Comparison of control systems for multirotor UAV [in Ukrainian

-In this paper , performance of fuzzy PD , fuzzy PI , fuzzy PD+I , fuzzy PID controllers are evaluated and compared. This paper also describes the speed control based on Linear Quadratic Regulator (LQR) technique. The comparison is based on their ability of controlling the speed of DC motor, which merely focuses on performance index of the controllers, and also time domain specifications such as rise time, settling time and peak overshoot. The controller is modelled using MATLAB software, the simulation results shows that the fuzzy PID controllers are the best performing candidates in all aspects but it as higher overshoot and IAE in comparison with optimal LQR. The Fuzzy PI controller exhibited null offset but suffers from poor stability and peak overshoot, whereas the fuzzy PD controller has fast rise time, with no overshoots but the IAE is much greater. Thus, the comparative analysis recommends fuzzy PID controller but it is usually associated with complicated rule base and tedious tuning. To circumvent these problems, the proposed LQR controller gives better performance than the other controllers.

The objective of this chapter is to present an optimal Fractional Order Proportional—Integral-Differential (FOPID) controller based upon Reduced Linear Quadratic Regulator (RLQR) using Particle Swarm Optimization (PSO) algorithm and compared with PID controller. The controllers are applied to Inverted Pendulum (IP) system which is one of the most exciting problems in dynamics and control theory. The FOPID or PID controller with a feed-forward gain is responsible for stabilizing the cart position and the RLQR controller is responsible for swinging up the pendulum angle. FOPID controller is the recent advances improvement controller of a conventional classical PID controller. Fractional-order calculus deals with non-integer order systems. It is the same as the traditional calculus but with a much wider applicability. Fractional Calculus is used widely in the last two decades and applied in different fields in the control area. FOPID controller achieves great success because of its effectiveness on the dynamic of the systems. Designing FOPID controller is more flexible than the standard PID controller because they have five parameters with two parameters over the standard PID controller. The Linear Quadratic Regulator (LQR) is an important approach in the optimal control theory. The optimal LQR needs tedious tuning effort in the context of good results. Moreover, LQR has many coefficients matrices which are designer dependent. These difficulties are talked by introducing RLQR. RLQR has an advantage which allows for the optimization technique to tune fewer parameters than classical LQR controller. Moreover, all coefficients matrices that are designer dependent are reformulated to be included into the optimization process. Tuning the controllers’ gains is one of the most crucial challenges that face FOPID application. Thanks to the Metaheuristic Optimization Techniques (MOTs) which solves this dilemma. PSO technique is one of the most widely used MOTs. PSO is used for the optimal tuning of the FOPID controller and RLQR parameters. The control problem is formulated to attain the combined FOPID controllers’ gains with a feed forward gain and RLQR into a multi-dimensions control problem. The objective function is designed to be multi-objective by considering the minimum settling time, rise time, undershoot and overshoot for both the cart position and the pendulum angle. It is evident from the simulation results, the effectiveness of the proposed design approach. The obtained results are very promising. The design procedures are presented step by step. The robustness of the proposed controllers is tested for internal and external large and fast disturbances.

This study considers the problem of designing a multi‐input and multi‐output (MIMO) proportional‐integral‐derivative (PID) controller via direct optimal or suboptimal linear quadratic regulator (LQR) approach. To design the controller, first the MIMO PID design problem is transformed into a state feedback control and then the gains of the state feedback controller are chosen through an optimal or suboptimal LQR design. Given a minimal state space representation (A, B, C) of the plant, a necessary and sufficient condition (based on matrices A, C) for which the optimal problem (i.e. PID design via optimal LQR) is solvable is obtained. When this optimal problem is not solvable, a suboptimal solution (i.e. PID design via suboptimal LQR), if exists, is obtained by converting the problem into trace minimisation one, which is solved using linear matrix inequality‐based method. Suitable examples are considered to illustrate the approaches.

Analysis of robust pole clustering in a sector region for uncertain LQR control systems

This paper introduces an application of genetic algorithm (GA) to determine weighting matrices Q and R elements in linear quadratic regulator (LQR) optimization process. The weighting matrices, Q and R are the most important components in LQR optimization and determine the output performances of the system. Commonly, a trial-and-error method has been used to construct the elements of these matrices. This method is simple, but very difficult to choose the best values that have good control performances. Because of this, the Bryson method can be employed to give better results. In this paper, we use GA to construct the weighting matrices Q and R properly with help of Bryson method. This idea gives a new alternative procedure in time varying feedback control to improve the stability performance. This design implemented in an inverted pendulum as a benchmark control problem.

To enhance wind energy technology, the present status and challenges associated with the wind turbine controls have to be studied. The function of different wind turbine control strategies such as PID control, PI control, linear quadratic optimal regulator, linear quadratic Gaussian optimal regulator, Robust Multivariable control, prognostic control or regulator and adaptive tuning of parameter are comprehensively reviewed and limitations are presented. The challenges related to wind turbine control are identified. Some of the required future works to improve turbine energy capturing capacity and its lifetime are discussed.KeywordsWind turbine controlEnergy capturing capacityChallenges

Optimal feedback control design using genetic algorithm in multimachine power system

A hybrid proportional double derivative and linear quadratic regulator (PD2-LQR) controller is designed for altitude (z) and attitude (roll, pitch, and yaw) control of a quadrotor vehicle. The derivation of a mathematical model of the quadrotor is formulated based on the Newton–Euler approach. An appropriate controller’s parameter must be obtained to obtain a superior control performance. Therefore, we exploit the advantages of the nature-inspired optimization algorithm called Grey Wolf Optimizer (GWO) to search for those optimal values. Hence, an improved version of GWO called IGWO is proposed and used instead of the original one. A comparative study with the conventional controllers, namely proportional derivative (PD), proportional integral derivative (PID), linear quadratic regulator (LQR), proportional linear quadratic regulator (P-LQR), proportional derivative and linear quadratic regulator (PD-LQR), PD2-LQR, and original GWO-based PD2-LQR, was undertaken to show the effectiveness of the proposed approach. An investigation of 20 different quadcopter models using the proposed hybrid controller is presented. Simulation results prove that the IGWO-based PD2-LQR controller can better track the desired reference input with shorter rise time and settling time, lower percentage overshoot, and minimal steady-state error and root mean square error (RMSE).

In the process of trajectory tracking using the linear quadratic regulator (LQR) for driverless wheeled tractors, a weighting matrix optimization method based on an improved quantum genetic algorithm (IQGA) is proposed to solve the problem of weight selection. Firstly, the kinematic model of the wheeled tractor is established according to the Ackermann steering model, and the established model is linearized and discretized. Then, the quantum gate rotation angle adaptive strategy is optimized to adjust the rotation angle required for individual evolution to ensure a timely jumping out of the local optimum. Secondly, the populations were perturbed by the chaotic perturbation strategy and Hadamard gate variation according to their dispersion degree in order to increase their diversity and search accuracy, respectively. Thirdly, the state weighting matrix Q and the control weighting matrix R in LQR were optimized using IQGA to obtain control increments for the trajectory tracking control of the driverless wheeled tractor with circular and double-shifted orbits. Finally, the tracking simulation of circular and double-shifted orbits based on the combination of Carsim and Matlab was carried out to compare the performance of LQR optimized by five algorithms, including traditional LQR, genetic algorithm (GA), particle swarm algorithm (PSO), quantum genetic algorithm (QGA), and IQGA. The simulation results show that the proposed IQGA speeds up the algorithm’s convergence, increases the population’s diversity, improves the global search ability, preserves the excellent information of the population, and has substantial advantages over other algorithms in terms of performance. When the tractor tracked the circular trajectory at 5 m/s, the root mean square error (RMSE) of four parameters, including speed, lateral displacement, longitudinal displacement, and heading angle, was reduced by about 30%, 1%, 55%, and 3%, respectively. When the tractor tracked the double-shifted trajectory at 5 m/s, the RMSE of the four parameters, such as speed, lateral displacement error, longitudinal displacement error, and heading angle, was reduced by about 32%, 25%, 37%, and 1%, respectively.

We wished to determine whether the individual bias (mean difference) and precision (standard deviation of the difference) values of 2 variables, arterial oxygen saturation (SaO2) and mixed venous oxygen saturation (SvO2), could be used to predict the bias and precision values of the combined dual oximetry variable (SaO2-SvO2). We simultaneously measured SaO2 by pulse oximetry and arterial blood gas co-oximetry and SvO2 by fiberoptic reflectance oximetry pulmonary artery catheter and venous blood gas co-oximetry in 238 data sets from 55 patients. Three different methods were used to predict the standard deviation of the difference of (SaO2-SvO2) [s delta(SaO2-SvO2)]: simple sum, root mean square (RMS) error, and RMS error with correction term. We derived the equation for the RMS error with correction term because initial results showed that the simple sum and RMS error methods did not predict s delta(SaO2-SvO2) well. The correction term accounts for the non-independence of simultaneous SaO2 and SvO2 measurements. The observed overall bias of the SaO2, SvO2, and (SaO2-SvO2) measurement methods were 0.17, -1.76, and 1.94, respectively. The observed overall s delta(SaO2-SvO2) of the (SaO2-SvO2) measurement method was 5.12. The simple sum method overestimated the actual s delta(SaO2-SvO2) by 38%, the RMS error method differed from the actual s delta(SaO2-SvO2) by 3%, and the RMS error with correction term method matched the actual s delta(SaO2-SvO2). The bias of a (SaO2-SvO2) measurement method is simply the bias of the SaO2 measurement method less the bias of the SvO2 measurement method. s delta(SaO2-SvO2) is best predicted by the derived equation, RMS error with correction term. The same principles and equations also apply to other situations in which 2 variables with the same dimensions are combined into 1 variable, such as (PaCO2-EtCO2) gradients and perfusion-pressure gradients. Although the difference between the s delta(SaO2-SvO2) predicted by the RMS error equation and the derived RMS error equation with correction term was small, the difference may be significant for other combined variables.

In this paper, the stability robustness of deterministic state feedback discretetime linear quadratic (LQ) optimal regulators for the performance index with cross-product terms is analyzed. Guaranteed stability margins for such a type of LQ optimal regulator are suggested for the first time. These stability margins are obtained on the basis of a modified return difference equality and are expressed directly in terms of the elementary cost and system matrices. Sufficient conditions to guarantee the required stability margins are presented. Finally, the connection between the suggested stability margins and the selection of weighting state, input, and cross-product matrices is investigated, and useful guidelines for choosing proper weighting matrices are presented.

Optimal Linear Quadratic Regulator for Markovian Jump Linear Systems, in the presence of one time-step delayed mode observations

Four-wheel independent steering and four-wheel independent driving electric vehicle (4WIS-4WID EV) has more control degrees of freedom (DOF). It benefits to realize torque allocation and differential steering control. Therefore, four wheel steering technology (4WS) and direct yaw control (DYC) are important research direction of vehicle stability. This paper designed a kind of novel adaptive linear quadratic optimal regulator (LQR) as a coordination controller for 4WIS-4WID EV stability control with 4WS and DYC. The deviation between the real value and ideal value is obtained and delivered to LQR controller. According to different speed and road surface conditions, sideslip angle β and stable area are calculated using phase plane method. The weight matrix Q and R of LQR controller is adaptive to velocity, adhesion coefficient and the \( \beta - \dot{\beta } \) phase plane. The performance of adaptive LQR is simulated in MATLAB/Simulink and Carsim platform. Compared with no control, 4WS, DYC, and fixed LQR strategies, the results show that the adaptive LQR controller with weight matrix adaption has better performance than the outputs form DYC, 4WS and fixed LQR in stability.

This paper presents design and control of a 2D Ball Balancer Arrangement using Particle Swarm Optimization (PSO) algorithm. The paper also compares the results of proposed control technique with Classical PID controller and Fuzzy logic controller. The Ball Balancer Arrangement is a nonlinear system with complex plant transfer function. Classical control methods such as Classical PID and Fuzzy logic controller are also able to control the Ball Balancer Arrangement but manual tuning and rule base optimization is slow and inefficient. PSO tuning on the other hand, is a heuristic approach which finds the solution with its own experience rather than relying on human expertise. Search space, population size, cost function and number of iterations are the few key parameters that PSO requires to find optimal gains for PID controller. The comparative analysis of PSO tuned PID with classical control methods show improved trajectory of the ball in terms of delay time, rise time, and settling time. The designing and simulation have been successfully performed in MATLAB/ Simulink environment.

This paper deals with the designing of linear optimal controller for Magnetic Levitation system (Maglev) in both simulation and real time. The Hamilton-Jacobi-Bellman (HJB) equation is employed to design the closed loop optimal control of infinite-time as well as finite-time Linear Quadratic Regulator (LQR) system with quadratic performance measure or index. The objective of the proposed controller is to stabilize the Maglev system and to control the ball position for tracking the desired ball position. The two different cases of weights of the LQR controller are selected on the trial and error basis for studying and improving the time response performance of the system. The performance comparison between infinite-time LQR and finite-time LQR is also investigated in both simulation and real time. To validate the effectiveness of proposed controller, it is compared with the classical PID controller between their relative time response and performance indices of the system. In the future, a detailed study of robustness in the presence of model uncertainties or external disturbance will be incorporated as a scope of further research.