Parallel eigenstructure assignment via LQR design and genetic algorithms

This paper proposes a novel linear quadratic regulator (LQR) weight selection algorithm by synthesizing the algebraic Riccati equation (ARE) with the Lagrange multiplier method for command following applications of a 2 degree of freedom (DoF) torsion system. The optimal performance of LQR greatly depends on the elements of weighting matrices Q and R. However, normally these weighting matrices are chosen by a trial and error approach which is not only time consuming but cumbersome. Hence, to address this issue, blending the design criteria in time domain with the ARE, we put forward an algebraic weight selection algorithm, which makes the LQR design both simple and modular. Moreover, to estimate the velocity of a servo angle, a high gain observer (HGO) is designed and integrated with the LQR control scheme. The efficacy of the proposed control scheme is tested on a benchmark 2 DoF torsion system for a trajectory tracking application. Both the steady state and dynamic characteristics of the proposed controller are assessed. The experimental results accentuate that the proposed HGO based LQR scheme can guarantee the system to attain the design requirements with minimal vibrations and tracking errors.

In this paper, a new algorithm for active control design of structures is proposed and investigated. The algorithm preserves the decoupling property of the modal vibration equation and eliminates the spillover problem, which is the main shortcoming in the independent modal space control (IMSC) algorithm. With linear quadratic regulator(LQR) control law, the analytical solution of algebraic Riccati equation and the optimal actuator control force are obtained, and the control design procedure is significantly simplified . A numerical example for the control design of a tall building subjected to wind loads demonstrates the effectiveness of the proposed algorithm in reducing the acceleration and displacement responses of tall buildings under wind actions.

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.

The sensitivity to initial conditions and the unpredictable nature of chaos makes chaos synchronization an important topic of both theory and practice. However they can be synchronized with appropriate control schemes. The paper suggests a novel approach of synchronizing chaotic systems using a Linear Quadratic Regulator (LQR) whose parameters are optimized using Particle Swarm Optimization (PSO). In the traditional LQR design, the weighting matrices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R$</tex> are tuned manually and this process can be difficult and suboptimal, particularly in highly nonlinear and sensitive systems like chaotic models. To address this, PSO is employed to automate the selection of these matrices by minimizing a cost function that depends on synchronization error. A master-slave synchronization scheme is designed and the LQR controller is designed to ensure that the slave system follows the master system trajectory. The results of the simulation show the effectiveness of the proposed method, as the error converges rapidly and the method performs better than the classical LQR designs.

The Active Magnetic Bearing system (AMB) is a mechatronic device which is used to suspend rotating parts of a machine so that they rotate without contact to the stationary part of the machine. AMBs are highly nonlinear, non-minimum phase and inherently unstable. This paper has aimed to obtain a robust optimal state-feedback control system for the stabilization of the AMB System, with the help of Genetic algorithm (GA) as an optimization tool which will solve the tedious manual tuning of the weighting matrices in the design of linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG).The system’s mathematical model has been developed and also the properties of the uncontrolled system have been analyzed. Since AMB is a MIMO system, the interaction of the inputs with the outputs has been analyzed using relative gain array analysis and frequency domain analysis of the system transfer functions. Then, the optimal state feedback controllers have been developed. Here, LQR and LQG controllers are developed.Finally, Comparative analysis between the controllers and between the design methods was carried out. The proposed GA based design methodology has resulted good Performance. In addition, the GA based design has also resulted improvements in robustness of the control systems. As far as gain margin (GM) and phase margin (PM) are concerned GA has resulted increase of 8.0*10–4 db and 6.02*10–3° in GM and PM respectively for LQR. Whereas, in LQG GA has resulted an increase of 3.8*10–5 db and 2.54*10–4°. KeywordsActive magnetic bearingGenetic algorithmLinear quadratic GaussianKalman filter

Parrot Mambo mini-drone is a readily available commercial quadrotor platform to understand and analyze the behavior of a quadrotor both in indoor and outdoor applications. This study evaluates the performance of three alternative controllers on a Parrot Mambo mini-drone in an interior environment, including Proportional–Integral–Derivative (PID), Linear Quadratic Regulator (LQR), and Model Predictive Control (MPC). To investigate the controllers’ performance, initially, the MATLAB®/Simulink™ environment was considered as the simulation platform. The successful simulation results finally led to the implementation of the controllers in real-time in the Parrot Mambo mini-drone. Here, MPC surpasses PID and LQR in ensuring the system’s stability and robustness in simulation and real-time experiment results. Thus, this work makes a contribution by introducing the impact of MPC on this quadrotor platform, such as system stability and robustness, and showing its efficacy over PID and LQR. All three controllers demonstrate similar tracking performance in simulations and experiments. In steady state, the maximal pitch deviation for the PID controller is 0.075 rad, for the LQR, it is 0.025 rad, and for the MPC, it is 0.04 rad. The maximum pitch deviation for the PID-based controller is 0.3 rad after the take-off impulse, 0.06 rad for the LQR, and 0.17 rad for the MPC.

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.

Model predictive control (MPC) is a multi-objective control technique that can handle system constraints. However, the performance of an MPC controller highly relies on a proper prioritization weight for each objective, which highlights the need for a precise weight tuning technique. In this paper, we propose an analytical tuning technique by matching the MPC controller performance with the performance of a linear quadratic regulator (LQR) controller. The proposed methodology derives the transformation of a LQR weighting matrix with a fixed weighting factor using a discrete algebraic Riccati equation (DARE) and designs an MPC controller using the idea of a discrete time linear quadratic tracking problem (LQT) in the presence of constraints. The proposed methodology ensures optimal performance between unconstrained MPC and LQR controllers and provides a sub-optimal solution while the constraints are active during transient operations. The resulting MPC behaves as the discrete time LQR by selecting an appropriate weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. In this paper, the effectiveness of the proposed technique is investigated in the application of a novel vehicle collision avoidance system that is designed in the form of linear inequality constraints within MPC. The simulation results confirm the potency of the proposed MPC control technique in performing a safe, feasible and collision-free path while respecting the inputs, states and collision avoidance constraints.

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.

A computationally efficient approach for robust gain-scheduled output-feedback LQR design for large-scale systems

Rotational Motion Control by Feedback with Minimum L1-Norm

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.

Generation of control torque for highly agile satellite missions is generally achieved with momentum exchange devices, such as reaction wheels and control moment gyros (CMGs) with high slew maneuverability. However, the generation of a high control torque from the respective actuators requires high power and thus a large mass. The work presented here proposes a novel type of control actuator that generates torques in all three principal axes of a rigid satellite using only a spinning wheel and a simple tilt mechanism. This newly proposed actuator has several distinct advantages including less mass and more simplicity than a conventional CMG and no singularities being experienced during nominal wheel operation. A new high performance bounded (HPB) linear quadratic regulator (LQR) control law has been presented that extends classical LQR by providing faster settling times, gain-scheduling the control input weightings to optimize its performance, and has much quicker computation times than classical LQR. This work derives a fundamental mathematical model of the actuator and demonstrates feasibility by providing three degree of freedom high fidelity simulations for the actuator using both classical LQR and HPB LQR.

The authors present a genetic approach to the optimal linear quadratic regulator (LQR) problem. Design of the optimal LQR depends on choosing weighting matrices. One must carry out a trial-and-error process to choose the proper weighting matrices in general. It is not a trivial problem. They show a new possibility using a genetic algorithm (GA) to find the proper weighting matrices and hence to obtain the optimal control gain. They apply the approach to the attitude control of an inverted pendulum system, which is known as the LQR problem. They perform computer simulations on the system with a 50 cm long inverted pendulum and obtain good results.