Discrete PID Controller Research Articles

PID Controller with an Override Mode for a Wall-Following Robot with a Rotating Sensor Compartment

This paper presents the design of a wall-following robot (WFR) with a rotating sensor compartment to reduce the number of distance sensors used. Two infrared (IR) sensors were fitted in the compartment that rotates back and forth at 45°, producing four measurement values at each rotation cycle. The WFR was regulated using a novel control scheme of PID controller with an override mode. A discrete PID controller in position form was used to run the WFR to follow straight wall segments or walls turning left, while an override mode governed the WFR to follow walls turning right. The sampling time was set to 300 ms. The parameters of the PID controller were tuned using a trial-and-error method. The Mean Absolute Errors (MAE) was selected as the cost function. The WFR conducted twelve trial runs along a trial track with a length of 200 cm, consisting of one right turn and one left turn. The parameters that yielded the lowest MAE of 0.90 cm were used for further tests. Subsequently, a closed track for testing was constructed with a length of 845 cm, consisting of 7 right turns and 2 left turns. The WFR completed five test runs successfully, each elapsing the test track twice. The lowest MAE during the tests was 1.06 cm. The favorable performance of the proposed WFR strengthens future development efforts to equip the robot with more hardware to fulfill specific tasks and to put the completion time into optimization consideration.

Optimization and discrete fractional-order PID controller applied to a pressure swing adsorption plant for the production and recovery of bioethanol

The results obtained demonstrate significant scientific and technological contributions. The DFOPID controller achieved a purity of 99.50% wt, a recovery of 74.53%, and an energy efficiency of 69.52%, effectively handling disturbances and trajectory changes. In comparison, the discrete PID controller reached a purity of 99.42% wt, a recovery of 74.19%, and an energy efficiency of 61.10%. While the DFOPID exhibited superior performance and faster response to trajectory changes and disturbances, the discrete PID showed better energy efficiency. Both controllers are viable for industrial applications and PSA processes, as they meet the required purity standards for biofuel production.

Synthesis of hardware and software for adaptive discrete high-order control systems based on a model of the desired transient process with a guaranteed degree of stability

In this work, analytical expressions for the connection between optimization criteria andsettings parameters of the adaptive PI-PID controller with variable parameters of the object andadaptive filter have been removed. A method for synthesizing a model of discrete controllersbased on given dynamic characteristics has been developed. A method has been developed forsynthesizing a model of a discrete PID controller based on given dynamic characteristics basedon the criterion of the transient process of a guaranteed level of stability. 3 figures, 0 tables, 32formulas, 19 bibliographic sources..Analytical expressions have been removed to link the optimization criteria andadjustment parameters of the adaptive PI-PID controller with the variable parameters of theobject and adaptive filter.A method for synthesizing a model of discrete controllers from specified dynamiccharacteristics has been developed. The average warehouse of output pulses at the output of anonlinear channel, which is formed at the output of such a regulator and is seen as an inertialinduced uninterrupted part, changes according to the law, which is designated as a reversetransmission the function of the lanyard of the new molded filter model at the collar of the non-linear element.A method has been developed for synthesizing a model of a discrete PID controller fromspecified dynamic characteristics based on the criterion of the required transient process of aguaranteed stability level.The modeling showed that while the parameters of the object and the adaptive filter willchange during the ASC operation, then, obviously, the optimal parameters for adjusting theadaptive PID controller will immediately change.

Decentralized leader-following consensus control design for discrete-time multi-agent systems with switching topology

The problem of consensus control of linear discrete-time multi-agent systems (MASs) with switching topology is considered in the presence of a leader. The goal of consensus control is to bring the states of all agents to the leader state while providing stability for local agents, as well as the MAS as a whole. In contrast to the traditional approach, which uses the concept of an extended dynamic multi-agent system model and communication topology graph Laplacian, this paper proposes a decomposition approach, which provides a separate design of local controllers. The control law is chosen in the form of distributed feedback with discrete PID controllers. The problem of local controllers’ design is reduced to a set of semidefinite programming problems using the method of invariant ellipsoids. Sufficient conditions for agents’ stabilization and global consensus condition fulfillment are obtained using the linear matrix inequality technique. The availability of information about a finite set of possible configurations between agents allows us to design local controllers offline at the design stage. A numerical example demonstrates the effectiveness of the proposed approach.

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers.

In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.

Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions

This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use.

An improved braitenberg policy for object tracking

In vision-based unmanned vehicle tracking of moving vehicles, it is difficult to achieve accurate tracking of motorized vehicles with conventional fixed-parameter PID controllers due to their varying speeds and changes over time. To generate control signals for the systems and move the controlled object, the PID controller performs calculations based on percentage, integral, and derivative data. This is the discrete PID controller method. In this paper an improved tracking method, the Braitenberg policy, is proposed and a series of experiments are conducted in Simulink. The experimental results verify that the method can achieve stable tracking in simple environment for both general and extreme cases. The method can be used for future experiments for both general and extreme cases. The method can be used for future experiments in more scenarios. Braitenberg policy provides stronger and more stable tracking performance in extreme cases compared to conventional PID control. The algorithm provides more opportunities for tracking research and a small idea for the integration of multiple algorithms.

Pressure Swing Adsorption Plant for the Recovery and Production of Biohydrogen: Optimization and Control

New biofuels are in demand and necessary to address the climate problems caused by the gases generated by fossil fuels. Biohydrogen, which is a clean biofuel with great potential in terms of energy capacity, is currently impacting our world. However, to produce biohydrogen, it is necessary to implement novel processes, such as Pressure Swing Adsorption (PSA), which raise the purity of biohydrogen to 99.99% and obtain a recovery above 50% using lower energy efficiency. This paper presents a PSA plant to produce biohydrogen and obtain a biofuel meeting international criteria. It focuses on implementing controllers on the PSA plant to maintain the desired purity stable and attenuate disturbances that affect the productivity, recovery, and energy efficiency generated by the biohydrogen-producing PSA plant. Several rigorous tests were carried out to observe the purity behavior in the face of changes in trajectories and combined perturbations by considering a discrete observer-based LQR controller compared with a discrete PID control system. The PSA process controller is designed from a simplified model, evaluating its performance on the real nonlinear plant considering perturbations using specialized software. The results are compared with a conventional PID controller, giving rise to a significant contribution related to a biohydrogen purity stable (above 0.99 in molar fraction) in the presence of disturbances and achieving a recovery of 55% to 60% using an energy efficiency of 0.99% to 7.25%.

Active Braking Strategy Considering VRU Motion States in Curved Road Conditions

Currently, the active braking system is primarily used to avoid collisions between vehicles and vulnerable road users (VRUs) traversing the road at a constant speed in straight road conditions. Research on the collision avoidance strategy has been conducted to enhance the protective effects of the active braking system for VRUs traversing the road in various motion states in curved road conditions. Firstly, the spatial position relationships between VRUs and turn-taking vehicles are established when VRUs traverse the road in various motion states from the outside or the inside of the curved road; a mathematical model is established to identify whether VRUs are in a dangerous condition. Secondly, the safe distance model is established to formulate the vehicle collision avoidance strategy. Thirdly, the active braking controller is designed based on the upper sliding mode control and the lower discrete PID control. Finally, the six collision test scenarios on the curved road are constructed by utilizing the Prescan and Matlab/Simulink software. The results show that the active braking system can avoid the collision between the vehicle and VRUs traversing the curved road in various motion states.

Design of discrete PID controllers for maximizing stability margins

AbstractThe objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed‐loop poles being inside the circle of radius centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number , a minimum value and the corresponding discrete PID controller set for achieving at least of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability‐margin discrete PID controller design, two numerical examples are provided.

Simulation and State Feedback Control of a Pressure Swing Adsorption Process to Produce Hydrogen

One of the separation processes used for the production and purification of hydrogen is molecular sieve adsorption using the Pressure Swing Adsorption (PSA) method. The process uses two beds containing activated carbon and a sequence of four steps (adsorption, depressurization, purge, and repressurization) for hydrogen production and purification. The initial composition is 0.11 CO, 0.61 H2, and 0.28 CH4 in molar fractions. The aim of this work is to bring the purity of hydrogen to 0.99 in molar fraction and implement controllers that can maintain the desired purity even in the presence of the disturbances that occur in the PSA process. The controller design (discrete PID and state feedback control) was based on the Hammerstein–Wiener model, which had an 80% fit over the rigorous PSA model. Both controllers were validated on a virtual plant of the PSA process, showing great performance and robustness against disturbances. The results obtained show that it is possible to follow the desired trajectory and attenuate double disturbances, while managing to maintain the purity of hydrogen at a value of 0.99 in molar fraction, which meets the international standards to be used as a biofuel.

Krok dyskretyzacji i nastawy PID w dyskretnym serwomechanizmie napięciowym

A method for selection of discretization step and discrete PID controller settings is presented for a model of servo with voltage controlled motor, described by an integrator with time constant. The method assumes a triple pole location of the closed-loop system to provide smooth control transients. Settling time is a design data. Influence of filtering degree in controller derivative component on reduction of discretization step is examined. Extended design problem with the filtering degree being an additional requirement is also considered.

Dominant pole region assignment with discrete time PI, PID and PIR controllers

Dominant pole region assignment with discrete time PI, PID and PIR controllers

The Development of an Optimally-Tuned PID Control for the Actuator of a Transport Robot

An optimally-tuned PID control for a transport robot actuator based on an induction motor was developed. Continuous-discrete and continuous mathematical models of the actuator were obtained. The parametric synthesis of PID controller on the basis of continuous and discrete actuator models were performed. Numerical simulations using SimInTech for the adaptive regulator taking into account the cargo weight (from empty to maximum loaded) were carried out. The scheme of automatic selection of actuator PID coefficients considering the cargo weight was proposed. The scheme of automatic selection of coefficients of PID regulator for an actuator with regard to the cargo weight was suggested. As a result of parametric synthesis of discrete PID control law optimum values of its amplification coefficients were determined. There was no overcontrol and the transient time, which satisfied the initial requirements for the optimization of the control algorithm by angular velocity.

A Biased Proportional-Integral-Derivative-Incorporated Latent Factor Analysis Model

Nowadays, as the number of items is increasing and the number of items that users have access to is limited, user-item preference matrices in recommendation systems are always sparse. This leads to a data sparsity problem. The latent factor analysis (LFA) model has been proposed as the solution to the data sparsity problem. As the basis of the LFA model, the singular value decomposition (SVD) model, especially the biased SVD model, has great recommendation effects in high-dimensional sparse (HiDs) matrices. However, it has the disadvantage of requiring several iterations before convergence. Besides, the model PID-incorporated SGD-based LFA (PSL) introduces the principle of discrete PID controller into the stochastic gradient descent (SGD), the learning algorithm of the SVD model. It could solve the problem of slow convergence speed, but its accuracy of recommendation needs to be improved. In order to make better solution, this paper fuses the PSL model with the biased SVD model, hoping to obtain better recommendation result by combining their advantages and reconciling their disadvantages. The experiments show that this biased PSL model performs better than the traditional matrix factorization algorithms on different sizes of datasets.

Discrete fractional order PID controller design for nonlinear systems

ABSTRACT In this study, a discrete fractional order PID controller for nonlinear systems is proposed. U-model is firstly employed to transform nonlinear systems into a linear-like model and model complexity is then degraded and easier for controller design. Then, a new discrete fractional order PID control law in difference equation is presented which takes advantage of two more adjustable parameters. Finally, robust stability of the control law is analysed. Both deterministic and stochastic examples are provided to illustrate the effectiveness and superiority of the proposed controller.

Применение программного обеспечения Simulink при проектировании судна

The article considers different types of controllers and regulators used in industry, laboratories and for daily tasks. In practice, the most commonly used controllers are discrete state controllers, PID controllers, fuzzy and neural controllers. The last two use more sophisticated concepts, such as artificial intelligence. Controllers can be divided into feed-forward and feedback controllers. The feed-forward controller works by giving a result based on waiting for the next step, while the feedback controller works to give an observable result that changes the processing value of the later step. PID controllers are very popular in the design of a ship's main power plant. There is considered a schematic diagram of the PID controller. The description of the ship model in the Simulink environment is presented, the specified model of the diesel engine, the mechanical regulator, areas of restrictions of the engine are illustrated. The model of the turbocharger is analyzed in detail. It consists of a turbine resting on the exhaust gases coming out of the cylinders, due to which the compressor starts and compresses the air at the inlet to the cylinders. There is given the equation formed by the ratio of integral to time. In accordance with the original model of the diesel engine Diesel Engine Module, the nominal efficiency is defined. A model of shaft dynamics based on Newton's second law for rotation is considered. The actual Simulink model is illustrated, which introduces transmission losses and saturation associated with the load capacity of the engine. The model uses three designs of propellers. The characteristics of the propellers on the container ship MSC Caitlin, the tanker “Ivan Poddubny” and the ferry “Olympiad” are given. The general model of the propeller is made and resistance of calm water is simulated. The additional model of wave resistance is presented.

Discrete fuzzy adaptive PID control algorithm for automotive anti-lock braking system

Due to the low slip rate and poor braking performance of automobile anti-lock braking system, a discrete fuzzy adaptive PID control algorithm for automobile anti-lock braking system is designed in this paper. Based on the theory of discrete fuzzy adaptive PID control algorithm, the braking force of a vehicle is analyzed and the anti-lock control target is set. The automobile adhesion coefficient and wheel slip rate are calculated as the input and output of the PID control algorithm to complete the control of the anti-lock brake system of the network automobile. Experiments show that the sliding rate of the discrete fuzzy adaptive PID control algorithm of the designed anti-lock system is close to 20%, which proves that the design method has good braking effect.

Fuzzy pid control of electromechanical actuator system

In order to meet the needs of modern high-performance aircraft, the fuzzy PID control strategy was used to design the electromechanical actuator control system. This control strategy combines the advantages of fuzzy control and PID control, and has better adaptability to time-varying complex systems. The electromechanical actuator control system adopted the three-loop structure, and current loop, speed loop and position loop were built on the platform of MATLAB / Simulink. Considering that the discrete universe fuzzy PID control algorithm has good real-time performance with small online computation, the fuzzy PID controller in discrete universe was designed in the position loop and the system was simulated. The simulation results show that the dynamic and steady performance of discrete universe fuzzy PID control is better than that of traditional PID control, and it is more suitable for electromechanical actuator system.

Designing a control system for the orientation of solar panels in the dynamic simulation environment of SimInTech technical systems

The energy efficiency of solar panels is largely determined by the accuracy of their orientation to the Sun. The article presents the results of the development of a software control system for the orientation of the solar panel, depending on the geographical location and calendar date. The system model is implemented in the environment of dynamic modeling of SimInTech technical systems and includes a model of a complex of electromechanical devices for solar panel orientation, a discrete PID controller and a software control unit, which are implemented on the basis of standard SimInTech blocks and submodels. The panel orientation system allows to change the coordinates of the azimuth and location that determine the orientation of the panel in three-dimensional space and control them according to a given program. The system is implemented as a package of projects that interact through a common signal base, which provides information exchange between projects, making the system model flexible and universal. The result of the control system is presented in the 3D module of the visual editor, which allows you to visually track the results of management and the efficiency of equipment use. To confirm the quality indicators of the orientation control of the solar panel the percentage of the received energy capacity is calculated.