Control Methods Comparison for the Real Quadrotor on an Innovative Test Stand

The electric motor is a device that converts electrical power into mechanical power. The DC motor has some advantages compared to the AC motor on its easier way to control the speed or position and wide adjustable range. However, it still has some issues, such as uncertainty and disturbance; most existing controllers still provide bad system performance or have major drawbacks in solving these issues. The alternative solution for a control method with simple, easy to design, and can be implemented in a multi-input multi-output system is the integral state feedback control technique, such as in Linear Quadratic Regulator (LQR). The weakness of LQR control is that there is no exact method to determine the best value of matrix Q and R used to calculate the state feedback gain; trial or manual tuning method is mostly used. Therefore, this paper proposed an improved LQR control using Particle Swarm Optimization (PSO) method and the Kalman filter estimator. The PSO was used to find optimal Q and R-value, while the Kalman filter reduced the number of sensors used to measure the system state. Both performance and energy consumption were compared using the Integral of Absolute Error (IAE) and total energy consumption. The simulation results showed that the proposed method is superior in performance and energy compared to manually-tuned LQR. However, based on the hardware implementation, although the manually-tuned LQR was found to have the smallest energy consumption, the proposed method has the smallest IAE, which can reduce the IAE by 11.28% with only 1% higher energy compared to manually-tuned LQR.

The linear quadratic regulator (LQR) is a classical optimal control approach that can regulate gait dynamics about target kinematic trajectories. Exoskeletons to restore gait function have conventionally utilized time-varying proportional-derivative (PD) control of leg joints. But, these PD parameters are not uniquely optimized for whole-body (full-state) performance. The objective of this study was to investigate the effectiveness of LQR full-state feedback compared to PD control to maintain bipedal walking of a sagittal-plane computational model against force disturbances. Several LQR controllers were uniquely solved with feedback gains optimized for different levels of tracking capability versus control effort. The main implications to future exoskeleton control systems include (1) which LQR controllers out-perform PD controllers in walking maintenance and effort, (2) verifying that LQR desirably produces joint torques that oppose rapidly growing joint state errors, and (3) potentially equipping accurate sensing systems for nonjoint states such as hip-position and torso orientation. The LQR controllers capable of longer walk times than respective PD controllers also required less control effort. During sudden leg collapse, LQR desirably behaved like PD by generating feedback torques that opposed the direction of leg-joint errors. Feedback from nonjoint states contributed to over 50% of the LQR joint torques and appear critical for whole-body LQR control. While LQR control poses implementation challenges, such as more sensors for full-state feedback and operation near the desired trajectories, it offers significant performance advantages over PD control.

Inverted pendulum mounted on a cart is an inherently unstable system which requires control effort to stabilize it at its upright position. In this single input multi output system the pendulum is balanced by controlling the horizontal motion of the cart. Various controller design techniques have been developed to control such systems like PID controllers, LQR controllers, Neural networks etc. The performance of the system for controlling methods of PD (Proportional Derivative) controller and LQR (Linear Quadratic Regulator) controller are compared by simulating in MATLAB SIMULINK and the results are validated through results obtained from a real inverted pendulum system.

This paper proposes the use Fuzzy logic controller and a Particle Swarm Optimization (PSO) based Linear Quadratic Regulator (LQR) controller for the balance of an electric unicycle. It also examines dynamics of the electric unicycle's schematic design, which has a backing seat for the passenger and is analogous to the Segway device equipped with a handle shaft for direction. A proportional derivative controller incorporated with a Fuzzy logic controller was designed for the suggested model of the electric unicycle for speed and position control (Fuzzy controller), and a Proportional Derivative (PD) controller was utilized to control the angle rate and angle of the unicycle. Comparison of the Fuzzy logic controller with a Particle Swarm Optimization (PSO) Linear Quadratic Regulator (LQR) controller was carried out based on error deviation and time response simulations. Command tracking or regulation of some initial state condition were examined and demonstrated by time based simulations of the modelled system. The results evidently indicate that the Fuzzy Proportional Derivative (PD) controller can effectively attain attitude equilibrium for the two wheeled unicycle and preventing it from falling down.

This study investigates the performance of four control strategies—Proportional-Derivative (PD), Feedforward-Feedback PD (FF-FB PD), Linear Quadratic Regulator (LQR), and Feedforward-Feedback LQR (FF-FB LQR)—implemented on a robotic transfemoral prosthesis. The performance metrics, including overshoot, settling time, trajectory tracking accuracy, and torque requirements, were evaluated using simulation models. The results indicate that the FF-FB LQR controller demonstrated superior performance, achieving the lowest overshoot (4.98%) and near-zero trajectory tracking error. All controllers required approximately 8.6 Nm of torque, suggesting consistent energy requirements across strategies despite their performance differences. The LQR controller exhibited the best stability, minimizing overshoot and improving overall system response. These findings highlight the advantages of feedforward-feedback control strategies, particularly the FF-FB LQR, for controlling robotic transfemoral prostheses with enhanced stability and accuracy.

The main objective of this research is to design a state-feedback controller for the rotary inverted pendulum module utilizing the linear quadratic regulator (LQR) technique. The controller maintains the pendulum in the inverted (upright) position and is robust enough to reject external disturbance to maintain its stability. The research work involves three major contributions: mathematical modeling, simulation, and real-time implementation. To design a controller, mathematical modeling has been done by employing the Newton-Euler, Lagrange method. The resulting model was nonlinear so linearization was required, which has been done around a working point. For the estimation of the controller parameters, MATLAB LQR function has been utilized. Simulation has been performed for the designed controller and it also has been implemented and tested over the real inverted pendulum. From the results, it is vivid that the designed controller keeps the inverted pendulum in an upright position and rejects the disturbances and falling under gravitational force by adjusting the rotation of the horizontal link.

This paper intends to compare controllers used for non-isolated (transformer less) interleaved double dual boost (IDDB) converter which provide high voltage gain and can be used for high-power applications. A control subsystem is required to improve dynamic behaviour of converter and to have a better output response. In most cases small signal model of converter is obtained which are linearized at an operating point to derive a controller which cannot take uncertainties into consideration. Robust control and Nonlinear control methods are probably areas which can handle uncertainties and non-linearities effectively. Conventional linear quadratic regulator (LQR) controller cannot assure stability if system is highly uncertain. A convex model of converter dynamics is obtained taking uncertainties into account. To apply LQR control in uncertain converter case linear matrix inequalities(LMIs) are used to optimize the performance index. A comparative study of LMI-LQR control, LQR Controller and PID controller is done.

In this paper, the differences between decoupled and coupled control of bank-to-turn (BTT) missiles have been studied in detail from three aspects: stabilizability, linear quadratic regulator (LQR) control and tracking control. It is found that for some parameters the BTT missile can be controlled by a decoupled way, especially for stabilizability and LQR control. However, for some others, the BTT missile cannot be decoupled and a coupled control method is needed. Therefore, for a practical flight control system, the decouplability should be studied before giving a decoupled control method. In addition, in order to avoid the disadvantages of LQR control method, an improved H∞ controller design method is given. Combined with tracking control problem, a new H∞ control method is established for trajectory tracking.

A linear quadratic regulator (LQR) of a power converter connected to a doubly fed induction generator (DFIG) of a wind energy conversion system (WECS) is presented. Active and reactive powers tracking of the grid side converter (GSC) is focused. The main future of this work is to present a robust stabilizing LQR controller that has no dependence on the parametric variation. Generally, the tracking control laws are calculated based on the value of their desired outputs. The standard LQR controllers give good performances in terms of stability margin and certain performance cost. However, LQR control does not ensure maintaining these performances mainly in case of parametric or reference variations. On the one hand, the WECS functioning is conditioned by the uncertain variations of wind velocity and on the other hand by load perturbation. In this paper, an invariant LQR compensator is calculated independently from parametric and reference changes. Moreover, the control problem involves Lyapunov stability condition that ensures the system stability over the admissible ranges of output references and parametric variations. Linear matrix inequalities (LMIs) formulation of the problem is established in order to optimize the LQR performance index. As a consequence, a new formulation of the stabilizing LQR state control is introduced. Finally the performances of the controller are discussed for different references of active and reactive powers.

Inverted pendulum systems, such as double or single, rotational or translational inverted pendulums are non-linear and unstable, which have been the most dominant approaches for control systems. The double inverted pendulum is one kind of a non-linear, unstable system, multivariable, and strong coupling with a wide range of control methods. To model these types of systems, many techniques have been proposed so that motivating researchers to come up with new innovative solutions. The Linear Quadratic Regulator (LQR) controller has been a common controller used in this field. Meanwhile, the Artificial Bee Colony (ABC) technique has become an alternative solution for employing Bee Swarm Intelligence algorithms. The research solutions of the artificial bee colony algorithm in the literature can be beneficial, however, the utilization of discovered sources of food is ineffective. Thus, in this paper, we aim to provide a double inverted pendulum system for stabilization by selecting linear quadratic regulator parameters using a bio-inspired optimization methodology of artificial bee colony and weight matrices Q and R. The results show that when the artificial bee colony algorithm is applied to a linear quadratic regulator controller, it gains the capacity to autonomously tune itself in an online process. To further demonstrate the efficiency and viability of the suggested methodology, simulations have been performed and compared to conventional linear quadratic regulator controllers. The obtained results demonstrate that employing artificial intelligence (AI) together with the proposed controller outperforms the conventional linear quadratic regulator controllers by more than 50 % in transient response and improved time response and stability performance

A recurrent dynamic neural network (RDNN) based on Hopfield model is applied to linear quadratic regulator controller of an irrigation canal. The Saint-Venant equations of open-channel flow are linearized using the Taylor series and a finite difference approximation of the original nonlinear, partial differential equations. Using the linear optimal control theory, a Linear Quadratic Regulator (LQR) controller is developed for an irrigation canal with a single pool. A Hopfield recurrent dynamic neural network is applied to solution of Riccati equation for calculating the LQR control gains. The main advantage of Hopfield neural network model is its robustness and flexibility when dealing with unknown perturbations and parameters. The results of this study shows that an RDNN based LQR controller (RDNN/LQR) for irrigation canals offers an alternative to traditional LQR controller when dealing with the disturbances in the irrigation canals.

Rotary inverted pendulum (RIP) system is a nonlinear, non-minimum phase, unstable and underactuated system. Controlling such system can be a challenge and is considered a benchmark in control theory problem. Prior to designing a controller, equations that represent the behaviour of the RIP system must be developed as accurately as possible without compromising the complexity of the equations. Through Takagi-Sugeno (T-S) fuzzy modeling technique, the nonlinear system model is then transformed into several local linear time-invariant models which are then blended together to reproduce, or approximate, the nonlinear system model within local region. A parallel distributed compensation (PDC) based fuzzy controller using linear quadratic regulator (LQR) technique is designed to control the RIP system. The results show that the designed controller able to balance the RIP system.

Purpose – This paper aims to present the design of a stability augmentation system (SAS) in the longitudinal and lateral axes for an unstable helicopter. Design/methodology/approach – The feedback controller is designed using linear quadratic regulator (LQR) control with full state feedback and LQR with output feedback approaches. SAS is designed to meet the handling qualities specification known as Aeronautical Design Standard (ADS-33E-PRF). A helicopter having a soft inplane four-bladed hingeless main rotor and a four-bladed tail rotor with conventional mechanical controls is used for the simulation studies. In the simulation studies, the helicopter is trimmed at hover, low speeds and forward speeds flight conditions. The performance of the helicopter SAS schemes are assessed with respect to the requirements of ADS-33E-PRF. Findings – The SAS in the longitudinal axis meets the requirement of the Level 1 handling quality specifications in hover and low speed as well as for forward speed flight conditions. The SAS in the lateral axis meets the requirement of the Level 2 handling quality specifications in both hover and low speed as well as for forward speed flight conditions. The requirements of the inter axis coupling is also met and shown for the coupled dynamics case. The SAS in lateral axis may require an additional control augmentation system or adaptive control to meet the Level 1 requirements. Originality/value – The study shows that the design of a SAS using LQR control algorithm with full state and output feedbacks can be used to meet ADS-33 handling quality specifications.

The purpose of this study is to build a two-stage Kalman filter (TSKF) for estimating the actuator control effectiveness factors of an unmanned aerial vehicle (UAV). The actuator faults can be determined and isolated using controller effectiveness factor estimates. A linear quadratic regulator (LQR) controller is designed for the modelled UAV. The control matrix is identified by the TSKF. In the case of actuator faults, LQR controller can be reconfigured for the identified control distribution matrix. For faulty actuator scenarios (change in elevator, throttle, aileron control effectiveness factors are taken into account), the designed system is tested, and the success of TSKF is shown. The closed-loop systems which include LQR-type controllers in the longitudinal and lateral dynamics are considered and simulations are done in this system to estimate the true states and the control effectiveness factors. True values of the effectiveness factors are estimated, and it is shown that the estimation of the states can be done effectively using TSKF for lateral and longitudinal models.

In this paper, we introduced the principle of using fast steering mirror (FSM) in compound-axis systems. Based on the modeling of a fast steering mirror, the linear quadratic regulator (LQR) controller design process is demonstrated. Several simulation experiments were done using the LQR controller that was designed, and the results were compared with two commonly used classical control theory controllers. The result of comparison and system analysis shows the effectiveness of the LQR algorithm.