Resonant controllers are widely used in applications involving reference tracking and disturbance rejection of periodic signals. The controller design is typically performed by a trial-and-error approach or by means of time and resource-consuming analytic methods that require an accurate plant model, intricated mathematics and sophisticated tools. In this paper, we propose an easily implementable, model-free method for tuning a proportional-multi-resonant controller applicable to general linear time-invariant causal plants. Just like the Ziegler-Nichols methods, the proposed methodology consist in identifying one specific point of the plant's frequency response -- which is easily obtained in a relay with adjustable phase experiment -- and then designing the controller with simple tuning formulas and tables. The method is analyzed in detail for three examples, showing its practical appeal and wide applicability.
This paper investigates the chattering and deadlock behaviors of the proportional-integral (PI) controller with an anti-windup (AW) limiter recommended by the IEEE Standard 421.5-2016. Depending on the simulation method, the controller may enter a chattering or deadlock state in some combinations of parameters and inputs. Chattering and deadlock are analyzed in the context of three numerical integration approaches: explicit partitioned method (EPM), execution-list based method (ELM), and implicit trapezoidal method (ITM). This paper derives the chattering stop condition for EPM and ELP, and an…
Norwegian University of Science and Technology（挪威科技大学）；SINTEF Digital（挪威科技工业研究院数字部门）；Oklahoma State University（俄克拉荷马州立大学）
Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights about the mathematical model governing the physical system. However, if a system is highly complex, it might be infeasible to produce a reliable mathematical model of the system. Without a model most of the theoretical tools to develop control laws break down. In these settings, machine learning controllers become attractive: Controllers that can learn and adapt to complex systems, developing contro…
This paper articulates design and performance analysis of digital controllers in discrete and continuous time domains for a single-joint robot arm manipulator. The investigated robot arm system is modeled as a single degree of freedom (DOF) plant and there is a feedback sensor implying a closed-loop system. The design approach incorporates discrete (z-plane) and continuous-time (warped s-plane or w-plane) domain parameters. Four digital controllers - phase-lag, phase-lead, proportional-integral (PI) and proportional-integral-derivative (PID) are theoretically designed and implemented to achiev…
Drones are effective for reducing human activity and interactions by performing tasks such as exploring and inspecting new environments, monitoring resources and delivering packages. Drones need a controller to maintain stability and to reach their goal. The most well-known drone controllers are proportional-integral-derivative (PID) and proportional-derivative (PD) controllers. However, the controller parameters need to be tuned and optimized. In this paper, we introduce the use of two evolutionary algorithms, biogeography-based optimization~(BBO) and particle swarm optimization (PSO), for mu…
This paper proposes a coordinate-free controller for a nonholonomic vehicle to circumnavigate a fully-actuated moving target by using range-only measurements. If the range rate is available, our Proportional Derivative (PD)-like controller has a simple structure as the standard PD controller, except the design of an additive constant bias and a saturation function in the error feedback. We show that if the target is stationary, the vehicle asymptotically encloses the target with a predefined radius at an exponential convergence rate, i.e., an exact circumnavigation pattern can be completed. Fo…
Hussaini Adamu Polytechnic（侯赛因·阿达姆理工学院）；Bayero University, Kano（卡诺贝罗大学）；Ahmadu Bello University（阿赫马杜·贝洛大学）
Robot manipulators are extensively used in industrial applications because of their immense importance such as in constructions automation. Therefore, designing controllers to suit the intensive purpose of the application is one of the major challenges for control researchers. This paper presents comparative analysis of three controllers on a 3-DOF robot manipulator. The proportional integral derivative (PID), proportional derivative (PD) and fuzzy logic (FL) controllers were designed and applied to each of the link of the robot by simulation. The performance of each control method was assesse…
Two ways of designing low-order discrete-time (i.e. digital) controls for low-order plant (i.e. process) models are considered in this tutorial. The first polynomial method finds the controller coefficients that place the poles of the closed-loop feedback system at specified positions for adroit controls, i.e. for a rapid and compressed transient response, when the plant model is known precisely. The poles and zeros of the resulting controller are unconstrainted, although an integrator may be included in the controller structure as a special case to drive steady-state errors towards zero. The …
A Distributed PI+Reset Scheme for Discrete-Time Economic Dispatch of A Grid-connected BESS Network
College of Artificial Intelligence, Nankai University（南开大学人工智能学院）；Tianjin Key Laboratory of Interventional Brain-Computer Interface and Intelligent Rehabilitation, Nankai University（南开大学天津介入式脑机接口与智能康复重点实验室）
A Novel $αβ$-Approximation Method Based on Numerical Integration for Discretizing Continuous Systems
School of Electrical Engineering, Xi’an Jiaotong University（西安交通大学电气工程学院）；SolaX Power Network Technology (Zhejiang) Co., Ltd.（固德威电网科技（浙江）有限公司）；State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University（西安交通大学电气工程学院电力设备电气绝缘国家重点实验室）；Key Laboratory of Technology in Rural Water Management of Zhejiang Province, College of Electric Engineering, Zhejiang University of Water Resources and Electric Power（浙江省农村水利技术重点实验室，浙江水利水电学院电气工程学院）
A resonance and an antiresonance peak characterize many industrial mechanisms dynamics driven by a Permanent Magnet Synchronous Motor (PMSM). The presence of the resonance peak can lead to vibrations and instability of the system. On that account, advanced methods exist to tune the speed Proportional Integral (PI) controller based on adaptive or fuzzy theory. However, those methods require expertise in control theory and are not available in commercial drives. For that, this paper proposes a Bode-based method for PI parameters selection in combination with a notch filter that can be easily set…
Although variable-speed three-blade wind turbines are nowadays quite popular, their control remains a challenging task. We propose a new easily implementable model-free control approach with the corresponding intelligent controllers. Several convincing computer simulations, including some fault accommodations, shows that model-free controllers are more efficient and robust than classic proportional-integral controllers.
Exponential stability of a PI plus reset integrator controller by a sampled-data system approach
Gipsa-lab（吉普萨实验室）；CNRS, LAAS（法国国家科学研究中心，图卢兹航空航天实验室）；Univ de Toulouse, UPS, LAAS（图卢兹大学，国立高等邮电学校，图卢兹航空航天实验室）；Dpto. Informática y Sistemas, University of Murcia（穆尔西亚大学，计算机与系统系）；Univ de Toulouse, LAAS（图卢兹大学，图卢兹航空航天实验室）
This paper presents three types of sliding mode controllers for a magnetic levitation system. First, a proportional-integral sliding mode controller (PI-SMC) is designed using a new switching surface and a proportional plus power rate reaching law. The PI-SMC is more robust than a feedback linearization controller in the presence of mismatched uncertainties and outperforms the SMC schemes reported recently in the literature in terms of the convergence rate and settling time. Next, to reduce the chattering phenomenon in the PI-SMC, a state feedback-based discrete-time SMC algorithm is developed…
Electrolysis systems use proportional-integral-derivative (PID) temperature controllers to maintain stack temperatures around set points. However, heat transfer delays in electrolysis systems cause manual tuning of PID temperature controllers to be time-consuming, and temperature oscillations often occur. This paper focuses on the design of the PID temperature controller for an alkaline electrolysis system to achieve fast and stable temperature control. A thermal dynamic model of an electrolysis system is established in the frequency-domain for controller designs. Based on this model, the temp…
The problem of controlling the mean and the variance of a species of interest in a simple gene expression is addressed. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a simple PI controller that satisfies certain sufficient conditions. Controlling both the mean and variance however requires an additional control input, e.g. the mRNA degradation rate, and local robust tracking of mean and variance is proved to be achievable using multivariable PI control, provided that the reference point satisfies necessary conditions imposed by the syst…
Proportional-integral-derivative (PID) controller is widely used across various industrial process control applications because of its straightforward implementation. However, it can be challenging to fine-tune the PID parameters in practice to achieve robust performance. The paper proposes a model-based reinforcement learning (RL) framework to design PID controllers leveraging the probabilistic inference for learning control (PILCO) method and Kullback-Leibler divergence (KLD). Since PID controllers have a much more interpretable control structure than a network basis function, an optimal pol…
This paper presents a systematic method for the selection of the Model Predictive Control (MPC) stage cost. We match the MPC feedback law to a proportional-integral (PI) controller, which we efficiently tune by high-performance Monte Carlo (MC) simulation. The PI tuning offers a wide range of tuning possibilities that is then inherited by the MPC design. The MC simulation tuning of the PI controller is based on the minimization of two different objectives; 1) the 2-norm tracking error, and 2) a bi-objective consisting of the 2-norm tracking error and a 2-norm input rate of movement penalty. We…
In this project, we designed a DC motor whose speed can be controlled by a PID controller. The proportional, integral and derivative gains (KP, KI, KD) of the PID controller are adjusted according to Fuzzy logic. First of all, the fuzzy logic controller is designed according to rules so that the systems is basically robust. There are 25 rules for the auto-tuning of each parameter of the PID controller. The FLC (fuzzy logic controller) has two inputs. The first is the motor speed error between the reference (setpoint) and the actual speed. The second is the variation of the speed error (derivat…
We consider the problem of steering a multi-agent system to multi-consensus, namely a regime where groups of agents agree on a given value which may be different from group to group. We first address the problem by using distributed proportional controllers that implement additional links in the network modeling the communication protocol among agents and introduce a procedure for the optimal selection of them. Both the cases of single integrators and of second-order dynamics are taken into account and the stability for the multi-consensus state is studied, ultimately providing conditions for …
