Linear Quadratic Control Research Articles

Application of PID Control Technology in Unmanned Aerial Vehicles

Abstract. The rapid advancement of unmanned aerial vehicle (UAV) technology underscores the essential role of PID (proportional-integral-derivative) control in ensuring flight stability, particularly through precise motor speed adjustments. Thus, this paper systematically analyzes the fundamental principles and limitations of traditional PID control, further highlighting its insufficient adaptability to dynamic external conditions, which includes load fluctuations and wind disturbances. In response to these challenges, it explores adaptive control strategies such as self-tuning PID and fuzzy logic PID, points out how these advanced methods can effectively improve flight stability by dynamically adjusting control parameters, and demonstrates their superiority over traditional PID through comparative analysis. In addition, the paper anticipates future developments in UAV control systems, thereby emphasizing the integration of artificial intelligence and machine learning technologies into PID control. And this integration seeks to optimize control strategies and markedly enhance the autonomous decision-making capabilities and adaptability of UAVs. Meanwhile, the paper also predicts the development trend of hybrid control systems, that is, combining PID with other advanced control methods (such as linear quadratic control) to enhance the overall control capabilities of UAVs. In short, it underscores the necessity for continuous innovation and in-depth research in response to the dynamic flight environment and the diverse mission requirements.

Inertial mass modeling and compensation for an energy-harvesting vehicle suspension system with limited-DOF parallel mechanisms actuator

An energy-harvesting suspension can improve the energy efficiency of vehicle. By introducing a lower-mobility parallel mechanism as motion transfer in the energy-harvesting suspension, the stiffness of the system is significantly improved. However, the overlage equivalent of inertial mass make the system is difficult to control and imped the development of this kind of suspension. To solve the problem, an equivalent linearization model to calculate the nonlinear inertial mass of low-DOF (Degree Of Freedom) parallel mechanism actuator is studied firstly. Furthermore, a 2-DOF 1/4 suspension system dynamic model that includes inertial mass is proposed to analyze the vehicle acceleration, dynamic tire load, and dynamic stroke. On this basis, the linear-quadratic Gaussian (LQG) controller is adopted to compensate the inertial mass of the suspension to improve the system performance. Results show that the proposed model accurately reflects the characteristics of the suspension inertial mass, the root-mean-square (RMS) value of the vehicle body acceleration and suspension dynamic stroke through compensation controller is reduced by 33.4% and 30.89%, respectively. Moreover, the RMS of the dynamic tire load is reduced by 3.06%, and the system stability is improved significantly.

Data-driven stabilization of an oscillating flow with linear time-invariant controllers

This paper presents advances towards the data-based control of periodic oscillator flows, from their fully developed regime to their equilibrium stabilized in closed loop, with linear time-invariant (LTI) controllers. The proposed approach directly builds upon the iterative method of Leclercq et al. (J. Fluid Mech., vol. 868, 2019, pp. 26–65) and provides several improvements for an efficient online implementation, aimed at being applicable in experiments. First, we use input–output data to construct an LTI mean transfer functions of the flow. The model is subsequently used for the design of an LTI controller with linear quadratic Gaussian synthesis, which is practical to automate online. Then, using the controller in a feedback loop, the flow shifts in phase space and oscillations are damped. The procedure is repeated until equilibrium is reached, by stacking controllers and performing balanced truncation to deal with the increasing order of the compound controller. In this article, we illustrate the method for the classic flow past a cylinder at Reynolds number $Re=100$ . Care has been taken such that the method may be fully automated and hopefully used as a valuable tool in a forthcoming experiment.

Approximation of optimal feedback controls for stochastic reaction-diffusion equations

In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error estimates. The approximation of optimal feedback controls by neural networks is discussed as an explicit application of our method. We illustrate our findings in the case of a linear quadratic control problem with a numerical example.

Research on intelligent optimal allocation control strategy for stability and braking of heavy tyre blowout vehicle

The traditional control strategy mainly compensates and corrects the driving state of heavy vehicles with a tyre blowout, and rarely considers the need for emergency braking. It is also difficult to effectively coordinate the problems of lateral yaw, slip and tailspin, and longitudinal braking performance degradation. For this, an intelligent optimization allocation control strategy combining stability control and braking control is innovatively designed in this article. The joint simulation model for heavy tyre blowout vehicles is built based on the Dugoff tyre blowout model and the TruckSim vehicle model. A linear quadratic form regulator stable control based on the particle swarm optimization algorithm optimization is used to dynamic equilibrium of the additional yaw moment generated by the vehicle tyre blowout. A logic threshold braking control based on adaptive adjustment is adopted to achieve an ideal braking effect for the vehicle. In order to simultaneously consider the stability and braking performance of vehicles with blowout tyre, a braking force distribution strategy and a fuzzy optimization allocation algorithm are proposed to achieve coordination of lateral and longitudinal control strategies. The results indicate that intelligent optimized allocation control can effectively correct the deviation trajectory of a heavy tyre blowout vehicle, enabling it to achieve rapid braking while maintaining stability.

Adaptive Linear Quadratic Control for Stochastic Discrete-Time Linear Systems With Unmeasurable Multiplicative and Additive Noises

Adaptive Linear Quadratic Control for Stochastic Discrete-Time Linear Systems With Unmeasurable Multiplicative and Additive Noises

A Linear Quadratic Regulation Controller Based on Radial Basis Function Network Approximation

This paper proposes a linear quadratic regulation (LQR) tracking control method based on a radial basis function (RBF) that successfully compensates for the shortcomings of the LQR method. The LQR method depends on the linearity of a model. Specifically, an RBF neural network is used to approximate and compensate for the nonlinear part of a controlled object in the PID type-I, type-II and type-III control loops to improve the performance of the system. Through the simulation of different industrial systems, such as underdamped, overdamped and critically damped systems, the method significantly improves the dynamic response performance indices, such as the rise time and settling time, of the system.

Development of mathematical modeling of a mobile robot's motion control system

This study focuses on developing a mathematical model for precise control and stabilization of unmanned aerial vehicles (UAVs) in various spatial conditions. Addressing the problem of achieving precise control and stability, the proposed solution designs a control system based on a linear-quadratic controller (LQR) and simulates it using a proportional-derivative (PD) controller implemented in Matlab/Simulink. The results demonstrate high precision and stability in controlling the UAV motion parameters – roll, pitch, yaw, and altitude. This important level of performance is achieved due to the adaptivity of the LQR-based control system, which optimizes control actions according to the unsteady dynamics of the UAV. The integration of the PD controller improves responsiveness and stability, providing precise motion control over a range of spatial states. These features effectively solve the problem by handling the complex dynamics of the UAV and providing precise control. The results are explained by the ability of the LQR to provide optimal control laws that minimize deviations using a quadratic cost function, while the PD controller quickly corrects errors and responds to disturbances. The benefits of this approach include a significant reduction in control errors by about 25–30 %, increased response speed to external disturbances, and reduced computational latency due to efficient processing compared to more resource-intensive methods such as model predictive control. The developed mathematical model can be applied in practice in conditions requiring robust real-time control and adaptation to dynamic changes in the environment. It is especially suitable for industries such as logistics, surveillance, and environmental monitoring, providing an effective and optimal solution for stabilizing and controlling the motion of UAVs in various spatial states. This approach improves the performance of UAVs and expands their capabilities in various operating conditions.

Attitude control of UAV bicopter using adaptive LQG

This paper aims to design a controller that is able to maintain the stability of the unmanned aerial vehicle (UAV) bicopter attitude when carrying a payload. When the value of the payload inertia is in uncertainty, it is necessary to design a controller that can carry out the adaptation process. This paper proposes an Linear Quadratic Gaussian (LQG) adaptive controller to control the attitude of the bicopter with uncertain payload conditions. The proposed adaptive mechanism is a development of LQG control that can follow the response of the reference model. The success of LQG adaptive control is tested by providing uncertain payload parameters. The simulation results show that the LQG adaptive controller successfully overcomes the influence of inertial disturbances originating from the payload. There is a gain ρ in the LQG adaptive mechanism, this gain is influenced by the parameter σ which acts as a learning rate that produces a response to adapt to the response of the reference model. From the test results obtained when the value of σ is enlarged there is an increased overshoot condition/value but the root mean square error (RMSE) value decreases. That means when the RMSE decreases, the response is getting closer to the model reference. To reduce the overshoot effect of increasing the value of σ, an improvement is made in the search for the gain value of ρ. From the test results, the value of σ=1 was chosen with the development of the gain equation ρ.

Feedback–feedforward signal control with exogenous demand estimation in congested urban road networks

To cope with uncertain traffic patterns and traffic models, traffic-responsive signal control strategies in the literature are designed to be robust to these uncertainties. These robust strategies still require sensing infrastructure to implement traffic-responsiveness. In this paper, we take a novel perspective and show that it is possible to use the already necessary sensing infrastructure to estimate the uncertain quantities in real time. Specifically, resorting to the store-and-forward model, we design a novel network-wide traffic-responsive strategy that estimates the occupancy and exogenous demand in each link, i.e., entering (exiting) vehicle flows at the origins (destinations) of the network or within links, in real time. Borrowing from optimal control theory, we design an optimal linear quadratic control scheme, consisting of a linear feedback term, of the occupancy of the road links, and a feedforward component, which accounts for the varying exogenous vehicle load on the network. Thereby, the resulting control scheme is a simple feedback–feedforward controller, which is fed with occupancy and exogenous demand estimates, and is suitable for real-time implementation. Numerical simulations for the urban traffic network of Chania, Greece, show that, for realistic surges in the exogenous demand, the proposed solution significantly outperforms tried-and-tested solutions that ignore the exogenous demand.

Adaptive tracking control method for shearer cutting trajectory based on the combined strategy

Adaptive tracking control method for shearer remains challenging caused by the contradiction between coal recovery rate and equipment safety under current technological limitations, has drawn more and more attention over the past decades due to its important role in reducing personnel, increasing safety, and improving efficiency for underground mining. Therefore, a novel adaptive tracking control method for shearer cutting trajectory based on the combined strategy is proposed, whose core is the switching method of the sub-strategies based on the linear quadratic regulator (LQR) and error band control (EBC) with switching threshold determined by the Multi-strategy Marine Predator Algorithm. The performance of the proposed method is demonstrated by comparing with the existing methods reported. The experimental results reveal that the proposed method maintains a high recovery rate while improving coal mining efficiency.

The Two-Wheeled Robot: Experimental Evaluation of Two Controllers

Abstract In this paper we present the theoretical and experimental comparison of two digital controllers intended for stabilization of a two-wheeled robot. The properties of an LQG controller and an LQR controller with H ∞ filter are evaluated. Using the μ-analysis, we show that both controllers ensure robust stability of the closed-loop system in the presence of unstructured uncertainty. The results from the closed-loop system experimental evaluation confirm the precise work of both controllers.

An active trailer steering design for long combination vehicles

This article proposes a trailer-axle arrangement for a long combination vehicle, i.e., a B-train double with trailer tridem-axle groups, in which the lead-axle of each group is an active trailer steering axle, and the two rear-axles are passive trailer steering axles. Given this trailer-axle arrangement, a cost-effective active trailer steering system is devised. It is assumed that in low-speed curved-path negotiations, a passive trailer steering system, e.g., self- or command-steering, will operate, while in high-speed operations, the active trailer steering system is to be activated. For the active trailer steering control, three controllers are evaluated, which are designed using the linear quadratic regulator, linear quadratic Gaussian, and µ-synthesis techniques. The performance of these designs is assessed using closed-loop simulation. The insightful findings from this study will provide guidelines for designing active trailer steering systems for long combination vehicles.

LQG control for networked control systems with packet dropouts and input delay: UDP case

LQG control for networked control systems with packet dropouts and input delay: UDP case

Optimal control of a doubly fed induction generator of a wind turbine in cooperation with weak and rigid grids

In this article a control method for a rotor side converter (RSC) of a doubly fed induction generator of a wind turbine is developed. The doubly-fed induction generator (DFIG) system of a wind energy power plant that improves grid symmetrization was applied. The issue of optimal control was treated as an extended linear quadratic regulator (ELQR) having an extra set of exogenous inputs, which are source voltages of the electric grid. No additional knowledge of equations modelling the exogenous inputs was assumed. The proposed method is much more efficient than the currently available linear quadratic control methods. The control objective for a weak grid was to maintain the given value of the voltage module on load terminals and the given value of active power transferred from the stator’s winding. First harmonic components of relevant waveforms were used for this purpose. This task also required the DFIG system to provide reactive power to the grid. In the case of a rigid grid, this reactive power would be too high. Therefore, in this case, it was assumed that the system would supply only part of the required active and reactive power, based on its capabilities. It was required that the voltage and current ratings of the system, mainly the DFIG, were not exceeded. Therefore, the parameters of the network in these difficult failure cases were corrected only partially. The behaviour of the grid in the conditions of failure, as well as the return to the steady state after failure disappearance, were studied.

Data integrity cyber-attack mitigation using linear quadratic regulator based load frequency control in hybrid power system

Abstract Hybrid power systems are the contemporary solution to meet the stiff climate change targets and also hold future for implementing distributed generation and microgrids. These systems have renewable sources as their key elements which in turn have high level of intermittency due to weather conditions and other reasons. At the same time, these hybrid power systems are also vulnerable to cyber threats owing to the intense adoption of various IoT Technologies (Internet of Things). Load frequency control (LFC) is a formidable task for the system operators under such scenario and robust control strategies are required to achieve the load frequency within tolerable limits. In this work Linear quadratic controller (LQR) has been proposed to address the challenges of hybrid power systems. Two area interconnected power systems are considered in this work with each one having different configuration with respect to source of power generation. Solar, wind, geo-thermal, electric vehicle charging infrastructure and pumped storage power plant are integrated together with conventional thermal power plant for showcasing the LQR based controller under data integrity cyber-attack scenario. The frequency response of the hybrid power system is demonstrated through MATLAB simulations.

Design and implementation of Golden Eagle optimized cascaded PI and LQR controller for PFC SEPIC converter in EV charging

This research article focuses on designing and implementing a single ended primary inductor converter (SEPIC) for an AC-DC converter, followed by an electric vehicle (EV) charger. It improves the high-power factor at the AC supply with minimum harmonic distortion. The Golden Eagle optimization techniques are adapted to optimize the tuning of Proportional-Integral (PI) and Linear Quadratic Regulator (LQR) controller parameters for better converter performance. The optimization is designed based on the eagle knowledge of hunting methods at various angles of spiral trajectories in capturing the animal. The SEPIC converter is designed and derived from the state space model by state space averaging, and the reduced model is obtained through the moment matching method to reduce computational complexity. The Golden Eagle Optimize the parameters of KP and KI of the PI controller and weighing matrix Q of the linear quadratic controller. The fitness function of the proposed optimization is the sum of the Integral Absolute error (IAE) and Integral Square error (ISE). The proposed optimization is implemented using MATLAB/SIMULINK software, and the simulation outcomes demonstrate an improved settling time, fast recovery against input and output variations, Total Harmonic Distortion (THD) of 1.75 %, and enhanced stability.

Optimal quantized feedback control for linear quandratic Gaussian systems with input delay

AbstractThis paper is concerned with the optimal quantized feedback linear quadratic Gaussian (LQG) control problem for a discrete‐time stochastic system with input delay as well as the measurements to be quantized before transmitted to the controller. In this scenario, the system is presented with several choices of quantizers, along with the cost of using each quantizer. The objective is to jointly select the quantizers and synthesize the controller to maintain an optimal balance between control performance and quantization cost. It is shown that this problem can be decoupled into two optimization problems when the innovation signal is quantized instead of state: one for optimal controller synthesis and the other for optimal quantizer selection. More specifically, a necessary and sufficient condition is derived for the optimal control problem based on Pontryagin's maximum principle. On the other hand, the optimal quantizer selection policy is established by dealing with a certain Markov decision process (MDP).

Design and evaluation of self-tuning optimal control for vibration suppression of magnetorheological semi-active suspension

The objective of this paper is to enhance the vibration damping capabilities of magnetorheological (MR) semi-active suspension by utilizing a self-tuning LQG control method. Firstly, to determine the mechanical model of MR damper using the hyperbolic tangent model, mechanical experiments were performed with a damping force test machine under various input excitations. Experimental and simulation data were compared to confirm the accuracy of the mechanical model for MR damper. The MR damper is then incorporated into the vehicle’s semi-active suspension system to create a quarter-car suspension model. In order to tackle the problems associated with low control accuracy and poor dynamic adjustment in traditional LQG controllers where the weighting matrix coefficients are difficult to determine, a self-tuning LQG controller based on gravity search algorithm (GSA-LQG) was designed. Finally, the designed controller performance was evaluated by the simulation and experimental results obtained from the random and sinusoidal excitation roads. Experimental data reveal that when subjected to GSA-LQG control, the suspension control performance is considerably enhanced compared to the passive control, PID control and conventional LQG control suspension. Based on these outcome, it can be concluded that the proposed algorithm is effective and the experimental platform is feasible.

Analytic optimal control for multi-satellite assembly using linearized twistor-based model

This paper presents Guidance and Control (G&C) systems for multi-satellite assembly in proximity operations. The systems utilize the twistor model, which is linearized through Taylor’s series. Decentralized control laws, designed using Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC), are employed to track an energy-optimal trajectory generated using the Hamiltonian approach. Data exchange between satellites and their neighbors is represented using graph theory. The decentralized MPC framework is implemented using the CasADi package. To ensure collision avoidance between the satellites, a repulsive control law is designed, considering symmetric input saturation in the actuators. The proposed G&C systems are tested using a high-fidelity nonlinear satellite relative motion model that incorporates orbital perturbations. Numerical simulations are performed in a MATLAB® environment, and the results are visualized using STK®. Furthermore, a comparative study is conducted to evaluate tracking performance and fuel consumption between the two control methods. The results demonstrate that the use of an optimal trajectory reduces fuel consumption for both control algorithms.