Linear Quadratic Regulator Control Scheme Research Articles

Optimal Coordinated Control for Speed Tracking and Torque Synchronization of Rigidly Connected Dual-Motor Systems

Dual-motor systems have been broadly used to drive large inertia loads. In this article, the optimal coordinated control problem of rigidly connected permanent magnet synchronous motor (PMSM) systems is investigated to enhance the speed tracking and torque synchronization performance. First, the mathematical model of rigidly connected dual-PMSM systems is established in terms of the model of the PMSM and the characteristics of gear transmission drive. Second, to minimize the speed tracking and torque synchronization errors, a novel optimal coordinated control scheme is proposed for rigidly connected dual-PMSM systems by combining the conventional master–slave control structure and the linear–quadratic regulator control strategy. Then, taking into account the inherent two-time-scale characteristics, a composite suboptimal coordinated controller is devised through optimal problems of slow and fast subsystems. Furthermore, the closed-loop stability is proved by singular perturbation theory. Finally, simulation and experimental studies are provided to corroborate our theoretical results. It is shown that the proposed method can effectively improve the speed tracking and torque synchronization performance of the rigidly connected dual-PMSM system simultaneously.

Integrated optimal control of distributed in-wheel motor drive electric vehicle in consideration of the stability and economy

From the perspective of handling stability and economy, this paper brings forward an integrated optimal control scheme of distributed in-wheel motor drive electric vehicles (IWMDEV). A linear quadratic regulator (LQR) controller is presented according to nominal model and ideal motions firstly. To tackle the uncertain parameters and random disturbance, a novel robust optimal (RO) control strategy is further proposed to design the top level controller by employing the combination of optimal control and high order sliding mode control. By virtue of the integral and terminal sliding mode surface, the resulting robust optimal control method can not only achieve better performance, but also converge in finite time without chattering phenomenon. As for the bottom level controller, an optimal algorithm is developed to determine the weights for each term in objective function of torque allocation dynamically and coordinate the relationship between driving safety and energy-saving performance timely. Finally, joint simulations are carried out. In comparison with LQR control strategy, the results demonstrate that the proposed control scheme could ensure the robustness and effectiveness in the presence of parametric perturbation and external disturbance. Moreover, the torque allocation algorithm, which considers both handling stability and energy consumption, proves to be an effectual approach.

CONTROL OF DYNAMIC TRIM FOR PLANING VESSELS WITH INTERCEPTORS IN TERMS OF COMFORT AND MINIMUM DRAG

Nowadays, interceptors are often used to decrease total resistance and enhance comfort by reducing dynamic trim for high-speed planing vessels. They can be controlled manually as well as automatically by using a suitable closed-loop control system. Thus, in the present study, an automatically controllable system is presented to minimize the total resistance by reducing the dynamic trim in calm water. To reach this aim, a mathematical model which can represent the 2 degree of freedom vertical motion of a prismatic planing vessel is presented. The coefficients used in the model are calculated by using the Savitsky method. The standard dynamic trim angle and the optimum ones in terms of resistance are calculated by using the same method. For control action, a linear full state feedback control strategy (linear quadratic regulator) is applied, and instantaneous blade heights are found considering the change in forward speed. Therefore, the control-oriented model is able to change the blade height to reach the optimum trim angle in terms of the total resistance of the vessel for different forward speeds and speed profiles. The results show that the designed linear quadratic regulator control strategy is successful for reference trim tracking problems.

Stepping quantum genetic algorithm-based LQR control strategy for lateral vibration of high-speed elevator

Abstract To effectively restrain the lateral vibration caused by the guide rail excitation and improve the ride comfort of the car system, a state-weighted linear quadratic regulator (LQR) control strategy is proposed. Firstly, based on the active control model of the 4-DOF car system with actuators distributed diagonally along the center of the car frame, an LQR controller for lateral vibration of high-speed elevator car systems is designed. Furthermore, in view of the tedious and time-consuming of the empirical method to choose state-weighted matrix Q, stepping quantum genetic algorithm (SQGA) is proposed to improve the performance of the controller. Finally, the time-frequency characteristic curves of the lateral vibration acceleration and the vibration displacement of the car system are compared and analyzed by MATLAB to verify the effectiveness of the proposed controller.

Vibration Suppression of Hub Motor-Air Suspension Vehicle

Aiming at the negative vibration effect caused by the increased unsprung mass of the hub motor-air suspension (HM-AS) vehicle and the unbalanced magnetic force (UMF) of the hub motor, a linear quadratic regulator (LQR) air suspension control strategy based on a genetic algorithm is proposed. Considering the coupling effect of road surface excitation and UMF, the model of the HM-AS vehicle is established. Then, according to optimal control theory and the genetic algorithm, the LQR controller is designed to suppress the vibration of the HM-AS vehicle, and the weight matrix of the LQR controller is optimized through the genetic algorithm. The simulation results show that the proposed LQR control strategy effectively improves the ride comfort and motor safety of the HM-AS vehicle.

Control of Linear Servo Carts with Integral-Based Disturbance Rejection

This paper describes a system designed for linear servo cart systems that employs an integral-based Linear Active Disturbance Rejection Control (ILADRC) scheme to detect and respond to disturbances. The upgrade in this control technique provides extensive immunity to uncertainties, attenuation, internal disturbances, and external sources of noise. The fundamental technology base of LADRC is Extended State Observer (ESO). LADRC, when combined with Integral action, becomes a hybrid control technique, namely ILADRC. Setpoint tracking is based on Bode’s Ideal Transfer Function (BITF) in this proposed ILADRC technique. This proves to be a very robust and appropriate pole placement scheme. The proposed LSC system has experimented with the hybrid ILADRC technique plotted the results. From the results, it is evident that the proposed ILADRC scheme enhances the robustness of the LSC system with remarkable disturbance rejection. Furthermore, the results of a linear quadratic regulator (LQR) and ILADRC schemes are comparatively analyzed. This analysis deduced the improved performance of ILADRC over the LQR control scheme.

Stabilization of a class of switched dynamic systems: the Riccati-equation-based Approach

Abstract Our paper deals with the stabilization of a class of time-dependent linear autonomous complex systems with a switched structure. The initially given switched dynamic system is assumed to be controlled by a specific state feedback strategy associated with the linear quadratic regulator (LQR) type control. The proposed control design guarantees stabilization of the closed-loop system for all of the possible location transitions. In the solution procedure of the Algebraic Riccati Equation related to the LQR control strategy, only the knowledge of the algebraic structure related to the switched system are needed. We prove that the proposed optimal LQR type state feedback control design stabilizes the closed-loop switched system for every possible active location. The theoretical approach proposed in this paper is finally applied to a model of the Single Wing Quadrotor Aircraft, when changing from its Quadrotor Flight Envelope to its Airplane Flight Envelope.

Vibration Control of Cable Net Façade by Smart Supports

A lack of curvature reduces the out-of-plane stiffness of cable net façades. Therefore, they may experience large deformations and severe damage under heavy vertical loads such as earthquakes and wind. Axially movable smart supports are proposed for controlling structural vibrations by controlling tension of the cables. The equation of motion of the cable net, controlled by the smart support, is developed following a finite element method based program to solve the equation. The linear quadratic regulator control strategy is utilized to find the optimal control gain. The results show that smart supports, especially when connected to the central cables, can significantly control the vibrational amplitude of the structure.

Robust Optimal Control for the Vehicle Suspension System With Uncertainties.

The suspension system is an important unit that affects vehicle performance, including handling stability and riding comfort. In order to improve vehicle performances, a novel robust optimal control strategy for the active suspension system in vehicles is proposed. To handle the parameter uncertainties and external random disturbances, the proposed optimal control strategy is designed by using the combination of the linear quadratic regulator (LQR) optimal control and sliding-mode control. First, by using the nominal model of the active suspension system without the uncertain parameters and the external random disturbances, an optimal control performance index is given, and the initial optimal controller is designed by using the LQR control strategy. Then, to handle the parameter uncertainties and the external disturbances, a robust optimal integral sliding-mode control strategy based on the initial optimal controller is designed, which not only can achieve the optimal control objective but also has good robustness to the uncertain parameters and external disturbances. By using the Lyapunov stability theory, stability analysis of the proposed robust optimal integral sliding-mode control strategy is performed. Finally, the collaborative simulation platform based on the Carsim and MATLAB/Simulink is developed. The simulation results illustrate the advantage of the proposed robust optimal control strategy for the suspension system.

Modeling and Optimal Control of Piezoactuated Rotating Box Beams with Sophisticated Couplings

The mathematical modeling and active control of piezoactuated pretwisted thin-walled rotating beams with a circumferentially asymmetric stiffness layup configuration are addressed. The effects induced by rotation (for example, dynamic stiffening, tennis-racket effects, etc.) are highlighted. The geometrical pretwist effect-induced additional inertial and elastic couplings are specifically discussed. A better idea of the relationship between control effectiveness and the synergistic effect devoted by elastic, inertial, and actuation couplings is obtained based on the linear quadratic regulator control strategy. It can be found that elastic couplings have a significant effect on control effectiveness of the system (especially on that controlled by the piezoelectrically induced transverse shear), whereas the influence of the rotation-induced centrifugal effects on control effectiveness is weaker. On the other hand, elastic couplings will reduce the sensitivity of the control authority to the piezoelectrically induced actuation couplings. And, the geometrical pretwist effect will further reduce this sensitivity since it will introduce more elastic couplings to the system.

A new criterion for comfort assessment of in-wheel motor electric vehicles

A novel optimization technique was implemented to investigate the effects of vibrations on comfort of occupants to maintain oscillations in an acceptable zone in accordance with the International Organization for Standardization 2631 standard. In this regard, a newly introduced comfort indicator was defined as discomfort criterion (DiC). The effectiveness of the proposed measure was investigated throughout the suspension optimization of an in-wheel motor electric vehicle which almost doubled the unsprung mass by adding an electric motor to the wheel assembly. First, a spatial oscillatory model of the electric vehicle with eight degrees of freedom was developed, and the linear quadratic regulator control scheme is selected to control an actuator in an active suspension. Road excitations were then generated by applying the power spectral density of road class B–C provided by the International Organization for Standardization 8608 standard. The exceedance from the reduced comfort limit (in accordance with the International Organization for Standardization 2631 standard) and wheel travel (WT) of the vehicle were considered as design objectives. Finally, using a novel optimization procedure, the optimum condition and impact factor of the design variables, as well as counterplots of the design objectives with respect to the effective design parameters, were extracted and analyzed. Results proved the proposed indicator, that is, discomfort criterion (DiC) as a reliable measure to assess suspension systems’ performance effectively.

Optimizing Signal Timing Control for Large Urban Traffic Networks Using an Adaptive Linear Quadratic Regulator Control Strategy

Traffic signal control is important for intersection safety and efficiency. However, most traffic signal control methods are designed for individual intersections or corridors. Although some adaptive control systems have been developed, the methods used are often proprietary and not published, making it difficult to evaluate their effectiveness. This study proposes an adaptive multi-input and multi-output traffic signal control method that not only can improve network-wide traffic operations in terms of reduced traffic delay and energy consumption, but also is more computationally feasible than existing centralized signal control methods. Considering intersection interactions, a linear dynamic traffic system model was built and adaptively updated to reflect how the signal control input of each intersection affects network-wide vehicle travel delay. Based on the system model, an adaptive linear-quadratic regulator (LQR) was designed to minimize both traffic delay and incremental changes in the control input. The proposed control method was evaluated in a microscopic traffic simulation environment with a 35-intersection network of Bellevue City, Washington. Simulation results show that the proposed method had shorter average traffic delays in the network when compared with the traffic delays controlled by the state-of-the-art max-pressure, self-organizing traffic lights, and independent deep Q network methods.

Genetic algorithm-based multi-objective design of optimal discrete sliding mode approach for trajectory tracking of nonlinear systems

In this paper, a novel multi-objective design of optimal control for robotic manipulators is considered. Generally, robots are known by their highly nonlinearities, unmodeled dynamics, and uncertainties. In order to design an optimal control law, based on the linear quadratic regulator, the robotic system is described as a linear time varying model. The compensation of both disturbances and uncertainties is ensured by the integral sliding mode control. The problem of deciding the optimal configuration of the linear quadratic regulator controller is considered as an optimization problem, which can be solved by the application of genetic algorithm. The main contribution of this paper is to consider a multi-objective optimization problem, which aims to minimize not only the chattering phenomenon but also other control performances including the rise time, the settling-time, the steady-state error and the overshoot. For that, a novel dynamically aggregated objective function is proposed. As a result, a set of nondominated optimal solutions are provided to the designer and then he selects the most preferable alternative. To demonstrate the efficacy and to show complete performance of the new controller, two nonlinear systems are treated in this paper: firstly, a selective compliance assembly robot arm robot is considered. The results show that the manipulator tracing performance is considerably improved with the proposed control scheme. Secondly, the proposed genetic algorithm-based linear quadratic regulator control strategy is applied for pitch and yaw axes control of two-degrees-of-freedom laboratory helicopter workstation, which is a highly nonlinear and unstable system. Experimental results substantiate that the weights optimized using genetic algorithm, result in not only reduced tracking error but also improved tracking response with reduced oscillations.

Effects of magnetization conditions on dynamic characteristics of spacecrafts with superconducting flux pinning docking interfaces

Depending on the self-stable levitation characteristics of superconductors with trapped magnetic flux, superconducting flux pinning docking interfaces (FPDIs) provide a promising approach for space applications. In this paper, we investigate the influence of magnetization conditions on the dynamic response between two satellites equipped with FPDIs. The flux pinning interactions between a high-temperature superconductor and a source magnet are approximated using a frozen image model. An analytic model of the docking process is derived based on the Kane method to simulate the dynamic response. A linearized dynamic model is derived, and linear quadratic regulator (LQR) control is applied to the FPDI to minimize the relative attitude deviations. The results show that improving the frozen magnetic flux density of superconductors is beneficial to the capture ability of the FPDI. Increasing the damping coefficient is also an efficient approach to improving the docking performance, but this approach is limited by the field cooling height. Damping materials with a lower density and a higher damping coefficient are proposed to be employed in the FPDI. The LQR control contributes to suppressing the amplitude of the oscillation and reducing the settling time in the docking process. Although the amplitude of oscillation in a noncontrol scheme converges more slowly than the LQR control scheme, it does not require the high dynamic response speed of a control system like the LQR control scheme, which contributes toward simplifying the structure of the FPDI. The principles presented above provide a guide for the design and implementation of FPDI in space docking missions.

Linear-Quadratic Regulator Algorithm-Based Cascaded Control Scheme for Performance Enhancement of a Variable-Speed Wind Energy Conversion System

Wind power generation is an important trend of global electricity generation. Enormous efforts should be spent to keep the operation of the wind power systems at optimal conditions. This paper presents a linear-quadratic regulator (LQR) algorithm based on an optimal control scheme for enhancing the characteristics of the wind turbine generator systems (WTGSs). The variable-speed wind turbine driving a permanent-magnet synchronous is connected to the electric network through fully controlled power converters. The machine-side converter and the grid-side inverter are controlled using a cascaded LQR control scheme. LQR is an optimal controller, which achieves a rapid convergence and less computational complexity. The modelling and the control strategies of the system under study are elucidated in details. Real wind speed data captured from Zaafarana wind farm, Egypt, are taken into account for obtaining realistic responses. The effectiveness of the proposed controller is compared with that achieved using the genetic algorithm-based optimized proportional-plus-integral controller, considering the network disturbances. The simulation results are carried out using MATLAB/Simulink software that validate the efficiency of the proposed control scheme for enhancing the characteristics of the WTGSs connected to electric networks.

Fault-Tolerant Station-Keeping on Libration Point Orbits

This paper extends a linear quadratic regulator-based control scheme for station-keeping on libration point orbits to enable continued tracking in the event of thruster failure. In the first instance it is shown that by using an extended state observer the fault (as well as disturbances) can be measured and compensated for at each sampling period using continuous thrust. It is proved that this control yields asymptotic tracking to a small bounded region around the desired reference orbit in the presence of these uncertainties. In addition, it is demonstrated that by combining this method with a sliding mode or an adaptive control, asymptotic tracking can be achieved. An advantage of this method is that the required gain for asymptotic tracking of the sliding mode component is much smaller than traditional methods; the gain magnitude is required to be larger than the magnitude of the disturbance estimation error rather than the magnitude of the disturbance. A comparison of the controllers performance against an linear quadratic regulator control scheme is undertaken in an application to low-thrust station-keeping on a halo orbit in the Earth–Moon–spacecraft system in the presence of disturbances and various thruster faults.

Feedback control strategies for active control of noise inside a 3-D vibro-acoustic cavity

This paper presents and compares three feedback control strategies for active control of noise inside a 3-D vibro-acoustic cavity. These are a) control strategy based on direct output feedback (DOFB) b) control strategy based on linear quadratic regulator (LQR) to reduce structural vibrations and c) LQR control strategy with a weighting scheme based on structural-acoustic coupling coefficients. The first two strategies are indirect control strategies in which noise reduction is achieved through active vibration control (AVC), termed as AVC-DOFB and AVC-LQR respectively. The third direct strategy is based on active structural-acoustic control (ASAC). This strategy is an LQR based optimal control strategy in which the coupling between the various structural and the acoustic modes is used to design the controller. The strategy is termed as ASAC-LQR. A numerical model of a 3-D rectangular box cavity with a flexible plate (glued with piezoelectric patches) and with other five surfaces treated rigid is developed using finite element (FE) method. A single pair of collocated piezoelectric patches is used for sensing the vibrations and applying control forces on the structure. A comparison of frequency response function (FRF) of structural nodal acceleration, acoustic nodal pressure, and piezoelectric actuation voltage is carried out. It is found that the AVC-DOFB control strategy gives equal importance to all the modes. The AVC-LQR control strategy tries to consume the control effort to damp all the structural modes. It is seen that the ASAC-LQR control strategy utilizes the control effort more intelligently by adding higher damping to those structural modes that matter more for reducing the interior noise.

A new algebraic LQR weight selection algorithm for tracking control of 2 DoF torsion system

Abstract 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.

Design and comparison of LQR and a novel robust backstepping controller for supercavitating vehicles

Traditional underwater vehicles are limited in speed due to dramatic friction drag on the hull. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase their underwater speed. Compared with fully wetted vehicles, the non-linearity in the modelling of cavitator, fin and in particular the planing force make the control design of supercavitating vehicles more challenging. Dominant non-linearities associated with planing force are taken into account in the model of supercavitating vehicles in this paper. Two controllers are proposed to realize stable system dynamics and tracking responses, a linear quadratic regulator (LQR) control scheme and a robust backstepping control (RBC) scheme. The proposed backstepping procedure, in association with integral filters technique, exploits the possibility of avoiding the overparameterization problem existing in the classical backstepping process. In particular, the achieved stability is robust to modelling errors in supercavitating vehicles. Compared with the LQR control scheme, the RBC scheme is seen to increase the robustness with saturation compensation algorithm, which can be useful for avoiding actuator saturation in magnitude.

Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter

This paper deals with the attitude tracking control problem for a 2 DoF laboratory helicopter using optimal linear quadratic regulator (LQR). As the performance of the LQR controller greatly depends on the weighting matrices (Q and R), it is important to select them optimally. However, normally the weighting matrices are selected based on trial and error approach, which not only makes the controller design tedious but also time consuming. Hence, to address the weighting matrices selection problem of LQR, in this paper we propose an adaptive particle swarm optimization (APSO) method to obtain the elements of Q and R matrices. Moreover, to enhance the convergence speed and precision of the conventional PSO, an adaptive inertia weight factor (AIWF) is introduced in the velocity update equation of PSO. One of the key features of the AIWF is that unlike the standard PSO in which the inertia weight is kept constant throughout the optimization process, the weights are varied adaptively according to the success rate of the particles towards the optimum value. The proposed APSO based LQR control strategy is applied for pitch and yaw axes control of 2 Degrees of Freedom (DoF) laboratory helicopter workstation, which is a highly nonlinear and unstable system. Experimental results substantiate that the weights optimized using APSO, compared to PSO, result in not only reduced tracking error but also improved tracking response with reduced oscillations.