Discrete Linear Quadratic Regulator Research Articles

LQR Control and Optimization for Trajectory Tracking of Biomimetic Robotic Fish Based on Unreal Engine.

A realistic and visible dynamic simulation platform can significantly facilitate research on underwater robots. This paper uses the Unreal Engine to generate a scene that resembles real ocean environments, before building a visual dynamic simulation platform in conjunction with the Air-Sim system. On this basis, the trajectory tracking of a biomimetic robotic fish is simulated and assessed. More specifically, we propose a particle swarm optimization algorithm-based control strategy to optimize the discrete linear quadratic regulator controller for the trajectory tracking problem, as well as tracking and controlling discrete trajectories with misaligned time series through introducing a dynamic time warping algorithm. Simulation analyses of the biomimetic robotic fish following a straight line, a circular curve without mutation, and a four-leaf clover curve with mutation are carried out. The obtained results verify the feasibility and effectiveness of the proposed control strategy.

Discrete LQR and ILQR methods based on high order Runge-Kutta discretizations

In this paper, discrete linear quadratic regulator (DLQR) and iterative linear quadratic regulator (ILQR) methods based on high-order Runge-Kutta (RK) discretizations are proposed for solving linear and nonlinear quadratic optimal control problems respectively. As discovered in Hager (2000) [11], direct approaches with RK discretization are equivalent with indirect approaches based on symplectic partitioned Runge-Kutta (SPRK) integration. In this paper, we will reconstruct this equivalence by the analogue of continuous and discrete dynamic programming. Then, based on the equivalence, we discuss the issue that the internal-stage controls produced by direct approaches may have lower order accuracy than the RK method used. We propose order conditions for internal-stage controls and then demonstrate that third or fourth order explicit RK methods cannot avoid the order reduction phenomenon. To overcome this obstacle, we calculate node control instead of internal-stage controls in DLQR and ILQR methods. Another advantage of our methods is high computational efficiency which comes from the usage of feedback technique. A simple numerical example will illustrate the validity of ILQR in solving nonlinear optimal control problems with high-order RK discretizations. In this paper, we also demonstrate that ILQR is essentially a quasi-Newton method with linear convergence rate.

Discrete Laguerre-based model predictive control for dynamic consensus of a vehicle platoon with time delay

Dynamic consensus of linear time-invariant multi-agent systems (MASs) using distributed model predictive control under the influence of input delay is addressed in this technical note. Model predictive control (MPC) is well suited to solve the consensus problem with its ability to handle multivariable systems and constraints. However, the increased computational complexity of MPC restricts its area of applications. An attempt to bridge this gap is made by proposing a Laguerre-based MPC design to bring down the computational load and make it viable for implementation. The effect of input delay on consensus is examined and the stability margin of a MAS with input delay is computed using the location of the closed-loop poles. A comparison of the proposed algorithm with conventional MPC establishes its superiority in convergence time, robustness to input delay and smoothness of the trajectories. The effectiveness of the proposed design is validated through the simulation of dynamic consensus on the benchmark problem of platoon configuration of vehicles. Abbreviations DLQR: discrete linear quadratic regulator; DMPC: distributed model predictive control; LMI: linear matrix inequality; LTI: linear time invariant; SISO: single-input single-output; MAS: multi-agent system; MIMO: multi-input multi-output; MPC: model predictive control

Linear quadratic regulator control with genetic algorithm convert applied to wind energy conversion

This document proposes a solution to the problem of physical sciences, such as control systems, this happens since in the industry almost all systems with applications necessarily need to guarantee stability and controllability. For this case we will implement a discrete linear quadratic regulator controller for a back-to-back converter, with a genetic algorithm, for the selection of the design matrices Q and R, for a doubly fed induction generator connected to a wind power system. The optimization technique that is presented is an alternative to techniques based on the reduction of errors through a measure, and the application problem is very current due to renewable energies that are becoming increasingly important in the energy sector. The description of the mathematical model of the converter in the state space is also relevant as a spearhead for other types of application, such a technique is shown in detail.

Research on automatic parking system based on linear quadratic regulator

PurposeThe purpose of this study is to solve the problem of path planning and path tracking in the automatic parking assistant system.Design/methodology/approachThis paper first uses the method of reverse driving to confirm few control points based on the constraints of the construction of the vehicle and the environment information, then a reference path with free-collision and continuous curvature is designed based on the Bézier curve. According to the principle of the discrete linear quadratic regulator (LQR), a tracking controller that combines feedforward control and feedback control is designed.FindingsFinally, simulation analysis are carried out in Simulink and CARSIM. The results show that the proposed method can obtain a better path tracking effect when the parking space size is appropriate.Originality/valueAccording to the principle of the discrete LQR, a tracking controller that combines feedforward control and feedback control is designed.

Online DMDc Based Model Identification Approach for Transient Stability Enhancement Using Wide Area Measurements

This letter proposes an online control strategy to enhance the overall damping of low-frequency power system oscillations of large inter-connected electrical networks. To achieve this objective, the proposed approach employs wide area measured signals to estimate an accurate online model of power system dynamics using the dynamic mode decomposition with control (DMDc) method. The DMDc technique applies singular value decomposition (SVD) to the collected data matrices such that an accurate low-order approximation of system dynamics is obtained. The estimated model is thereafter utilized in designing the wide area damping controller (WADC) using discrete linear quadratic regulator (DLQR). Furthermore, kalman filtering is deployed to update the states of the designed controller and to remove the noise that is contained in the measured signals. The effectiveness of the proposed method is tested on the 10 machines, 39-bus New England test system.

A model predictive controller for precision irrigation using discrete lagurre networks

The increasing demand for water is depleting the natural water resources worldwide. One of the major consumers of water is the agricultural industry. Traditional means of irrigation results in a lot of water wastage due to which the notion of precision irrigation was introduced using embedded devices. Many of the existing techniques for precision irrigation produce either sub-optimal results or have high computational complexity not suitable for low cost and simple embedded devices such as Raspberry-Pi (RPi). To solve this issue, this paper presents a precision irrigation technique based on discrete time model predictive control (MPC). To reduce the computational complexity of the proposed techniques, the use of Laguerre functions to approximate the control horizon is proposed. Using simulations in MATLAB, the results shows that the proposed technique can approximate the behavior of a discrete linear quadratic regulator with sufficient accuracy. The experimental results in a greenhouse environment, show that the proposed that the proposed technique can reduce water consumption by 30% over a period of 21 days. Moreover, a performance analysis of the proposed technique is presented to show that the proposed technique has significantly lower the computational complexity as compared to other conventional MPC techniques, i.e., it results in a computational complexity at least three time lower than existing techniques. Thus, the proposed precision irrigation control technique can be an attractive choice for real time agricultural application.

Discrete-time attitude stabilization of reusable reentry vehicle by convex optimization

This article addresses the attitude stabilization control of reusable reentry vehicle subjected to parametric variations and environmental perturbations. The nonlinear kinematic model of the vehicle is discretized and bluethen linearized using the global feedback linearization. A discrete time linear quadratic regulator with proportional-integral gain and disturbance rejection (LQRPI + D) is proposed to stabilized the system. The control formulation is based on convex optimization feasibility problem in terms of the linear matrix inequality. As illustrated by numerical simulations, the proposed technique provides better results compared to some existing methods.

Data Driven State Reconstruction of Dynamical System Based on Approximate Dynamic Programming and Reinforcement Learning

A data-driven approximation formulation for the state reconstruction problem of dynamical systems is presented in this paper. Without the assumption of an explicit mathematical model, the Hamilton–Jacobi–Bellman (HJB) based approach of a data-driven state reconstruction design method for monitoring and output-feedback control of dynamical systems is presented. The proposed state reconstruction design is based on a dynamic programming approach. To evaluate the proposed state reconstruction, computational experiments are conducted using only dynamical system model output data. The sensitivity of the algorithm parameters is also analyzed and discussed. The performance evaluation is analyzed in terms of the error metrics of the discrete linear quadratic regulator with output feedback under the value iteration algorithm through a reinforcement learning strategy.

Discrete-Time DC-Link Voltage and Current Control of a Grid-Connected Inverter with LCL-Filter and Very Small DC-Link Capacitance

The paper presents a controller design for grid-connected inverters (GCI) with very small dc-link capacitance that are coupled to the grid via an LCL filter. The usual controller designs would fail and result in instability. The proposed controller has a cascaded structure with a current controller as inner control loop and an outer dc-link voltage controller. The controller design is performed in discrete time and it is based on a detailed stability analysis of the dc-link voltage controller to determine the controller parameters which guarantee stability for all operating points. The inner loop is a state-feedback current controller that is designed based on the discrete linear-quadratic regulator (DLQR) theory. An additional integral error feedback assures steady-state accuracy of the current control loop. The simulation and experimental results validate performance and stability of proposed controller design.

Integrating LQR with GRNN for LFC of energy delivery system interconnected via AC/DC tie-lines

The present study shows an early attempt to integrate the design of discrete linear quadratic regulator (LQR) with generalised regression neural network (GRNN) to achieve the standards of load frequency control (LFC) of an energy delivery system linked via AC/DC tie-lines for assorted operating conditions. The design of state cost weighting matrix ( Q ) has been performed for different conditions namely (i) for controllability and observability technique, (ii) for optimisation and (iii) by providing equal weightage to all the system states while designing the discrete LQR LFC. The enactment of LFC design is checked for standard load disturbance considering the different sample time with diverse structures of Q . Further, the feedback gain matrix obtained via implementing the discrete LQR for control areas of power system using different models of Q is used to meritoriously train the GRNN for assorted operating conditions. At last, the performance of the designed GRNN is evaluated for extensive operating conditions with and without non-linearities and the obtained results are compared with multi-layer perceptron founded artificial neural network and genetic algorithm founded LFC of an energy delivery system.

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

SummaryThis work presents a multivariable predictive controller applied on a redundant robotic manipulator with three degrees of freedom. The article focuses on the design of a discrete model‐based predictive controller (DMPC) using the Laguerre function as a control effort weighting method to enhance the solution of Hildreth's quadratic programming and to minimize the trade‐off problem in constrained case. The Laguerre functions are used to simplify and enhance the control horizon effect through parsimonious control trajectory, thus reducing the computational load required to find the optimal control solution. Furthermore, these results can be confirmed by simulations and experimental tests on the manipulator and comparing it to the traditional DMPC approach and the discrete linear quadratic regulator.

Measurement‐based wide‐area damping of inter‐area oscillations based on MIMO identification

Interconnected power grid exhibits oscillatory response after a disturbance in the system. One such type of oscillation, the inter-area oscillation has the oscillation frequency in the range of 0.1–1 Hz. The damping of inter-area oscillations is difficult with local controllers, but it can be achieved using a wide area damping controller (WADC). For effective control, the input to the WADC should be the most observable signal, and the WADC output should be sent to the most controllable generator. This study presents a measurement-based novel algorithm for multi-input-multi-output (MIMO) transfer function identification of the power system to estimate such oscillation frequencies. The wide-area control loop is estimated using the MIMO transfer function, and the WADC design is a combination of the discrete linear quadratic regulator and Kalman filtering for the damping of inter-area oscillations. Since the MIMO identification is performed using the actual measurements, the proposed method can accurately monitor changes in the power grid, whereas the conventional methods are derived from small-signal analysis of a linearized model that does not consider changing operating conditions. The overall algorithm is implemented and validated on a RTDS/RSCAD® and MATLAB® real-time co-simulation platform using two-area and IEEE 39-bus power system models.

Online Coherency Based Adaptive Wide Area Damping Controller for Transient Stability Enhancement

This paper proposes a novel wide-area control strategy to enhance the transient stability of a large inter-connected power grid. The proposed control strategy achieves maximal damping of the inter-area oscillations by calculating the optimal number of cluster centers based on a novel online coherency grouping. To achieve this objective, the critical electro-mechanical mode is selected using localness index method during transient conditions. In addition, the online identification of the full model is performed to estimate the states to be controlled during the grid disturbances. Thereafter, a discrete linear quadratic regulator (DLQR) is directly applied to the estimated states, and the corresponding signals are channelized through the loop of most controllable and observable machines of each coherent group. The efficacy of the proposed method is tested on IEEE 39 bus and IEEE 68 bus standard benchmark model. The results demonstrate faster damping with minimal computation burden compared to existing solutions such as a classical slow coherency and a multi-input multi-output (MIMO) based wide area damping controllers.

Tuning heuristics and convergence analysis of reinforcement learning algorithm for online data-based optimal control design

A heuristic for tuning and convergence analysis of the reinforcement learning algorithm for control with output feedback with only input / output data generated by a model is presented. To promote convergence analysis, it is necessary to perform the parameter adjustment in the algorithms used for data generation, and iteratively solve the control problem. A heuristic is proposed to adjust the data generator parameters creating surfaces to assist in the convergence and robustness analysis process of the optimal online control methodology. The algorithm tested is the discrete linear quadratic regulator (DLQR) with output feedback, based on reinforcement learning algorithms through temporal difference learning in the policy iteration scheme to determine the optimal policy using input / output data only. In the policy iteration algorithm, recursive least squares (RLS) is used to estimate online parameters associated with output feedback DLQR. After applying the proposed tuning heuristics, the influence of the parameters could be clearly seen, and the convergence analysis facilitated.

Current Control of Grid-Tied LCL-VSI With a Sliding Mode Controller in a Multiloop Approach

Despite several studies and approaches, the design of current controllers for grid-connected converters via LCL filters is still a challenging task. This is mainly due to the parametric uncertainties and the grid background voltage distortions to which the system is submitted. In order to overcome these inherent system challenges, this paper proposes a multiloop control framework that simplifies the system dynamics of the overall circuit by splitting it in two equivalent sub-circuits. An inner loop is implemented as a fast sliding mode controller that controls the filter capacitor voltage in a fast and robust way. As a result, the plant, viewed by the outer loop, yields a voltage-controlled voltage source connected to the grid through an L filter. Thus, multiple resonant controllers are included in the state-space representation of this simplified system, allowing the design of a state-feedback controller in the outer loop for asymptotic tracking of the grid current with disturbance rejection of the grid background voltage. Here, a discrete linear quadratic regulator algorithm is used for designing the state-feedback gains. A simple design procedure is presented, as well as simulations and experimental results, to show the good performance of the proposed control scheme even under significant uncertainties and disturbances of the system.

Bipedal walking and push recovery with a stepping strategy based on time-projection control

In this paper, we present a simple control framework for online push recovery on biped robots with dynamic stepping properties. Owing to relatively heavy legs in our humanoid robot COMAN, we use a linear model called 3LP, which is composed of three pendulums to take swing and torso dynamics into account. Based on 3LP equations, we formulate discrete linear quadratic regulator (LQR) controllers and use a particular time-projection method to adjust footstep locations during the motion continuously. This process, which is based on pelvis and swing foot tracking errors, naturally considers swing dynamics and leads to leg-retraction properties. Suggested adjustments are added to the Cartesian 3LP gaits and converted into joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies are also used to ensure enough ground clearance in perturbed walking conditions. The proposed control architecture is robust, yet uses very simple state estimation and basic position tracking. We rely on series elastic actuators to absorb impacts while introducing simple laws to compensate for spring compressions. Extensive experiments on COMAN (real) and Atlas (simulated) robots demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness with minimal reliance on the ankles and avoiding any active zero moment point (ZMP) control. The proposed architecture is therefore generic, computationally very fast and yet with no critical parameter to tune.

From template to anchors: transfer of virtual pendulum posture control balance template to adaptive neuromuscular gait model increases walking stability.

Biomechanical models with different levels of complexity are of advantage to understand the underlying principles of legged locomotion. Following a minimalistic approach of gradually increasing model complexity based on Template & Anchor concept, in this paper, a spring-loaded inverted pendulum-based walking model is extended by a rigid trunk, hip muscles and reflex control, called nmF (neuromuscular force modulated compliant hip) model. Our control strategy includes leg force feedback to activate hip muscles (originated from the FMCH approach), and a discrete linear quadratic regulator for adapting muscle reflexes. The nmF model demonstrates human-like walking kinematic and dynamic features such as the virtual pendulum (VP) concept, inherited from the FMCH model. Moreover, the robustness against postural perturbations is two times higher in the nmF model compared to the FMCH model and even further increased in the adaptive nmF model. This is due to the intrinsic muscle dynamics and the tuning of the reflex gains. With this, we demonstrate, for the first time, the evolution of mechanical template models (e.g. VP concept) to a more physiological level (nmF model). This shows that the template model can be successfully used to design and control robust locomotor systems with more realistic system behaviours.

Online discrete-time LQR controller design with integral action for bulk Bucket Wheel Reclaimer operational processes via Action-Dependent Heuristic Dynamic Programming

In this paper, a novel approach for online design of optimal control systems applied to the bulk resumption process by bucket wheel reclaimer (BWR) is presented. This approach is based on reinforcement learning paradigms, more specifically Action Dependent Heuristic Dynamic Programming (ADHDP), that learn online in real-time the Discrete Linear Quadratic Regulator (DLQR) optimal control solution with integral action. Due to the geometric irregularities of the storage yard stacks and variation in physical and chemical characteristics of the stacked material, the flow control of solid bulks by bucket wheel reclaimer requires methods that are suitable with the high degree of imprecision of process variables and environment uncertainties. The resumption of bulk solids is carried out by dividing the stack into layers, each layer is approximately 4 m high, and the layers are divided into workbenches up to 12 m in length. To take up a workbench several translation steps are required (penetration in the stack), with the translation step varying from 0 to 1 m. In order to maintain the desired ore flow throughout the process, the BWR lance speed must be periodically adjusted. The main advantage of the proposed control method is that besides the decision rule is fully independent of plant model, the gains of the resulting controller are self-adjustable. The control system was designed in such a way that the ADHDP-based DLQR controller with integral action would act in real-time in the plant control, using only the input and output signals and states measured along the system trajectory.

Low-Cost Hardware-in-the-Loop Platform for Embedded Control Strategies Simulation

The increasing need for testing and prototyping designs under more realistic conditions is responsible for the advancement of new types of simulation. In this scenario, one type of simulation which has gained high notoriety and applicability is the one known as Hardware-in-the-Loop (HIL). This technique allows real and virtual components of a system to be tested together, making it possible to perform tests under realistic (and even extreme) conditions without harming the real system or a prototype built only for testing. The objective of this work was to develop a low-cost HIL simulation platform to be used for many different applications, unlike most commercial ones, that are developed for one exclusive field of application, such as automotive, aerospace, power electronics, among others. Thus, the main contribution of this work is the project of a HIL platform capable of simulating different types of systems, making it possible to validate embedded control strategies designed for them. Two different applications are tested in order to validate the HIL platform: an active suspension and a satellite attitude control air bearing table, both controlled using a discrete Linear Quadratic Regulator (LQR) designed for each of them.