LQR Technique Research Articles

DESIGN And IMPLEMENTATION Of HYDRIC CONTROLLER For TWOWHEELED ROBOT

The two-wheeled robotic machine (TWRM) with five degrees of freedom (DOF) is a type of mobile robot that consists of two wheels and a body that can rotate and move in different directions. The proposed architecture of the TWRM in this paper features five DOFs, which allows for greater flexibility and range of motion. However, this also makes controlling the system more challenging, as thecenter of mass (COM) changes while performing tasks in multiple directions. To address this issue, the study utilizes a state-space model created by linearizing the non-linear modeling equations at the equilibrium point using the Lagrangian modeling. To stabilize the TWRM, several controllers were evaluated, including PID, LQR, and LQR with PID methods. The PID controller is a popular feedbackcontrol strategy that adjusts the control output based on the error between the desired and actual values of the systemoutput. LQR is a state-space control technique that aims to minimize a cost function that expresses the system's performance criteria. The PID with LQR technique combines the strengths of both strategies, with PID used as a feed-forward to control the intermediate body (IB) and end-effector and LQR used as state feedback to regulate all states. The controllers were evaluated under variouscircumstances, including disturbance signals, trackingpathways, and moving actuators. Simulation results showedthat the LQR with LQR controller performed better thanthe other two control systems in terms of least overshoot,rising time, and applied input forces. This suggests that thePID with LQR technique is a robust and effective controlstrategy for stabilizing the TWRM and improving itsperformance for various tasks.

Observer-Based Control of Inductive Wireless Power Transfer System Using Genetic Algorithm

In this paper, we studied the feedback stabilization of an inductive power transfer system based on available output measurement. The proposed controller relies on a full-order state observer in order to estimate the unmeasured state. The control design problem is challenging due to the large dimension of the closed-loop system, which requires too many tuning parameters to be determined when conventional control methods are employed. To solve this issue, we propose an LQR methodology based on a genetic algorithm such that the weighing coefficients of the cost function matrices can be automatically computed in an optimized manner. The proposed approach combines the method of eigenstructure assignment and the LQR technique in order to design both the controller and the observer gain matrices. The design methodology provides a systematic way to compute the parameters of the LQR technique for a wireless power transfer system in an optimized manner, which can be a useful design tool for many other applications. The effectiveness of the approach was verified by numerical simulation on the dynamic model of the wireless power transfer system. The results show that the proposed design outperforms conventional design methods in terms of a better performance and reduced design iterations effort.

Secondary yaw control to improve curving vs. stability trade-off for a railway vehicle

Active primary/secondary suspensions have been proposed to solve the trade-off between curving and stability in railway vehicles. One concept is known as secondary yaw control (SYC), which consists of applying a controllable yaw torque between the carbody and the two bogies. This has been studied in the past mainly to enhance the vehicle's curving ability, but this paper extends the idea by examining the implications of designing a bogie with soft yaw stiffness between the bogie frame and the wheelsets and using SYC to provide active stabilisation. To this aim, a state feedback control law is designed according to the LQR technique. The paper presents the general concept of the active suspension control to be investigated and the specific control strategies applied. Then the effectiveness of the proposed actuation concept is investigated by means of numerical simulations performed on mathematical models of the passive and actively controlled vehicles implemented in a fully nonlinear multi-body simulator.

Development of Steering Control System for Motorcycles

This paper discusses a new steering control system for motorcycles. One of the features of the system is to use only one motor taking system failure into account, while two motors are used in most steer-by-wire systems to provide the driver (rider) with shaped reaction torque. The system under development can also provide reaction torque, which cannot be shaped arbitrarily unlike the existing systems. In this way, the reduction of control freedom makes it more difficult to improve the maneuverability and safety simultaneously. With this mechanism, therefore, a handlebar suspension composed of a spring and damper is investigated to improve the stability of this system. Furthermore, a controller for avoiding falls in an emergency is designed by applying the LQR technique and integral sliding mode control (ISMC) theory.

축소 차수 모델 기반 제어기와 결합한 PI 관측기 기반 제어 시스템의 안정성 해석

System model order reduction is a popular technique employed by control systems engineers due to its ability to reduce model complexity. However, control systems designed based on reduced-order model may cause closed-loop system instability when applied to the full-order model. In addition, conventional control system improvement methods such as increasing the controller gains or using robust control techniques in particular disturbance observers can further deteriorate system performance. In order to shade light on this phenomena, this paper presents an analytical study of the effects of high observer gain on the stability of observer compensated control systems whereby both the controller and the observer are designed using the reduced-order system model. The analysis is performed by carrying out stability analysis of the closed-loop system through root locus method and Routh-Hurwitz stability criterion. The paper also presents a comparative analysis between placing all the closed-loop poles of the controller at a single location or multiple locations using LQR technique for the aforementioned class of controller. The results obtained from the analysis have been validated through a DC motor position control system application.

Power System Dynamic Stability Improvement with UPFC using LQR Technique

Many damping controller devices based on other techniques have been proposed time to time. For the study of the damping performance, it has been proposed a power systems model with ‘UPFC’ and power oscillation damping controller in the present article. The proposed controller performance has been studied under different simulation condition results and that also includes various loading condition, i.e., normal with 100 percent, under loading 80 percent and overloading with 120 percent at different operational points. Finally, a better result has been observed by using the proposed damping controlling device than earlier available existing devices. However, the result obtained by using Eigen value analysis is supported by the facts obtained by the settling time analysis and the analysis of simulation results.

Earth–Moon L1 libration point orbit continuous stationkeeping control using time-varying LQR and backstepping

Different periodic-gain stationkeeping control strategies in Earth–Moon L1 libration point orbits are proposed based on continuous LQR control and Floquet theory. The strategies are based on time-periodic infinite horizon LQR and backstepping technique with time-invariant LQR. Furthermore, a dead-band periodic-gain controller is proposed to account for the limited lifespan of the thrusters. The proposed controllers are shown to be more fuel efficient than conventional feedback linearization for the same settling time envelope of the tracking error.

Performance Study of PID Controller and LQR Technique for Inverted Pendulum

The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. It is unstable without control. The process is non linear and unstable with one input signal and several output signals. It is hence obvious that feedback of the state of the pendulum is needed to stabilize the pendulum. The aim of the study is to stabilize the pendulum such that the position of the carriage on the track is controlled quickly and accurately. The problem involves an arm, able to move horizontally in angular motion, and a pendulum, hinged to the arm at the bottom of its length such that the pendulum can move in the same plane as the arm. The conventional PID controller can be used for virtually any process condition. This makes elimination the offset of the proportional mode possible and still provides fast response. In this paper, we have modelled the system and studied conventional controller and LQR controller. It is observed that the LQR method works better compared to conventional controller.

A Comparative Study of Semi-Active Quarter Car Suspension Control Strategies for Magnetorheological Damper

This paper addresses the problem of controlling quarter-vehicle semi-active suspension system. Presently, the suspension system involves a magnetorheological (MR) damper featuring hysteretic behavior captured through the Bouc-Wen model. The control objective is to regulate well the chassis vertical position despite the road irregularities. In addition to these irregularities, the difficulty of the control problem lies in the nonlinearity of the system model and the inaccessibility to measurements of the hysteresis internal state variable. The observer provide the online estimates of the hysteresis internal state. The later is performed using Lyapunov control design. Three controllers are developed, such as: the backstepping method, the Skyhook control and the LQR technique. Then each control policy is applied to the model equipped with a MR damper. The performances of each control algorithm are compared with the passive suspension in the time domains through the numerical simulation. The results show that the performance of a MR suspension system is highly dependent on the choice of algorithm employed, and the backstepping strategy exhibits an excellent performance.

Control of a 2-DOF ultrasonic piezomotor stage for grommet insertion

The treatment of a common disease called “Otitis Media with Effusion (OME)” involves the surgeon inserting a grommet in the eardrum to bypass the Eustachian tube for draining fluid when medication fails. In this paper, a novel device for myringotomy and grommet insertion is first designed and introduced. Due to the advantages of high precision and fast response, a 2-DOF ultrasonic piezomotor (USM) stage is chosen to provide the motion sequences of the device, especially a precise path tracking during the grommet insertion. This paper briefly presents the mechanical design of the device and the configuration and control of the 2-DOF USM stage. The model of the USM consisting of a linear and nonlinear term is built. A PID controller is used as the main controller and tuned with the help of LQR technique. Since there are nonlinear dynamics caused by friction and hysteresis existing in the system, a nonlinear compensation including a sign function and sliding mode control is designed to reject the nonlinearity. Moreover, a decoupling controller is designed to eliminate the coupling effects between the two USM stages. The experimental results show that the LQR-assisted PID controller with compensation can achieve very good system performance and the decoupling controller can further improve the performance.

Launch Vehicle Attitude Control System using PD plus Phase Lag

In this paper is discussed the rigid body dynamics and three different controllers to stabilize a highly unstable rocket. Along the paper, it is shown a tutorial to design the PD and PID controllers based on LQR technique. However, these controllers cannot offer a good time domain response due to the high aerodynamic coupling. Then, a PD plus phase lag controller is proposed to overcome this problem. This controller which is designed based on the vehicle dynamics, offers a better time response and keep the stability margins on acceptable levels.

Hybrid approach for pole assignment using LQR technique and Ant System metaheuristic

We present in this paper a new metaheuristic using Ant System metaheuristic to search an optimal command law in LQR sense that gives for a feedback system a given values by pole assignment. In fact, these hybrid techniques of conventional and non conventional methods present a good compromise between the simplicity of use and the quality of proposed solutions in a reasonable computing time. The results obtained by using this technique show its efficiency in the proposed problem and can be considered as a competitive method for those issued from a complicate mathematic formulation.

A Suboptimal Controller Design Methodology for Input-Output Feedback-Linearizable Systems

This paper addresses suboptimal control of nonlinear systems which can be feedback-linearized from input to output. The case of input-to-state linearizable systems is also covered as a special case. The method is thus applicable to all nonlinear systems which can be partially linearized using the method of output-feedback linearization while having a stable internal (or zero) dynamics. The well-known LQR technique applied to the linearized system does not guarantee the suboptimality of the nonlinear system. This paper uses output feedback linearization technique to partially linearize the system and then designs an output-feedback for the feedback-linearized system in such a way that it ensures suboptimal performance of the original nonlinear system. The proposed method can optimize any arbitrary smooth function of states and input. The proposed controller is, however, suboptimal due to the facts that (1) the form of the controller is a linear static feedback of the linearized state, (2) the search algorithm may fall into a local extremum rather than a global, and (3) the calculated controller depends on the initial conditions. The method is successfully applied to control design of the longitudinal subsystem of a laboratory double-rotor helicopter and the results are discussed and compared with those of the LQR method.

Power system stabiliser for multimachine power system using robust decentralised periodic output feedback

Power system stabilisers (PSSs) are added to excitation systems to enhance the damping during low-frequency oscillations. The design of decentralised robust PSS for four machines with ten buses using periodic output feedback is proposed. The nonlinear model of a multimachine power system is linearised at different operating points and 16 linear state-space models are obtained. For each of these models an output injection gain is obtained using LQR technique. A decentralised robust periodic output feedback gain which realises these output injection gains is obtained using the linear matrix inequality approach. This method does not require states of the system for feedback and is easily implemented. The robust decentralised periodic output control is applied to the nonlinear model of a multimachine system at different operating (equilibrium) points and gives encouraging results for the design of power system stabilisers.

Design of power system stabiliser for single-machine system using robust periodic output feedback controller

Power system stabilisers (PSS) are added to excitation systems to enhance the damping of low-frequency oscillations. The design of PSS for a single machine connected to an infinite bus using periodic output feedback is proposed. The non-linear model of a machine is linearised at different operating points and 16 linear plant models are obtained. For each of these plants an output injection gain is obtained using the LQR technique. A robust periodic output feedback gain which realises these output gains is obtained using an LMI approach. This robust periodic output control is applied to a non-linear plant model of the machine at different operating (equilibrium) points. This method does not require the complete set of states of the system for feedback and is easily implementable.

Short and long period optimization of drug doses in the treatment of AIDS

Numerical optimization techniques are useful in solving problems of computing the best inputs for systems described by mathematical models and when the objectives can be stated in a quantitative form. This work concerns the problem of optimizing the drug doses in the treatment of AIDS in terms of achieving a balance between the therapeutic response and the side effects. A mathematical model describing the dynamics of HIV viruses and CD4 cells is used to compute the short term optimal drug doses in the treatments of patients with AIDS by a direct method of optimization using a cost function of Bolza type. The model parameters were fitted to actual published clinical data. In order to simplify the numerical procedures, the control law is expressed as a series and the sub-optimal control is obtained by truncating the higher terms. When the patient reaches a clinically satisfactory state, the LQR - Linear Quadratic Regulator technique is used to determine the long period maintenance doses for the drugs. The doses computed using the LQR technique tend to be smaller than equivalent constant-dose therapy in terms of increase in the counts of CD4+T cells and reduction of the density of free viruses.

Sliding surface design for discrete VSS using LQR technique with a preset real eigenvalue

This paper presents an LQR-based sliding surface design procedure that allows one to specify a desired weighting matrix and a desired real eigenvalue which is important in discrete VSS. The procedure computes a weighting matrix that simultaneously stays “closest” to the desired one and yields the desired eigenvalue. Sliding surface is then determined from the LQR gain matrix and the desired eigenvalue. It is shown that feasible weighting matrices almost always exist and are not unique. Moreover, the underlying constrained optimization problem is convex and least-squares method may be used to simplify or solve the problem. The paper ends with two numerical examples that illustrate the design procedure.

Modal control of beam flexural vibration

An active control system was developed to control the flexural vibrations of a beam with a modal filtering with only one secondary actuator. Segmented piezoelectric actuators and sensors were used for driving and sensing the bending beam vibrations. The primary actuator was fed by a broadband random disturbance signal in order to excite the first five modes of the structure. However, only the second to fifth modes were controlled. The control algorithm was implemented on a DSP board and the input and output signals were filtered using high order low pass filters. These filters, implemented on the DSP board avoid the degrading effect on the control performances of the higher order modes and which are not controlled. The modal filtering was achieved by computing. To this end, it is based on a previous identification procedure. This latter models, in one step, the dynamics of the structure and also the transfer function of the electronic circuits of the controller. The identified filtered modes were then used to compute the gain matrix using a LQR technique (linear quadratic regulator). Simulations of the active control were carried out and practical implementation of the control algorithms was performed. Experimental and simulation results were then compared and discussed.

Design of decentralized constant-volume controllers for open-channels by solving a least squares problem

In this paper we consider a mathematical model for open-channels that expresses the dynamic relationships, in terms of transcendental functions, between the gate opening sections and the corresponding stored water volume variations in the different canal reaches with respect to an initial reference configuration of uniform flow. Series expansion around s = 0 gives a state variable linear and time invariant model as well as the corresponding rational transfer matrix. Both a proportional and a proportional integral decentralized constant-volume control law are designed by solving a linear least squares problem. Such a procedure enables us to impose the desired structure on the feedback gain matrix by means of the optimization of the controller parameters. It makes the closed loop transfer function approach a target function as closely as possible over a specified frequency range. In this paper, the target closed loop functions are designed by means of an LQR technique applied to the linear time-invariant model obtained by means of the Taylor series expansion.

Application of state feedback in an autopilot design

The paper presents the use of modern state-space control theory in the design of an autopilot. The design utilises an observer to determine the angle of attack of a tail-controlled vehicle and the application of the LQR technique to determine the state feedback gains. Computer modelling and simulation are used to evaluate the autopilot performances under different glide and boost conditions. The performances are compared with that from a conventional three-loop autopilot [1] operating under similar flight conditions. Results indicated that the use of state feedback in the autopilot could enhance the vehicle performances under extreme glide and boost conditions.