Ziegler-Nichols Tuning Research Articles

Investigation and Analysis of Fuzzy Logic Controller Method on DC-DC Buck-Boost Converter

This study evaluates the performance of PID, Mamdani FLC, and Sugeno FLC controllers on a DC-DC Buck-Boost Converter to determine their suitability for various control applications. The Buck-Boost Converter, operating in conventional configuration, was modeled using MATLAB/Simulink with parameters: input voltage (12 V), output voltage (24 V), resistor (6.5 Ω), capacitor (1.5 µF), and inductor (10 µH). The converter's switching frequency was set at 20 kHz to ensure stability under varying load and input conditions. PID control was implemented using the Ziegler-Nichols tuning method, while fuzzy controllers utilized Gaussian membership functions and 3×3 fuzzy rule bases. Mamdani employed the centroid defuzzification method, whereas Sugeno used weighted average defuzzification. The simulation tested performance metrics, including rise time, overshoot, output stability, and voltage ripple, under conditions of load and input voltage variations. Results show that PID achieved the fastest rise time (72.452 ms) but exhibited higher sensitivity to input changes. Sugeno provided the most stable output with minimal ripple, while Mamdani demonstrated greater adaptability but less stability compared to Sugeno. Statistical analysis confirmed significant differences in rise time but no differences in overshoot across methods. These findings highlight the strengths of each method, with Sugeno being optimal for stability and precision, PID for fast response, and Mamdani for complex fuzzy logic applications.

Optimizing actual PID control for walking quadruped soft robots using genetic algorithms

The construction of soft robots’s models and controllers remains a significant challenge. In this paper, we propose a new walking control method for the quadruped soft robot named genetic algorithm-optimized PID. First, we construct the control model correlating valve voltage with leg bending based on the geometrical analysis. This modeling approach leverages the characteristics of novel leg structure and bend sensor, thereby streamlining the control model for locomotion of quadruped soft robotic. Moreover, We apply the genetic algorithm to automatically tune parameters and optimize PID controllers, aiming to enhance control performance. The application of the proposed method to the walking control has been uniquely demonstrated on a real 3D-printed quadruped soft robot. Experimental results indicate that the genetic algorithm-optimized PID controller significantly improves trajectory tracking compared to the Ziegler-Nichols tuning method. This optimization increases the robot’s walking speed from 5 mm/s to 8 mm/s, reduces the error rate by 2.4064%, decreases overshoot by 12.55%, and shortens response time by 0.5 s, substantially enhancing the controller’s overall performance. Additionally, compared to particle swarm optimization, the proposed method further improves performance by reducing the error rate by 0.4079%, overshoot by 8.4%, and response time by 1.0 s.

Water Level Control in Coupled Tank System with PLC and IoT-Based PID Method

There are many advanced technological discoveries in industry, including the coupled tank. Coupled tanks are several tanks connected to each other. One of the quantities that is often controlled in the industry is the control of water levels. Water level control in a PLC and IoT-based coupled tank system is a medium for controlling and monitoring water levels remotely in real-time. The sensor used is a Differential Pressure Transmitter (DPT) with a pump motor actuator which is connected to an Omron PLC using an inverter. There is a disturbance in the form of setting the control valve opening. The control method used is the PID method with Ziegler-Nichols tuning and trial and error. Both methods analyzed which performance of the system response characteristics was better. It is proven that PID tuning is suitable for water level control of coupled tank systems.

Multi-objective optimization of PI controller for BLDC motor speed control and energy saving in Electric Vehicles: A constrained swarm-based approach

Proportional Integral Derivative (PID) controllers are widely employed in industrial applications due to their effectiveness, simplicity, and versatility. Within the automotive sector, one notable application of the Proportional Integral (PI) controller is in the realm of electric motors, particularly the Brushless Direct Current (BLDC) motors powering Electric Vehicles (EVs). The precision of speed control over BLDC motors, renowned for their efficiency and reliability, is paramount for optimizing vehicle performance and ensuring energy efficiency. PIDs must be tuned each time they are used in an application to optimize performance. A well-known empirical hit and trial tuning strategy is the Ziegler–Nichols method, which results in sub-optimal performance in the presence of locally optimal solutions of large-dimensional search spaces. Existing Artificial Intelligence methods tailored for PID controller tuning often focus on singular optimization aspects, neglecting potential performance gains achievable through multi-objective considerations. Furthermore, prevalent swarm-based PID optimization methods typically initialize the population randomly without imposing any bounds on input parameters, thus rendering them susceptible to inconsistent, unreliable, sub-optimal solutions in unconstrained search environments. In our research endeavors, we mathematically model the multi-objective optimization of BLDC motor speed control, energy usage, and efficiency using constrained Differential Evolution and Particle Swarm Optimized PID controllers. The Ziegler–Nichols tuning method is used to ascertain the initial PI parameters and define bounds within the input space. Our methodology addresses a critical gap by integrating real-time road gradient data into the EV control system, enhancing precision and minimizing energy consumption, especially during challenging road conditions. The proposed approach significantly improves motor speed control and energy efficiency in EVs. With our proposed swam-based optimization over 30 iterations, MSE decreased by approximately 95.4% (from 3.8834 to 0.1809), while energy consumption reduced by about 3.1% (from 1.015 kWh to 0.984 kWh). These results highlight the effectiveness of our method in enhancing both speed control precision and energy efficiency. In addition, code related data is available at Github.

A fast relay feedback auto-tuning tilt-integral-derivative (TID) controller method with the fractional-order Ziegler–Nichols approach

The relay feedback auto-tuning method, which was an early commercialized approach, has maintained its popularity due to its simplicity and robustness. However, the classical proportional integral derivative (PID) controller auto-tuning method often results in unacceptable overshoot, especially for integrating and higher-order processes. By integrating the TID controller with the relay feedback technique, we significantly enhance dynamic control performance without relying on prior knowledge of the system. However, the direct application of the classical auto-tuning method to the TID controller encounters challenges due to the additional fractional-order transfer function s−1n. Therefore, we have developed a fractional-order Ziegler–Nichols (FOZ-N) approach, specifically designed to adjust the parameters of the TID controller. The proposed FOZ-N method is fast, simple, and capable of achieving the desired performance. In contrast to the previous Ziegler–Nichols tuning method, the TID controller parameters Kt and Ki are determined to shift the critical point (−1/Ku,j0) to the FOZ-N point (−0.5,−j0.7) on the Nyquist curve, ensuring system robustness and dynamic performance. The impact of the fractional order parameter s−1n and ratio r is explored through time-domain analysis, where these parameters are determined to ensure optimal dynamic performance. Additionally, we provide a detailed tuning procedure along with a helpful example. To demonstrate the advantages of the proposed auto-tuning TID controller over the Ziegler–Nichols PID controller, Optimal PID controller, simple internal model control (SIMC) PID controller, and Ziegler–Nichols FOPID controller, we present a simulation illustration involving multiple different systems. To validate the practical outcomes of this paper, we present experimental results on the temperature control of a Peltier cell.

Deep reinforcement learning for PID parameter tuning in greenhouse HVAC system energy Optimization: A TRNSYS-Python cosimulation approach

The control of indoor temperature in greenhouses is crucial as it directly impacts the crop's thermal comfort and the performance of heating, ventilation, and air-conditioning (HVAC) systems. Conventional feedback controllers, like on/off, can sometimes make HVAC system work at full capacity when only half that capacity is needed. In contrast, the proportional-integral-derivative (PID) controller, provides precise control based on its P, I, and D parameters. However, it lacks a formal design procedure for optimizing a specified objective function. Previous studies have utilized conventional PID tuning approaches to track room setpoint temperature for residential buildings, data centers, and office buildings, with limited research in greenhouse applications. To address this gap, this study proposes a flexible PID controller that employs a deep reinforcement learning (DRL) algorithm to optimize its parameters, by tracking the setpoints and energy consumption of a greenhouse planted with tomatoes. This approach is different from the typical method of using the trained RL agent directly in HVAC controls. Through a self-made TRNSYS-Python cosimulation framework, the DRL agent interacts directly and in real time with the greenhouse and its plants. Consequently, optimized PID parameters were established and tested in the simulated environment. The resulting performance, in terms of both energy consumption and its ability to maintain the crop’s comfort temperature, was compared with the simulated on/off and manually tuned PID controllers. Compared to the on/off baseline control, the proposed PID optimized parameters reduce energy use by 8.81% to 12.99% and the manually tuned PID parameters with the Ziegler-Nichols tuning method reduce energy use by 7.17 %. Additionally, the proposed method had a deviation of 2.07% to 3.13%, while the manually tuned PID controller and the on/off controller had deviations of 7.27% and 3.27%, respectively, from the minimum comfortable temperature. This study serves as a framework for improving the energy efficiency of greenhouse HVAC system operations.

Controller design and performance study of DC-DC bidirectional converter for speed regulation of permanent magnet direct current machine

This paper presents the design of a controller for a bidirectional DC-DC converter for speed control of a permanent magnet DC machine (PMDC). In recent years, this electric drive system has often been used in electric vehicles or hybrid electric vehicles. In this application, the development of a controller is required to support the various functions of the machine. The design methodology of the controller should provide satisfactory dynamic performance under both motor and generator operation of the PMDC machine. In this regard, the control of the bidirectional DC/DC converter is necessary. From the perspective of speed control, the condition for absolute stability is derived from the small-signal model of the PMDC drive system. Then the Ziegler-Nichols tuning table is used to determine the gain of the proportional-integral (PI) controller in the conventional way. From further investigation, it was found that the transient response and stability margin of the speed control loop in the conventional case are

Position control of Stewart platform with electric linear actuator

In recent decades, several technological applications have depended on manipulators like Stewart platform due to its accuracy and precision. Based on actuation type, Stewart platforms could be rotary or linearly actuated. Electric linear actuators are devices commonly consist of DC or AC motors coupled with lead screw or mechanism of gears and spindle which are used to convert rotary motion into linear (push or pull) motion. To increase accuracy and precision and achieve the desired linear actuator response, controllers should be used. The main aspiration of this work is to investigate the feasibility of using PID controllers for position control of Stewart platform with linear actuators. The mathematical model has been derived and the model transfer function has been obtained. To meet the required response of performance characteristics, the PID controller has been designed based on analysis of root-locus. Model simulation analysis has been carried out on both MATLAB and Simulink. For the electric linear actuator, comparison between the obtained response and the results of Ziegler-Nichols tuning method has been discussed on basis of the specifications of the time response. The PID controller parameters for the electric linear actuator has been tested experimentally and compared with simulation results.

Design and Develop a Non-Invasive Pulmonary Vibration Device for Secretion Drainage in Pediatric Patients with Pneumonia

The study aimed to develop a non-invasive pulmonary vibration device, specifically tailored for pediatric patients, to address a range of pulmonary conditions. The device employs a PID control system to ensure consistent and precise vibrations. The primary contribution of this research is the successful development, testing, and implementation of this innovative device. Utilizing technical components such as an Arduino, a vibration DC motor, and an ADXL335 accelerometer, the device was engineered to deliver stable and continuous vibrations even when subjected to external pressures or interactions with the patient. Controllers, including P, PI, PD, and PID types, were rigorously compared. The Ziegler-Nichols tuning technique was applied for meticulous evaluation of vibration control specifically within the context of this non-invasive pulmonary vibration device. Our findings revealed that the PID controller displayed superior accuracy in vibration control compared to P, PI, and PD controllers. Clinical trials involving pediatric patients showed that the PID-controlled device achieved treatment outcomes comparable to conventional methods. The device's precise control of vibration strength provides an added benefit, making it a well-tolerated, non-invasive treatment option for various pulmonary conditions in pediatric patients. Future research is necessary to assess the long-term effectiveness of the device and to facilitate its integration into standard clinical practice. In summary, this study represents a significant advancement in pediatric pulmonary care, demonstrating the critical role that PID control systems adapted for non-invasive pulmonary vibration devices can play in enhancing treatment precision and outcomes.

Development of Decentralized Speed Controllers for a Differential Drive Wheel Mobile Robot

This research presents a comprehensive mathematical model and a control-oriented model for a differential drive wheel mobile robot (DDWMR). The components and their interconnection within the robot are thoroughly modeled. The proposed mathematical models are used to analyze the characteristics of the robot. The control-oriented model is a simplified one which will be used to design speed controllers. The performance of the proposed system is evaluated through four case studies, focusing on both stand-alone motor systems and the entire DDWMR. The tracking performance is evaluated using metrics such as absolute error integration and root mean square error. Simulation results show that under ideal step command, the pole-zero cancellation PI speed controller achieves the best tracking performance, while PID controllers obtained from Matlab’s Auto-tuning App perform best for standalone motor systems. For motors in a DDWMR, the PID controller with parameters derived from the Ziegler-Nichols tuning rules provides optimal tracking performance. These simulation results show that there is no universal controller that can achieve the best performance in all situations; rather, each controller is suited to specific circumstances. Nonetheless, in all case studies, better motor speed tracking leads to improved trajectory tracking performance for the robot.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Analisa Perbandingan Pengendali PID pada Motor DC Menggunakan Metode Ziegler-Nichols dan Trial and Error

The purpose of this research is to design a PID control on a DC motor using 2 tuning methods, namely Trial & Error and Ziegler-Nichols. The results showed that the Pittman DC Motor system response from the Pittman DC motor was very unstable, in which there were still many oscillations and a very high overshoot value. In the Trial & Error method, the system response value was obtained on the P controller, namely, rise time = 0.000551 s, settling time = 0.00468 s, overshoot = 37.1 %, peak time = 0.972 s, and time delay = 0.00134 s. on the PI controller namely, rise time = 0.000396 s, settling time = 0.00534 s, overshoot = 47.7%, peak time = 1.23 s, and time delay = 0.00102 s. on the PID controller namely, rise time = 0.000223 s, settling time = 0.00502 s, overshoot = 64.6%, peak time = 1.54 s, and time delay = 0.000601 s. In the Ziegler-NIchols method, the response value of the system to the P controller is obtained, namely, rise time = 0.00118 s, settling time = 0.00564 s, overshoot = 15.4%, peak time = 0.178 s, and time delay = 0.00262 s. on the PI controller namely, rise time = 0.000275 s, settling time = 0.00531 s, overshoot = 58.3%, peak time = 1.44 s, and time delay = 0.000767 s. on the PID controller, namely, rise time = 0.00133 s, settling time = 0.00446 s, overshoot = 12.6 %, peak time = 0.0237 s, and time delay = 0.00288 s. The simulation results show that the value for the Ziegler-Nichols tuning method is better than the Trial & Error method, perhaps because the input value for the Trial & Error method is larger.

Optimal detuning of multivariable proportional integral controller based on data‐driven approach for an activated sludge process

AbstractThe study deals with designing a multivariable centralized proportional‐integral (PI) controller for an activated sludge process (ASP) by adopting a new tuning technique. To overcome the tedious task of manual tuning by a classical method that was based on Ziegler–Nichols tuning, a novel approach is developed by formulating the optimization problem and considering it along with the theoretical results to calculate the controller parameters. The proposed method is then compared with the reported method to demonstrate the advantages of the proposed approach. A nonlinear ASP model is selected to evaluate the performance of the designed controller. The simulation carried through the proposed optimization technique exhibits a significant improvement in closed‐loop performance for tuning the centralized controller. It is observed that the proposed method minimizes the effort of tuning the controller significantly. The proposed controller achieves better load disturbance response and lower overshoot than the reported method. The proposed method could improve integral absolute error (IAE) and integral time absolute error (ITAE) performance indices, ranging between 18.69% to 53.80% and 16.42% to 52.97% for a step change in and , respectively, which are better compared to the reported method. The study also assesses the control system's robustness for their uncertainties with the time constant and time delay.

IPDT Model-Based Ziegler-Nichols Tuning Generalized to Controllers with Higher-Order Derivatives.

The paper extends the earlier work entitled "Making the PI and PID Controller Tuning Inspired by Ziegler and Nichols Precise and Reliable", to higher-order controllers and a broader range of experiments. The original series PI and PID controllers, based on automatic reset calculated by filtered controller outputs, are now augmented by higher-order output derivatives. This increases the number of degrees of freedom that can be used to modify the resulting dynamics, accelerates transient responses, and increases robustness to unmodeled dynamics and uncertainties. The fourth order noise attenuation filter used in the original work allows for the addition of an acceleration feedback signal, thus resulting in a series PIDA controller or even a jerk feedback that leads to a PIDAJ series controller. Such a design can further use the original process and filter approximation of the step responses through the integral-plus-dead-time (IPDT) model, while allowing experimentation with disturbance and setpoint step responses of the series PI, PID, PIDA and PIDAJ controllers, and thus, evaluating the role of output derivatives and noise attenuation from a broader perspective. All controllers considered are tuned using the Multiple Real Dominant Pole (MRDP) method, which is complemented by a factorization of the controller transfer functions to achieve the smallest possible time constant for automatic reset. The smallest time constant is chosen to improve the constrained transient response of the considered controller types. The obtained excellent performance and robustness allow the proposed controllers to be applied to a wider range of systems with dominant first-order dynamics. The proposed design is illustrated on a real-time speed control of a stable direct-current (DC) motor, which is approximated (together with a noise attenuation filter) by an IPDT model. The transient responses obtained are nearly time-optimal, with control signal limitations active for most setpoint step responses. Four controllers with different degrees of derivative with generalized automatic reset were used for comparison. It was found that controllers with higher-order derivatives may significantly improve the disturbance performance and virtually eliminate overshoots in the setpoint step responses in constrained velocity control.

Design of a Liquid Jamming Gripper

We present the design of a universal gripper based on the principle of liquid jamming. The phase change behavior of a mineral oil subjected to cooling is used for adaptive gripping and release of objects. The mineral oil is enclosed in a soft, compliant membrane molded into a spherical shape. The membrane with the liquid easily adapts to the shape of the object to be picked up. A thermoelectric cooling system is designed with a conductive spreader immersed in the oil to quickly cool the liquid held in a membrane. Once the membrane gripper conforms to the shape of the object partially enclosing it, the liquid is cooled below the phase change temperature, thus freezing the liquid and hardening the gripper around the object and effectively gripping it. We describe the design methodology of the gripper, part selection, and mechanical design. A proprietary controller developed by Venture Corporation is used for controlling the TEC module and the controller is based on a simple PID optimized using Ziegler–Nichols tuning for the P, I, and D values. The hardware is evaluated and the basic gripping functions on different odd-shaped objects are demonstrated. An invention disclosure has been submitted to the NUS IP office (ILO).

IMPLEMENTASI KONTROLER PID DENGAN METODE TUNING ZIEGLER-NICHOLS DAN COHEN-COON PADA SISTEM SCADA KENDALI LEVEL AIR

Didactics or mini plant teaching aids help students in colleges to understand the use of industrial equipment The SCADA-based water level control system is one of the teaching aid simulator equipment for monitoring and controlling water levels. In this research, PLC is used as a controller with three I/O modules digital input module, digital output, and analog input and output. Arduino is also used as an analog output converter from PLC to actuator. The control method used is PID control. In the PID control, there are control parameters, namely Kp, Ki, and Kd. The third parameter was determined by the Ziegler-Nichols tuning method and compared with the Coohen-Coon method. The SCADA software that used is Wonderware Intouch on a system using a kepserver. The results of this study indicate that the Cohen-Coon tuning method for proportional control Kp = 1 produces the best response in water level control with a settling time of 21s and a rise time of 18s.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

Implementation of proportional–integral control in Baglog steamer temperature control

Sterilization is the oyster mushroom cultivation process. Sterilization is used to kill nuisance microorganisms that can inhibit mushroom growth. The sterilization process is 8 hours at a temperature of 70–95 oC. This process of frequent breakdown is caused by the unstable temperature sterilization space and is controlled manually. Based on these problems, the right solution is to use a steamer that can be controlled automatically using the proportional–integral (PI) control method. PI controller consists of proportional gain and integral gain. To determine the value of proportional gain and integral gain, this study used the Ziegler-Nichols tuning method using the S curve. The results of the PI control parameters obtained the value of Kp=25.2 and Ki=0.302. Thus, producing a transient response graph with Mp=94.5; Os=0.45; PO=0.47; Tr=16,440 s. The system can work according to setpoint 95 oC and maintain a stable temperature according to the setpoint with these results. And the sterilization time becomes fast from 8 hours to 6 hours.

Design of a Combined Proportional Integral Derivative Controller to Regulate the Temperature Inside a High-Temperature Tubular Solar Reactor

Abstract Solar fuels are proven to be promising candidates for thermochemical energy storage. However, the transient nature of solar radiation is an obstacle to maintaining a stable operational temperature inside a solar reactor. To overcome this challenge, the temperature of a solar reactor can be regulated by controlling the incoming solar radiation or the feedstock flowrate inside the reactor. In this work, a combined proportional integral derivative (PID) controller is implemented to regulate the temperature inside a high-temperature tubular solar reactor with counter-current flowing gas/particles. The control model incorporates two control systems to regulate incoming solar radiation and gas flow simultaneously. The design of the controller is based on a reduced-order numerical model of a high-temperature tubular solar reactor that is vertically oriented with an upward gas flow and downward particle flow. The reactor receives heat circumferentially through its wall over a finite segment of its length. Formulation of the heat transfer model is presented by applying the energy balance for the reactor tube and considering heat and mass transfer inside. A set of governing differential equations are solved numerically by using the finite volume method to obtain reactor wall, particles, and gas temperatures along the reactor length with various boundary conditions. Simulation results are used to tune the PID controller parameters by utilizing the Ziegler–Nichols tuning method. Both the simulation results and the controller performance are visualized on the labview platform. The controller is challenged to track different temperature setpoints with different scenarios of transient solar radiation. The performance of the PID controller was compared to experimental results obtained from an industrial PID controller embedded in a 7 kW electric furnace. Results show that the combined PID controller is successful in maintaining a stable temperature inside the reactor by regulating the incoming solar radiation and the flowrate via small steady-state error and reasonable settling time and overshoot.

Proportional Integral Speed Controller for Apron Feeder of a Limestone Crusher in a Cement Factory

The paper describes types of limestone crusher properties and comparison between different types of crushers with respect to reduction ratio and feeding material. The type which we deal with in this paper is hammer impact crusher with apron feeder speed control system. The old conventional speed control system, which was depending on relay logic and timers, has been recently replaced by a new advanced system using PLC and SCADA system. The main advantages of the new control system are: increasing production rate, saving time in fault detection, monitoring and data logging. The ability of Proportional Integral Derivative (PID) controllers to regulate many practical industrial processes has led to their wide acceptance in industrial applications. This paper presents the application of the Ziegler-Nichols tuning method to design and testing a PI controller for an apron feeder speed control system of a practical limestone crusher in a cement factory. After tuning the speed PI-Controller of the apron feeder of the limestone crusher, it has been noted that the crusher production rate has increased from 879 ton/hour to 964 ton/ hour, i.e. the production rate increased by 85 ton/hour. The crusher is running 12 hour per day and 300 days per year, thus the annual crusher production will increase by 306,000 ton/year

Robust Control of a Biophysical Model of Burst Suppression

Abstract Burst suppression is a phenomenon in which the electroencephalogram (EEG) of a pharmacologically sedated patient alternates between higher frequency and amplitude bursting to lower frequency and amplitude suppression. The level of sedation can be quantified by the burst suppression ratio (BSR), which is defined as the amount of time that an EEG is suppressed over the amount of time measured. Maintaining a stable BSR in patients is an important clinical problem, which has led to an interest in the development of BSR-based closed-loop pharmacological control systems. Methods to address the problem typically involve pharmacokinetic (PK) modeling that describes the dynamics of drug infusion in the body as well as signal processing methods for estimating burst suppression from EEG measurements. In this regard, simulations, physiological modeling, and control design can play a key role in producing a solution. This paper seeks to add to prior work by incorporating a Schnider PK model with the Wilson–Cowan neural mass model to use as a basis for robust control design of biophysical burst suppression dynamics. We add to this framework actuator modeling, real-time burst suppression estimation, and uncertainty modeling in both the patient's physical characteristics and neurological phenomena to form a closed-loop system. Using the Ziegler–Nichols tuning method for proportional-integral-derivative (PID) control, we were able to control this system at multiple BSR set points over a simulation time of 18 h in both nominal, patient varied with noise added and with reduced performance due to BSR bounding when including patient variation and noise as well as neurological uncertainty.