Ziegler-Nichols Research Articles

Optimisation of fractional‐order PI controller for bidirectional quasi‐Z‐source inverter used for electric traction system

This study presents the optimisation of fractional-order proportional–integral (FOPI) controllers for a bidirectional quasi-Z-source inverter (QZSI) in an electric vehicle (EV) off-road application. An ant colony optimisation Nelder–Mead (ACO-NM) algorithm is used for the optimisation of the controller parameters. This optimisation method is applied to enhance the performance of FOPI control for bidirectional QZSI. Ziegler–Nichols (ZN) with relay and the pole placement tuning method are also used for the FOPI controller design for comparison purposes. The modelling and the control design of bidirectional QZSI for an electric traction system are presented and discussed. Simulations are performed to verify the efficacy of the proposed controller structure with the bidirectional QZSI for two standardised driving cycles. The result shows that the FOPI controller designed with the ACO-NM algorithm provides more suitable ageing performance index values for the battery. The ACO-NM algorithm permits to reduce the root-mean-square value and the standard deviation by 2 and 5% of the battery current compared to the ZN tuning method and direct battery supply topology, respectively. The bidirectional QZSI with this type of controller can globally enhance the performance of EVs by optimising the electric power consumption and extending its driving range.

Adaptive Particle Swarm Optimization of PID Gain Tuning for Lower-Limb Human Exoskeleton in Virtual Environment

Tuning of a proportional-integral-derivative (PID) controller for a complex multi-joint structure, such as an exoskeleton, using conventional methods is difficult and imprecise. In this paper, an optimal PID tuning method for a 3-dimensional model of a lower-limb human exoskeleton in gait training condition is presented. The dynamic equation of the human-exoskeleton is determined using a Lagrangian approach, and its transfer function is established in a closed-loop control system. PID controller gains, initialized by the Ziegler–Nichols (Z-N) method, are used as the input to an adaptive particle swarm optimization (APSO) algorithm for minimizing the multi-joint trajectory error. The optimized controller is tested in the Gazebo virtual environment and compared with the Z-N and conventional optimization methods. The numerical analysis shows that the PID controller tuned by a combination of Z-N and APSO improves the performance of a lower-limb human exoskeleton in gait training.

Comparison of Z-N and PSO based tuning methods in the control strategy of prosthetic limbs application

The aim of the study is to compare Ziegler-Nichols (Z-N) and Particle Swarm Optimization (PSO) based tuning methods for controller tuning in the driving mechanism of prosthetic limbs. By adopting suitable control strategies like P, PI and PID in the driving system, the positioning of knee and hip joints can be attained in the ideal time of 1.4s for completing one locomotion cycle. The gain constants (KP , KI , and KD) of the controllers were tuned manually and also using Z-N and PSO; thereby appropriate constants were determined so that the joints could be moved to the desired position. The performance of P, PI, and PID controllers were compared and PID was identified as the ideal control strategy which exhibited least error and good stability. It was observed that the conventional Z-N method produced a big overshoot, and so a modern approach called PSO was employed to enhance its capability. The PSO based PID controller optimization resulted in less overshoot as well as it helped in optimizing the gain constants so as to improve the stability of the system when compared to the classical method.

Ziegler-Nichols Tuning Method

The objective of this article is to study the speed control of a DC motor using PID controller and understand the Ziegler-Nichols (ZN) tuning method for a PID controller. PID controllers are widely used in many industries such as paper mill, cotton textile industries. PID controller also finds its applications in drones. The usefulness of PID lies in its general applicability.

Hybrid Pitch Angle Controller Approaches for Stable Wind Turbine Power under Variable Wind Speed

The production of maximum wind energy requires controlling various parts of medium to large-scale wind turbines (WTs). This paper presents a robust pitch angle control system for the rated wind turbine power at a wide range of simulated wind speeds by means of a proportional–integral–derivative (PID) controller. In addition, ant colony optimization (ACO), particle swarm optimization (PSO), and classical Ziegler–Nichols (Z-N) algorithms have been used for tuning the PID controller parameters to obtain within rated stable output power of WTs from fluctuating wind speeds. The proposed system is simulated under fast wind speed variation, and its results are compared with those of the PID-ZN controller and PID-PSO to verify its effeteness. The proposed approach contains several benefits including simple implementation, as well as tolerance of turbine parameters and several nonparametric uncertainties. Robust control of the generator output power with wind-speed variations can also be considered a significant advantage of this strategy. Theoretical analyses, as well as simulation results, indicate that the proposed controller can perform better in a wide range of wind speed compared with the PID-ZN and PID-PSO controllers. The WT model and hybrid controllers (PID-ACO and PID-PSO) have been developed in MATLAB/Simulink with validated controller models. The hybrid PID-ACO controller was found to be the most suitable in comparison to the PID-PSO and conventional PID. The root mean square (RMS) error calculated between the desired power and the WT’s output power with PID-ACO is found to be 0.00036, which is the smallest result among the studied controllers.

A physically based PID controller for the power maneuvering of nuclear reactors

Development of rapid and efficient regulators for the load following operation of nuclear power plants is an ongoing research interest. A physics-based PID regulation approach which adopts Ziegler-Nichols tuning mechanism is therefore attempted in this work. To this end, the prompt jump approximation inspiring the broader singular perturbation framework is resorted. PID parameters obtained in this regard give rise to a rapid and efficient closed loop power tracking performance during load following operation. Stable closed loop tracking at various operating power levels is moreover procured through this approach. • A simple PID controller designed for load following purposes. • Ziegler-Nichols (Z-N) framework is adopted. • The prompt jump (PJ) approximation employed to refine the Z-N tuning method.

Simulation and Control of a Six Degree of Freedom Lower Limb Exoskeleton

In this paper, the development of controlling a six Degree of Freedom (DOF) Lower Limb Exoskeleton (LLE) model using the Robot Operating System (ROS) is presented. Moreover, this work proposes a method to analyze kinematic properties and control of the LLE before the prototype. The model of the LLE is described using Extensible Markup Language (XML) programming in the Unified Robot Description Format (URDF). The dynamic equation of the six-DoF LLE is determined by using Newton-Euler. In addition, a Proposition-Integral-Derivative (PID) controller is established in a feedback closed-loop control system. The PID controller is tuned via Ziegler-Nichols (Z-N). The tuned PID controller is tested in the Gazebo environment to confirm the performance of the proposed method. The nodes and topics flow chart of the programmed 3-D model of the LLE is described. Furthermore, a desired angular trajectory based on the phase on walking is defined for each joint of the LLE. The result shows that the actual pursue the desired angular trajectory for each joint. The average and maximum error of the angular trajectories for all the joints are less than 0.05 radian. It can be ascertained that our developed LLE model in the Gazebo simulator can be used for giving an overview of the walking pattern.

Comparison of Particle Swarm Optimization and Ziegler Nichols Techniques

Two tuning techniques namely: Particle Swarm Optimization (PSO) and Ziegler Nichols (ZN) technique are compared. PSO is an optimization technique based on the movement and intelligence of swarms. PSO applies the concept of social interaction to problem solving. It is a computational method that optimizes a problem by iteratively trying to improve a candidate solution about a given measure of quality. Ziegler Nichols tuning method is a heuristic method of tuning a PID controller. The ZN close loop tuning is performed by setting the I (integral) and D (derivative) gains to zero and increasing proportional gain to obtain sustained oscillations. The DC Motor is represented by second order transfer function is used as a plant, which is controlled using PID controller. The PID controller parameters are chosen by tuning the controller using PSO algorithm and ZN method. The response of the system to unit step input is plotted and performance measures are evaluated for comparing PSO algorithm and ZN technique. Here we have compared the two tuning methods based upon the settling time (Ts), peak overshoot (Mp) and the two performance indices namely Integral square error (ISE) and Integral Absolute error (IAE).

Effects of Temperatures and Viscosity of the Hydraulic Oils on the Proportional Valve for a Rice Transplanter Based on PID Control Algorithm

This study was conducted to develop a proportional-integral-derivative (PID) control algorithm considering viscosity for the planting depth control system of a rice transplanter using various hydraulic oils at different temperatures and to evaluate the performance of the control algorithm, and compare the performance of the PID control algorithm without considering viscosity and considering viscosity. In this study, the simulation model of the planting depth control system and a PID control algorithm were developed based on the power flow of the rice transplanter (ERP60DS). The primary PID coefficients were determined using the Ziegler-Nichols (Z-N) second method. Routh’s stability criteria were applied to optimize the coefficients. The pole and double zero points of the PID controller were also applied to minimize the sustained oscillations of the responses. The performance of the PID control algorithm was evaluated for three ISO (The International Organization for Standardization) standard viscosity grade (VG) hydraulic oils (VG 32, 46, and 68). The response characteristics were analyzed using statistical method (ANOVA) and Duncan’s multiple range test (DMRT) at a significant level of 0.05 were performed through the statistical software SPSS. The results show that the control algorithm considering viscosity is able to control the pressure of the proportional valve, which is associated with the actuator displacement for various types of hydraulic oils. It was noticed that the maximum pressure was 15.405 bars at 0, 20, 40, 60, 80, and 100 °C for all of the hydraulic oils. The settling time and steady-state errors were 0.45 s at 100 °C for VG 32 and 0% for all of the conditions. The maximum overshoots were found to be 17.50% at 100 °C for VG 32. On the other hand, the PID control algorithm without considering viscosity could not control the planting depth, because the response was slow and did not satisfy the boundary conditions. The PID control algorithm considering viscosity could sufficiently compensate for the nonlinearity of the hydraulic system and was able to perform for any of temperature-dependent viscosity of the hydraulic oils. In addition, the rice transplanter requires a faster response for accurately controlling and maintaining the planting depth. Planting depth is highly associated with actuator displacement. Finally, this control algorithm considering viscosity could be helpful in minimizing the tilting of the seedlings planted using the rice transplanter. Ultimately, it would improve the transplanter performance.

Comparison of Ziegler-Nichols and Cohen Coon tuning method for magnetic levitation control system

Magnetic levitation is an example of a nonlinear system that is naturally unstable. In the control system field, it can be also used to check the effectiveness of control methods. Unlike other researches overcoming by analytical method, this research investigates the solution of the nonlinearity of the magnetic field by placing two effect hall sensors on the top and bottom of magnetic coils. After decreasing the effect of nonlinearity, two PID control tuning methods, Ziegler Nichols (ZN) and Cohen Coon (CC), are compared to obtain an appropriate control structure and its initial parameters. The experimental result shows that the best control structure of ZN method is PID whereas its initial parameters, Kp, Ti, and Td, are 15.33, 0.036 and 0.009, respectively. The rise-time and settling time of the response are 0.54s and 0.59s. The appropriate control structure is PI control whereas Kp and Ti are 30.05 and 0.012 from CC method. The rise-time and settling time resulted are 0.8s and 0.67s. The ZN method with PID control structure has a better response with smaller rise-time and settling time than PI control from CC Method. This research is benefit for solving a problem dealing with magnetic levitation control.

TR Optimization in High-Performance Drilling Machine for Various Control Actions & Algorithm

Drilling industry has moved into a paradigm shift with the controlled Proportional Integral Derivative (PID) tuning, which provides optimum outcomes in recent decades. Interestingly the outcomes of several aspects of these PIDs are quite important for the industry sector. Many of the large industry or construction firms’ project that was seemed impossible at one point of time is now feasible. A significant amount of research has been commenced for tuning of PID controllers from the last six decades. Many tuning methods have also been proposed. Most of the tuning methods are model-based like Ziegler Nichols (ZN) method. It provides initial tuning of PID, which offer consistent result, but there is always suggested to fine-tune the PID controller further for the particular process to get optimum results. This paper represents a comparison for the several control schemes such as PID controller, PI with PD in feedback, PID with PD in feedback, PID-D and PID-PD controller and lead compensator. This relative study based upon rise time, settling time and peak-overshoot. The block diagrams were simulated in MATLAB, and their results are compared.

Design of genetic algorithm-based PID controller for a joule heated shape memory spring driven ball and beam system

The ball and beam system is a highly nonlinear laboratory model which helps to understand the modern and classical control theory. This paper presents the position control of a ball and beam system, which is actuated by shape memory alloy (SMA) springs in the antagonistic configuration. The system is designed such that the SMA actuator provides the bidirectional controlled force on the pulley to the beam through the shaft. This bidirectional motion of the beam needs to be controlled for the proper positioning of the ball with an appropriate controller design. Hence it is proposed to design/tune the controller optimally for the effective control and improved performance of the system which is not feasible using conventional Ziegler Nichols (ZN) design. The objectives of this paper are: 1) to use SMA spring as an actuator for ball and beam system; 2) to optimise the PID controller gain with genetic algorithm (GA); 3) to compare the performance of Ziegler Nichols (ZN) PID and GA-PID in simulation and experimentation to show the competence of GA-PID with ZN-PID through performance error indices.

Optimal design of battery charge management controller for hybrid system PV/wind cell with storage battery

The renewable energy sources (RES) became a fundamental necessity to the majority of electric systems and also the isolated systems like the water pumping and petroleum excavators systems. The RES typically required energy storage system because of variations in the power during the day. Because of increment popular of utilising batteries, the charging and discharging procedure of battery system should have been well managed through an adaptive controlled system. In this paper, a standalone power system utilising photovoltaic, wind energy and batteries are contributed in providing the required load. The charging balance of batteries is accomplished by utilising a new hybrid genetic algorithm (GA)-based proportional integral (PI) controller with adaptive neuro-fuzzy inference system (ANFIS). This new hybrid GA-based PI with ANFIS control method is compared with the GA-based PI controller and the conventional PI controller based on Ziegler Nichols (ZN) technique. Dynamic simulations exhibit the right performance of the hybrid GA-based PI with ANFIS control for the proposed power system under study and the better performance than the GA-based PI controller and ZN-based PI controller.

Tuning of parameters of PID controller using Grey Wolf Optimizer

In this paper, the Grey Wolf Optimizer (GWO) is used for tuning the parameters of PID (Proportional, Integral and Derivative) controller. The GWO is a meta-heuristic approach inspired by grey wolves (Canis lupus). The GWO algorithm consists of four types of grey wolves known as alpha (∝) as a leader or decision maker, beta (𝛽) as to assist alpha in decision making, delta (𝛿) as a subordinate wolf and omegas (𝜔) the followers. The hunting behavior of GWO continues with the three main following steps and they are searching for prey, encircling the prey and attacking the prey. Firstly, the parameters of the PID controller are tuned using the Ziegler-Nichols (Z-N) technique. Then these tuned parameters along with some randomly assumed coefficients are used as the first iteration step for the GWO algorithm. The tuning principle of GWO ensures the minimization of performance index. The performance index used in this paper is Integral Square error (ISE). The GWO algorithm for tuning the parameters of PID controller is validated by controlling the highly nonlinear in-verted pendulum system. Simulation results showed that the GWO algorithm minimizes the ISE of the system and stabilized the system within the stipulated time.

Ziegler-Nichols optimization for quadrotor attitude control

Quadrotor and multirotor aircraft, which do not need a pilot to fly, are used for recreational or work purposes, with the quadrotor being the type most used in practical implementations. The quadrotor represents a promising field of research due to its ability to fly and manoeuvre, gaining recognition as a technological solution in many areas. An aircraft quadrotor is a complex control system that allows great flexibility of flight. The identification and control of the variables in multirotor aerial systems such as quadrotors is challenging, however, because the quantities involved are not always available, known and accurate. Among the various control methods that have been investigated, proportional-integral-derivative (PID) control offers good results and simplicity for application in quadrotors, but achieving stability and high performance is challenging, with the fundamental task being tuning the controller gains. Improving the control system performance is also challenging, especially when the load varies. Here, Ziegler-Nichols (ZN) theory was used to tune the controller gains for pitch and roll attitude command, followed by evaluation of improvements in the system response. The optimized application of ZN theory to a quadrotor (termed optimized ZNAQ) is proposed and obtains a significant improvement in the control system response performance, demonstrating that optimized ZNAQ is valid for tuning the controller PID gains and more efficient than the original ZN theory approach.

New opposition cuttlefish optimizer based two‐step approach for optimal design of fractional order proportional integral derivative controller for time delay systems

AbstractIn this article, an optimal design of the fractional order proportional integral derivative (FOPID) controller for time delay system is proposed. The proposed optimal design is the combined performance of both the cuttlefish optimizer (CFO) and Opposition‐based learning (OBL) scheme called CFOBL scheme. The proposed CFOBL uses the concept of opposition based population initialization and opposition based position updating to improve its searching behavior, computational speed and convergence profile in the basic CFO. In FOPID controller, apart from the three tuning parameters (GP, GI, and GD) there are two additional tuning parameters that are λ and μ. Here, CFOBL is used to tune the three controller parameters and also to find the optimal values of λ and μ. The uniqueness of the proposed technique is to reduce the FOPID controller's fault in the higher order time delay scheme by the aid of the controller's increase limits. The objective of the proposed technique is chosen by considering the set point parameters and the accomplished parameters from the time delay system. The proposed technique is used to avoid high‐order delays and reliability constraints such as small overruns, time resolution and fixed condition defects. This technique is performed on the MATLAB/Simulink platform and the results are compared with different existing techniques such as Ziegler‐Nichols (ZN) tuning method, curve fitting (CF) technique, Wang technique, and regression technique.

Optimal design of non‐fragile PID controller

AbstractThis paper solves the controller gains uncertainty problem, which may lead to undesirable responses and an unstable system when implemented. A non‐fragile or resilient controller can overcome this problem. The paper suggests a new method to design a non‐fragile proportional‐integral‐derivative (PID) controller for voltage regulation. This method is carried out by applying a constrained genetic algorithm (GA) as a powerful optimization technique to determine the optimal gains of the PID controller. In addition, new developed conditions from the Routh– Kharitonov theorem are taken into account during the optimization operation to ensure system stability and system response. A new time domain objective function is proposed to establish the optimal permissible limits of controller gains to ensure a constraint of good response. The results of the proposed non‐fragile PID controller are compared with the non‐constrained GA‐based PID controller, artificial bee colony (ABC) algorithm‐based PID controller, and Ziegler Nichols (ZN)‐based PID controller. This achieves better results compared with different methods. The controller gains uncertainties test is applied to ensure the non‐fragility of the proposed controller. Furthermore, the system parameters variation test is applied to check the robustness of the controller based on the suggested method. The designed PID controller by this method is more resilient and less design time is required. The proposed controller and the system are carried out and studied by utilizing MATLAB/Simulink.

Two Heuristic PID Tuning for a 4-DOF Robot Arm Control

This paper discusses the development of closed-loop position control for the joint motor of a 4-DOF robot arm. In developing a practical robot, types of input and control algorithm are important elements in the control system. The objectives of this paper are to select an input type that could produce smooth arm’s motion and to apply PID control for the joints. Step and parabolic inputs have been tested as reference trajectory where the former used step signal as the constant value of motor angle while the latter requires calculation using spline interpolation method based on initial and end points of each joint motion given by user. From the latter, a parabolic curve input which consists of point-to-point values calculated for each 1ms sampling time was produced. Meanwhile, the PID position control tuned by trial and error and Ziegler Nichols (Z-N) methods were carried out and measured for comparison in terms of steady state error, overshoot and response time in real-time experiments. It could be observed that step input has caused abrupt movements and vibration to the arm body compared to the parabolic input that moved the arm smoothly to imitate motion like human. Meanwhile, the intuitive values of trial and error method were found to produce not much different with the Z-N tuned gains but comparatively produced small error against the parabolic input reference during the transient state. The result from this study is useful in the future to ensure position accuracy of robot joints when attending object for manipulation.

Artificial Intelligence-Based Optimal PID Controller Design for BLDC Motor with Phase Advance

This paper proposes the artificial intelligence (AI)-based optimal PID controller design optimization of brushless direct current (BLDC) motor speed control with phase advance approach. The proposed control system allows the speed adjustment of the BLDC motor by phase advance technique. In this paper, two selected AI algorithms, i.e., the adaptive tabu search (ATS) and the intensified current search (ICS) are conducted as the optimizer for the PID controller design. The proposed control system is simulated by MATLAB/SIMULINK. Results obtained by the ATS and ICS will be compared with those obtained by the Ziegler-Nichols (ZN) tuning rule and the genetic algorithm (GA). It shows that the speed response of the BLDC motor by phase advance with the PID controller optimized by the ICS outperforms better than the ZN, GA and ATS.

Temperature control of vacuum dividing wall column – case study on oleochemical fatty acid fractionation

Analysis of oleochemical compositions in distillation column often have large process delays. Inferential control is commonly used by means of stage temperature as the measured variable which provide more responsive in composition control. This work aims to evaluate the performance of temperature control in vacuum dividing wall column (VDWC) for fatty acid oleochemical fractionation. Product purity at 99% used as inferred parameter to determine the temperature. Sensitivity analysis was used to determine the relationship between stage and temperature difference for changes in the manipulated variables. The most sensitive tray was selected and implemented to a Distillate- Side Stream- Boilup (DSV) control configuration in Aspen Dynamics following the work by Othman (2019b). Controller adopted with PI and PID settings using Ziegler-Nichols (ZN) and Internal Model Control (IMC) tuning calculation method. Both methods were compared based on the settling time and overshoot. The best setting was then fine-tuned before tested to set point tracking without any disturbances. From the sensitive analysis, temperature at stage 6, 29 and 34 were selected used as controlled variable which inferred distillate, middle and bottom product purity at 99% respectively. PID controller setting based on ZN method provide the best setup with fastest settling time and smallest overshoot and provide good performance for set point tracking.