-Driven Scenario Optimization for Automated Controller Tuning With Probabilistic Performance Guarantees

Systematic design and verification of advanced control strategies for complex systems under uncertainty largely remains an open problem. Despite the promise of black-box optimization methods for automated controller tuning, they generally lack formal guarantees on the solution quality, which is especially important in the control of safety-critical systems. This letter focuses on obtaining closed-loop performance guarantees for automated controller tuning, which can be formulated as a black-box optimization problem under uncertainty. We use recent advances in non-convex scenario theory to provide a distribution-free bound on the probability of the closed-loop performance measures. To mitigate the computational complexity of the data-driven scenario optimization method, we restrict ourselves to a discrete set of candidate tuning parameters. We propose to generate these candidates using constrained Bayesian optimization run multiple times from different random seed points. We apply the proposed method for tuning an economic nonlinear model predictive controller for a semibatch reactor modeled by seven highly nonlinear differential equations.

Automatic controller tuning using a zeroth-order optimization algorithm

Abstract. We develop an automated controller tuning procedure for wind turbines that uses the results of nonlinear, aeroelastic simulations to arrive at an optimal solution. Using a zeroth-order optimization algorithm, simulations using controllers with randomly generated parameters are used to estimate the gradient and converge to an optimal set of those parameters. We use kriging to visualize the design space and estimate the uncertainty, providing a level of confidence in the result. The procedure is applied to three problems in wind turbine control. First, the below-rated torque control is optimized for power capture. Next, the parameters of a proportional–integral blade pitch controller are optimized to minimize structural loads with a constraint on the maximum generator speed; the procedure is tested on rotors from 40 to 400 m in diameter and compared with the results of a grid search optimization. Finally, we present an algorithm that uses a series of parameter optimizations to tune the lookup table for the minimum pitch setting of the above-rated pitch controller, considering peak loads and power capture. Using experience gained from the applications, we present a generalized design procedure and guidelines for implementing similar automated controller tuning tasks.

Data-Driven Adaptive Control for Laser-Based Additive Manufacturing with Automatic Controller Tuning

Closed-loop control is desirable in direct energy deposition (DED) to stabilize the process and improve the fabrication quality. Most existing DED controllers require system identifications by experiments to obtain plant models or layer-dependent adaptive control rules, and such processes are cumbersome and time-consuming. This paper proposes a novel data-driven adaptive control strategy to adjust laser voltage with the melt pool size feedback. A multitasking controller architecture is developed to incorporate an autotuning unit that optimizes controller parameters based on the DED process data automatically. Experimental validations show improvements in the geometric accuracy and melt pool consistency of controlled samples. The main advantage of the proposed controller is that it can adapt to DED processes with different part shapes, materials, tool paths, and process parameters without tweaking. System identification is not required even when process conditions are changed, which reduces the controller implementation time and cost for end-users.

Adaptive fuzzy control of state-feedback time-delay systems with uncertain parameters

This paper describes an effective and relatively simple design method for an adaptive multi-input single-output (MISO) fuzzy controller for a linear plant with partially known parameters including transport delay. The model reference adaptive control idea was applied, incorporating a reference model that defines the desired closed-loop performance. The reference model containing the fuzzy controller and the plant provides control system performances that are not inferior to those attainable with linear state feedback. The frequency-domain stability conditions for nonlinear state feedback are formulated. They are crucial for the proposed approach and guarantee stability and convergence of the adaptation process. Unlike in other works, the number of MISO fuzzy controller inputs has no restrictions. In this way, the design procedure generalizes the results reported thus far. The idea of automatic fuzzy controller tuning to obtain quasi-optimal system behavior is proposed. The adaptive fuzzy controller design procedure is exemplified for third- and fourth-order systems with delayed feedback.

Auto-Tuning Process of State Feedback Speed Controller Applied for Two-Mass System

The state feedback controller is increasingly applied in electrical drive systems due to robustness and good disturbance compensation, however its main drawback is related to complex and time consuming tuning process. It is particularly troublesome for designer, if the plant is compound, nonlinear elements are taken into account, measurement noise is considered, etc. In this paper the application of nature-inspired optimization algorithm to automatic tuning of state feedback speed controller (SFC) for two-mass system (TMS) is proposed. In order to obtain optimal coefficients of SFC, the Artificial Bee Colony algorithm (ABC) is used. The objective function is described and discussed in details. Comparison with analytical tuning method of SFC is also included. Additionally, the stability analysis for the control system, optimized using the ABC algorithm, is presented. Synthesis procedure of the controller is utilized in Matlab/Simulink from MathWorks. Next, obtained coefficients of the controller are examined on the laboratory stand, also with variable moment of inertia values, to indicate robustness of the controller with optimal coefficients.

Fractional order automatic tuning of [formula omitted] controller for stable processes

This paper presents modified fractional order relay based automatic tuning of PIλD controller for stable processes with load disturbance. The modified relay comprises of PIλcontroller introduced with the ideal relay in series. The proportional gain of PIλ controller is assumed as unity and the integral time constant is chosen such that, the system attains minimum 0° phase margin. λ of PIλ controller helps in reducing the harmonics in the output which ultimately leads to improvement in the accuracy of the proposed scheme. The limit cycle, thus, obtained helps in extracting the critical frequency and peak amplitude which helps in controller design. The designing of PIλD controller is based on the measured parameters from modified relay. Subsequently, the derivative time constant is derived in the design of PIλD controller using phase margin criteria and Nyquist curve is used to obtain the proportional gain. The integral time constant for PIλD controller is same as that of PIλ controller for auto tuning test. The auto tuning method and PIλD controller design, thus proposed, is validated using typical examples through simulation.

The Fastest Response Algorithm for Thermal Plants with a Time Delay: Application in a Hybrid System Containing a PID Controller and an Automatic Tuning Unit

The article discusses matters concerned with improving the performance of automatic closed-loop control systems of thermal plants with a time delay in responding to a change in the setpoint. The improvement is achieved by applying the fastest response algorithm (FRA) according to the Pontryagin maximum principle and using linear prediction of the controlled variable. It is shown that, during operation with switching the maximum control outputs applied to a plant with a time delay, linear prediction is inefficient, and self-oscillations may occur in the system. The technical solution proposed for eliminating self-oscillations implies the use of a hybrid closed-loop control system comprising an FRA, a PID controller, and an automatic controller tuning (ACT) unit, which performs the function of determining the plant model parameters and optimizing the controller parameters. The actuator is considered as a proportional section that is used as part of the plant. The control limitations are related to the level of the control output applied to the plant. The ACT unit comprises accelerated controller tuning algorithms that use active plant identification methods based on analyzing the response to an impulse input and two cycles of the excited self-oscillations. These algorithms make it possible to determine four parameters of the second-order plant model with a time delay. The self-oscillations occurring in systems with the FRA and plants with a time delay are eliminated at the end of the transient by making a switchover to PID control. Four embodiment versions of a system with the FRA are analyzed, specifically, those with and without control output reversal and also with using the plant simulation model without a time delay that is obtained from the ACT operating in parallel with the plant. For practical embodiment of the MSRA as part of a hybrid system, it is recommended to use its version without control output reversal. Relations for calculating the controlled variable prediction coefficient in terms of the plant model parameters in a wide range are obtained. Two examples of using the hybrid system equipped with industry-grade controllers for a temperature control system are given: one with the electric heater power controlled using a pulse-width modulator and the other with a constant speed actuator.

Controller Tuning Based on Bayesian Optimization

This paper proposes an approach for automatic controller tuning based on experimental data only. It determines the controller parameters for a given cost function without knowing the true plant dynamics via Bayesian optimization. The validity of the proposed method is tested through some numerical simulations. Then, the proposed method is applied to PID controller tuning for an actual motor positioning system. The experimental results show that the proposed method improves the control performance effectively.

Gain Scheduled Attitude Control of Fixed-Wing UAV With Automatic Controller Tuning

Fixed-wing unmanned aerial vehicles (UAVs) have become increasingly important in military, civil, and scientific sectors. Because of the existing nonlinearities, effective control this type of UAV remains a challenge. This paper proposes a gain scheduled proportional-integral derivative (PID) control system for fixed-wing UAVs where a family of PID cascade control systems is designed for several operating conditions of airspeed. This is done using an automatic tuning algorithm, where the controllers are automatically selected by deploying an airspeed sensor positioned ahead of the aircraft. Furthermore, the actual gain scheduling is carried out by forming an interpolation between the family members of the linear closed-loop system, which ensures a smooth transition from one operating point to another. Experimental results are conducted in a wind tunnel to show the successful design and implementation of the gain scheduled control system for the fixed-wing UAV and the significant performance improvement over a linear control system without controller adaptation.

A Robust PID Autotuning Method Applied to the Benchmark PID18

In this paper a proportional-integral-derivative (PID) autotuning control strategy is presented and applied to the benchmark system presented at the 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control (PID18). The automatic tuning of controller gains is based on a single sine test, with user-defined robustness margins guaranteed. Its performance is compared against a model based designed controller with computer-aided design tool based on frequency response (FRtool) and against the benchmark reference controller. The closed loop control simulations, applied on the benchmark, indicate that the method properly performed.

Multivariable Fractional Order PI Autotuning Method for Heterogeneous Dynamic Systems

In this paper the application of robust Fractional Order Proportional-Integral (FO-PI) autotuning control strategy is presented and applied to heterogeneous dynamic systems using decentralized control. The automatic tuning of controller gains is based on a single sine test, with user-defined robustness margins guaranteed. Its performance is compared against two other fractional order controllers based on PI gain-crossover autotuning method and Internal Model Control (IMC). The closed loop control simulations applied on the heterogeneous dynamic systems indicate that the proposed method performs properly.

Self-Tuning Mechanism for the Design of Adaptive Secondary Mirror Position Control

Deformable mirrors (DMs) are electromechanical devices used in ground-based telescopes to compensate for the distortions caused by the atmospheric turbulence, the main factor limiting the resolution of astronomical imaging. Adaptive secondary mirrors (ASMs) represent a new type of DMs; two of them have been recently installed on the 8-m-class large binocular telescope (LBT). ASMs are able to jointly correct rigid and nonrigid wave-front distortions thanks to the use of force actuators distributed on the overall mirror surface. As an offset, each actuator needs to be piloted by a dedicated controller, whose parameters must be accurately tuned to obtain the desired mirror shape. At the present time, the calibration of the controller parameters is executed manually. This paper presents a novel automatic controller tuning procedure that does not rely on the modeling of the mirror dynamics. The experimental validation on a prototype reproducing the three innermost rings of the LBT ASM is reported.

Unfalsified Control to a pH Neutralization Process with Noisy Measurements

In this paper, we demonstrate an application of unfalsified control to the nonlinear control of a pH neutralization in continuous stirred tank reactors under noisy measurements. The adaptation of controllers can be performed by two mechanisms: 1) The switching of an active controller in a current controller set and 2) An adaptive controller set generated by an evolutionary algorithm (EA) and a diversity operator. This leads to an automatic controller tuning for PI controller structure. Finally, we show that the proposed algorithm can handle highly nonlinear dynamics of the neutralization process with noisy measurements well.

Closed-Loop Automatic Tuning Technique for an Event-Based PI Controller

A methodology for the closed-loop automatic tuning of an event-based PI controller is proposed in this article. In particular, the technique consists of performing two relay feedback experiments with a symmetric send-on-delta (possibly roughly tuned) PI controller already in place. The evaluation of the process variable allows for the determination of the parameters of a first-order-plus-dead-time process transfer function that is eventually employed to tune the controller parameters. Simulation and experimental results demonstrate the effectiveness of the methodology.