Delay Scheduling of a LQR and PID Controlled Pendubot Using CTCR Method

Abstract. Microbial-explicit soil organic carbon (SOC) cycling models are increasingly being recognized for their advantages over linear models in describing SOC dynamics. These models are known to exhibit oscillations, but it is not clear when they yield stable vs. unstable equilibrium points (EPs) – i.e., EPs that exist analytically but are not stable in relation to small perturbations and cannot be reached by transient simulations. The occurrence of such unstable EPs can lead to unexpected model behavior in transient simulations or unrealistic predictions of steady-state soil organic carbon (SOC) stocks. Here, we ask when and why unstable EPs can occur in an archetypal microbial-explicit model (representing SOC, dissolved OC (DOC), microbial biomass, and extracellular enzymes) and some simplified versions of it. Further, if a model formulation allows for physically meaningful but unstable EPs, can we find constraints in the model parameters (i.e., environmental conditions and microbial traits) that ensure stability of the EPs? We use analytical, numerical, and descriptive tools to answer these questions. We found that instability can occur when the resupply of a growth substrate (DOC) is (via a positive feedback loop) dependent on its abundance. We identified a conservative, sufficient condition in terms of model parameters to ensure the stability of EPs. Principally, three distinct strategies can avoid instability: (1) neglecting explicit DOC dynamics, (2) biomass-independent uptake rate, or (3) correlation between parameter values to obey the stability criterion. While the first two approaches simplify some mechanistic processes, the third approach points to the interactive effects of environmental conditions and parameters describing microbial physiology, highlighting the relevance of basic ecological principles for the avoidance of unrealistic (i.e., unstable) simulation outcomes. These insights can help to improve the applicability of microbial-explicit models, aid our understanding of the dynamics of these models, and highlight the relation between mathematical requirements and (in silico) microbial ecology.

Single-input interval type-2 fuzzy PID (SI-IT2-FPID) control approach is a simple and effective way of adding nonlinear characteristics to linear PID controllers to increase the control performance and the capability of handling system nonlinearities. In the SI-IT2-FPID approach, the nonlinear characteristic of the PID controller is provided by a single-input–single-output interval type-2 fuzzy controller (IT2-FC) positioned before the PID controller. In the literature, a constant footprint of uncertainty (C-FOU) structure is used in SI-IT2-FPID controller design procedures in almost all studies. However, the C-FOU structure limits the performance of the SI-IT2-FPID controller. In this study, an online footprint of uncertainty (FOU) tuning mechanism is proposed for SI-IT2-FPID controllers in order to increase their control performances. Online tuning of FOUs of interval type-2 membership functions (IT2-MFs) enhances the capability of SI-IT2-FPID controllers to handle system nonlinearities since FOU levels of IT2-MFs have a dominant effect on the control and robustness performance of SI-IT2-FPID controllers. In the proposed method, FOUs of IT2-MFs of an IT2-FC are adjusted by an analytical function based on the system error and the change of the error. In this way, the simple structure of the SI-IT2-FPID controller is preserved. In order to illustrate the control and robustness performance of the proposed controller, simulation studies are carried out on three benchmark systems, namely a second-order nonlinear system, a ball and beam system, and a first-order plus dead time system. Additionally, the performance of the proposed controller is compared to a SI-IT2-FPID controller with C-FOU and a classical PID controller. The simulation results show that the proposed controller exhibits better control and robustness performance than the other controllers.

In this paper, a formulation of a sandwich plate integrating an elastic central layer (isotropic or composite) between two piezoelectric sub-layers (actuators and/or sensors), which can be taken as a smart (intelligent) structure and allowing active control vibrations is presented. A 9-node finite element quadratic plate element with 5 degrees of freedom per node is used which takes into account the effect of transverse shear with an additional degree of freedom for each node of the piezoelectric sub-layer. At First, the static control of the deflection by taking the two piezoelectric sub-layers as actuators with two configurations of the total and partial recovery of the surface is undertaken. Thus, the influence of patches position, for the second configuration, on the attenuation of vibrations is analyzed. In a Second step, the active vibration control using two types of LQR and PID controllers with different control parameters is tested and compared for the two recovery configurations (total and partial) of the piezoelectric elements. It is demonstrated throughout the present results that the performances of the partial recovery are almost as good as those of the total recovery despite a ratio of the surfaces piezoelectric patches which is 1/3. It is also noticed that the PID controller is more efficient than the LQR controller. But, if using the PSO (Particle Swarm Optimization) algorithm, the LQR's parameters are optimized and give almost the same performances as those of the PID controller.DOI: http://dx.doi.org/10.5755/j01.mech.24.5.20645

Most of today's industrial computers are applied to embedded systems because the industrial computers can be implanted with the operating systems to manage the peripheral equipments. The industrial computer can deal with multi-tasking efficiently by process scheduling. The digital signal processor has the advantage of highly computational capability, but it can’t deal with multi-tasking because of the lack of operating systems. This thesis is based on controller area network (CAN) bus network to construct a distributed real-time monitoring and control system. This system consists of subsystems of master, slave, and monitor. The master subsystem is constructed by a PC/104+, Linux-RTAI operating system and PCI to CAN communication interface. There are two slaves with the cores of digital signal processors (DSP). One is to control an inverted pendulum using the LQR controller, the other is to control a dc motor using the PID controller. The monitor subsystem consists of a monitoring interface and universal serial bus (USB) to CAN communication interface. In the experiments, the master subsystem sends the control commands to the slaves. The slaves excute the control tasks according to the received commands and return the responses to the monitor. The monitor is able to show the system responses on the screen to facilitate the system analysis. This thesis verifies the performance of the distributed control system through experiments.

In the last two decades, there have been great advances in using Unmanned Aerial Vehicles (UAVs) in several applications. This rapid growth is due to their ability to carry out several types of tasks with high flexibility aligned with reduced risks to human life and cost-effectiveness. The increasing demands for more complex assignments have improved UAVs' capabilities, propelling the rise of platforms with a high degree of autonomy for performing simultaneous tasks with less human intervention. One of the great challenges of maneuvering a UAV for a stabilized flight consists of a highly-coupled nonlinear system with fast dynamics. Thus, attitude control is an essential issue for stabilizing the vehicle or for keeping it in the desired orientation. The PID controller is often used due to its simple structure, good stability properties, and less dependence on the exact system model. However, its tuning process may become complicated in the face of the system nonlinearities. In this scenario, an adjustment error can cause it to lose its flight stability. Therefore, the main contribution of this work is the development of a Fuzzy-PID hybrid controller to control a quadrotor UAV's height stability. The work also considers a classic PID controller for comparison purposes with the proposed hybrid controller. The ROS/Gazebo platform was used to carry out the experiments with both control structures. From the results, it was possible to verify that both PID and Fuzzy-PID controllers could perform the attitude control of the UAV. However, the hybrid control strategy obtained some advantages, such as self-adjustment through system variations.

In this paper, a high-performance optimal fractional emotional intelligent controller for an Automatic Voltage Regulator (AVR) in power system using Cuckoo optimization algorithm (COA) is proposed. AVR is the main controller within the excitation system that preserves the terminal voltage of a synchronous generator at a specified level. The proposed control strategy is based on brain emotional learning, which is a self-tuning controller so-called brain emotional learning based intelligent controller (BELBIC) and is based on sensory inputs and emotional cues. The major contribution of the paper is that to use the merits of fractional order PID (FOPID) controllers, a FOPID controller is employed to formulate stimulant input (SI) signal. This is a distinct advantage over published papers in the literature that a PID controller used to generate SI. Furthermore, another remarkable feature of the proposed approach is that it is a model-free controller. The proposed control strategy can be a promising controller in terms of simplicity of design, ease of implementation and less time-consuming. In addition, in order to enhance the performance of the proposed controller, its parameters are tuned by COA. In order to design BELBIC controller for AVR system a multi-objective optimization problem including overshoot, settling time, rise time and steady-state error is formulated. Simulation studies confirm that the proposed controller compared to classical PID and FOPID controllers introduced in the literature shows superior performance regarding model uncertainties. Having applied the proposed controller, the rise time and settling time are improved 47% and 57%, respectively.

Analytical study on the motions around equilibrium points of restricted four-body problem

This paper presents the comparative study of Model Predictive Controller (MPC) with PID Controller implemented for flow control loop in LABVIEW. Classical PID controller is mostly used in process instrumentation yet tuning of PID controller is the crucial part to be dealt with. Moreover, changes in the parameters of the loop components affects the tuning of the controller, hence over a period of time retuning of PID controller is required. On the other hand MPC controller works on the process model which predicts and optimizes the process performance. Here, Flow control loop performance was studied for MPC and PID controller. MPC worked on 1st order state space system model and PID was tuned using Internal Model Control (IMC) method. The result of implementation shows that, MPC controller performs much better than PID controller. Set point of with less settling time and zero peak overshoot was observed in MPC whereas PID has comparatively more settling time and peak overshoot.

There are a lot of methods for the stabilization of quadcopters and the newest are based on AI. A neural network is a simplified model that imitates the human brain's processes. In the research paper, we present a neural network control model for quadcopter stabilization. A single hidden layer network model was estimated to investigate the dynamics of the UAV. A control system with a classical PID controller was used to train the neural network model. This method is used for examining how the neural network imitates the stabilization of the quadcopter in real flight mode. The novelty of the work was to design of small size 3 layers NN model that runs in real-time in a quadcopter. The PID and machine learning controllers' operation results were compared to each other andshown in the experiment.

In this paper, the fractional order PID (FOPID) control scheme of a 3-axis motion platform is proposed. Firstly, a mathematical model of the 3-axis motion platform is derived, then a control law is developed to track the angular position. Tuned FOPID controller is compared with classic PID controller (IOPID). The simulation results are provided to verify the efficiency and correctness of the proposed control algorithm.

The wheeled mobile robots have been widely applied in daily applications for its simplicity, robustness, stability and low-cost of manufacturing. Typically, PID controller is implemented to drive a mobile robot. However, the performance of the robot is greatly depended on the PID control parameters are tuned and the robustness of the mechanical system. Since the analog controllers were replaced by digital controller, PID control parameters could be automatically tuned to adapt the variation of the system parameters and operating condition. In this manuscript, a mathematical model is developed for a line following mobile robotic system which is used as a restaurant serving robot. The serving robot is controlled by an adaptive PID controller using Q-learning algorithm. The simulation and experimental results are compared to verify the advantage of the adaptive PID controller over classical PID controller.

This study compares the result of the PID controller to the LQR controller when used in the on-orbit stabilization of a satellite in the low earth orbit. The results from the PID controller show that the controller is too weak when used alone as the controller could not stabilize the system after 500 s which is not even allowable in practical application. For the LQR controller, a performance metric was set which is: i. the settling time is to be ≤ 10 seconds, ii. Maximum power consumption ≤ 1.5 Watts and iii. Zero (0) steady-state error / final value. The LQR controller meets system performance by achieving a settling time of roll (peak amplitude=0.26 s, settling time=10.0 s), Pitch (peak amplitude=0.395 s, settling time=5.52 s), Yaw (peak amplitude=0.350 s, settling time=5.52 s) and Total power consumption are 1.26 watt with a maximum torque of 3.22 mNm. Because power consumption and precision are critical in satellite applications, particularly military surveillance satellites. As a result, for an aerospace engineer to achieve their space mission, for instance, space mission like low earth orbit surveillance satellites, flexible solar panels, a high accuracy pointing accuracy, it will be impossible to adopt a PID controller except the engineer is ready for the complexity of design filters and compensators. An LQR design in this study can take care of all this complexity with minimum power consumption.

A closed form equation is derived that describes the stable manifold for each of the n-1 type-1 unstable equilibrium points (UEPs). These stable manifolds can be obtained without having to compute the postfault stable equilibrium points for each of the stable manifolds. The equation describing the stable manifold for each UEP can be written knowing only the postfault stable equilibrium point. The n-1 stable manifolds for the UEPs constrain the power across the cutset of branches that encircle each of the n-1 generators that are not assumed to be the swing machine. For a point to lie on the stable manifolds of a specific UEP, the sum of power flows across all branches in the cutset that surround the generator that corresponds to a specific UEP must equal the sum of the power flows across this cutset at the postfault equilibrium point. These results are intuitive since the equal-area criterion could be used to characterize the region of stability for a single-machine infinite-bus system in the exact same manner. >

This paper describes the design, simulation, optimisation and implementation of a 1-Degree-of-Freedom (1-DOF) discrete PID controller for the buck converter working in Continuous Conduction Mode (CCM) based on Field Programmable Gate Array (FPGA) device. The converter operates at a switching frequency of 500 KHz. The elaborated PID control algorithm takes advantage of the conjugation of Xilinx ISE digital designing environment with MATLAB/Simulink simulation and testing environment, through Xilinx System Generator toolbox. This results in a faster and efficient design flow. First the PID controller is designed using Simulink Control Design Toolbox or ‘sisotool’ from MATLAB to generate the required set of compensator coefficients to meet the start-up and the transients characteristics. The controller is then realized using Xilinx System Generator (XSG) Blockset. The design example certifies the validity of the classical discrete 1-DOF PID controller as an efficient, more compact and reliable control method for rapid system prototyping for designs developed using the MATLAB/Simulink environment.

The double inverted pendulum is a multivariable, nonlinear control system. The fuzzy controller of double inverted pendulum is studied in the paper. The mathematical model is gained by the Lagrange equation and the controllability of double inverted pendulum system in unstable equilibrium point is analyzed. On the base of above, the fuzzy controller for double inverted pendulum is designed by the fuzzy control theory. The dimensions and control rules of the fuzzy controller are depressed by designing a fusion function using the optimization control theory. Simulation and real-time control results prove that the fuzzy controller is effective and feasible.