Linear Model Predictive Control Controller Research Articles

On the simplification of the internal nonlinear robot models for the MPC-based visual servoing

Visual servoing enables tracking and grasping of static and moving objects and locating regions of interest. Its implementation requires the coordination of low-level control tasks with high-level supervision and planning. The use of the PID-based manipulation control addresses only the dynamical response and requires the use of optimization-based techniques at the supervisory level. On the contrary, model predictive control (MPC) simplifies the design as it combines both tasks within a single algorithm. However, successful MPC implementation depends on the quality of the internal model utilized by the algorithm. Robots are intrinsically and significantly nonlinear control objects, so their models are inherently complex. This leads to computational problems. Standard solutions are to shorten the MPC horizons or to parallelize calculations. The approach suggested here returns to the problem roots, i.e. to the model. This study proposes simplified models that allow the use of the MPC. General Hammerstein–Wiener-like model is applied to an arm, which is further simplified into the linear dynamics used as the predictive supervisory control over the torque control. The head uses linear dynamics used by the supervisory MPC working with the base servomotors. It is shown that they are computationally efficient and sufficiently accurate. It is shown that the linear MPC controllers, which use the suggested simplified dynamic robot models, can successfully support visual servoing with accurate control. They are compared with standard PID-based structures and show their superiority. The proposed approach is successfully validated using Matlab and Gazebo robot simulator and is ultimately confirmed by experiments on a real robot.

Economic Performance of Model Predictive Control at Back-off Operating Point

In this paper, we address the economic performance of Model Predictive Control (MPC) while operating at a backed-off operating point. Operating the plant at a constrained optimal point will often cause constraint violations due to uncertainties such as disturbances and measurement errors, etc. To ensure dynamic feasibility, the concept of economic back-off is used. In this work, we select the set point as the economic back-off point such that the dynamic operating region should have the least variability in the active constrained variables while ensuring the feasibility of other variables. In other words, the dynamic operating region is oriented by the proper design of a controller such that variability in active constrained variables is as low as possible. This controller design can be transformed into equivalent objective function weights of the MPC controller. In this study, we demonstrate that the determined back-off point is optimal for both linear controller and MPC controller when there are no unconstrained degrees of freedom. For the case with unconstrained degrees of freedom, the back-off point determined using the presented approach is optimal only for a linear controller but suboptimal for an MPC controller. Demonstrative case studies are presented to illustrate the economic performance of the MPC controller at the determined economic back-off point.

Optimization of Energy Consumption of Industrial Robots Using Classical PID and MPC Controllers

Industrial robots have a key role in the concept of Industry 4.0. On the one hand, these systems improve quality and productivity, but on the other hand, they require a huge amount of energy. Energy saving solutions have to be developed and applied to provide sustainable production. The purpose of this research is to develop the optimal control strategy for industrial robots in order to minimize energy consumption. Therefore, a case study was conducted for the development of two control strategies to be applied to the RV-2AJ Mitsubishi robot arm with 5 DOF, where the system is a nonlinear one. The first examined controller is the classical linear proportional integral derivative (PID) controller, while the second one is the linear model predictive control (MPC) controller. In our study, the performances of both the classical PID model and the linear MPC controller were compared. As a result, it was found that the MPC controller in the execution of the three defined reference trajectories [(1) curve motion, (2) N-shaped motion, and (3) circle motion] was always faster and required less energy consumption, whereas in terms of precision the PID succeeded in executing the trajectory more precisely than the MPC but with higher energy consumption. The main contribution of the research is that the performances of the two control strategies with regard to a complex dynamic system were compared in the case of the execution of three different trajectories. The evaluations show that the MPC controller is, on the one hand, more energy efficient; on the other hand, it provides a shorter cycle time compared to the PID controller.

Path tracking control of intelligent vehicles via a speed-adaptive MPC for a curved lane with varying curvature

When driving on a curved lane with varying curvature, human drivers usually make a small range of longitudinal speed adjustments to maintain a yaw response that feels more stable. Taking this type of response as a reference, intelligent vehicles must also make adjustments to their longitudinal speed within a small range during the path tracking process with curvature changes. The current variable curvature path tracking algorithm using model predictive control (MPC) basically assumes that the vehicle moves at a constant speed, which does not match the small-range adjustment of the longitudinal speed and thereby affects the accuracy of path tracking. In this paper, considering the small range of speed variation in the path tracking process, the path and speed decoupling control in Frenet coordinates are used to replace the longitudinal-lateral-yaw complex coupling dynamics control. Meanwhile, considering the problem that the steady-state error of the MPC controller caused by curvature variation in the path tracking process cannot be eliminated, the adaptive weight control (AWC) and adaptive feedforward (AFF) models based on BP neural network (BPNN) data learning are designed to dynamically adjust the lateral error weight and feedforward factors of the MPC controller. As a result, a more accurate path tracking effect is achieved. Simulation results in the joint CarSim-Simulink environment show that the proposed algorithm significantly improves the adaptive capability of the linear MPC controller in response to time-varying conditions and has a higher tracking accuracy.

Nonlinear Model Predictive Control Using Feedback Linearization for a Pressurized Water Nuclear Power Plant

The present work aims to introduce a nonlinear control scheme that combines intelligent feedback linearization (FBL) and a model predictive control (MPC) for a pressurized water reactor (PWR). The nonlinear plant model that is considered in this study is described by the first-principles approach, and it consists of 38 state variables. First, system identification using a dynamic neural network (DNN) structure is performed to obtain a standard affine nonlinear system. The quasi-Newton algorithm is employed to find the best DNN model. Then, an FBL is formulated to address the nonlinearity of the DNN model. An MPC controller is developed based on the FBL system to improve the system performance. The designed controller is compared with a linear MPC controller that is based on state-space models to evaluate the performance of the proposed controller. The proposed approach improves the load-following operation and offers better disturbance rejection capability than the conventional MPC. In addition, numerical measures are employed to compare and analyze the performances of the two control strategies.

New Integrated Vehicle Stability Control of Active Front Steering and Electronic Stability Control Considering Tire Force Reserve Capability

To address the problem of the mutual interference and control distribution in the integrated stability control of active front steering (AFS) and electronic stability control (ESC), this study proposes a new integrated stability controller of AFS and ESC based on holistic control framework. A distribution rule of longitudinal and lateral tire force based on equal reserve capacity of tire force is designed to distribute the control right of steering and braking. A UniTire model with combined slip condition is also designed for the integrated control of steering and braking. Model predictive control (MPC) is adopted to address the constrained multi-objective control problem. To reduce the complexity of the system and improve the real-time performance of the system, a linear time-varying MPC controller is designed by linearizing the nonlinear system, and then the constrained MPC control problem is transformed into a quadratic programming problem for solving. Finally, the proposed method is validated on the basis of Matlab/Simulink and CarSim co-simulation platform. Results show that the proposed method has obvious effects on solving the mutual interference and control right distribution of steering and braking and improving vehicle stability.

Robust Linear Control of Boost and Buck-Boost DC-DC Converters in Micro-Grids with Constant Power Loads

Power distribution systems nowadays are highly penetrated by renewable energy sources, and this explains the dominant role of power electronic converters in their operation. However, the presence of multiple power electronic conversion units gives rise to the so-called phenomenon of Constant Power Loads (CPLs), which poses a serious stability challenge in the overall operation of a DC micro-grid. This article addresses the problem of enhancing the stability margin of boost and buck-boost DC-DC converters employed in DC micro-grids under uncertain mixed load conditions. This is done with a recently proposed methodology that relies on a two-degree-of-freedom (2-DOF) controller, comprised by a voltage-mode Proportional Integral Derivative (PID) (Type-III) primary controller and a reference governor (RG) secondary controller. This complementary scheme adjusts the imposed voltage reference dynamically and is designed in an optimal fashion via the Model Predictive Control (MPC) methodology based on a specialized composite (current and power) estimator. The outcome is a robust linear MPC controller in an explicit form that is shown to possess interesting robustness properties in a wide operating range and under various disturbances and mixed load conditions. The robustness and performance of the proposed controller/observer pair under steady-state, line, and mixed load variations is validated through extensive Matlab/Simulink simulations.

Recent Advances in Quadratic Programming Algorithms for Nonlinear Model Predictive Control

Over the past decades, the advantages of optimization-based control techniques over conventional controllers inspired developments that enabled the use of model predictive control (MPC) in applications with very high sampling rates. Since at the heart of most linear and nonlinear MPC controllers resides a quadratic programming (QP) solver, the implementation of efficient algorithms that exploit the underlying problem structure drew the attention of many researchers and the progress in the field has been remarkable. The aim of this paper is to summarize the main algorithmic advances in the field and to provide a consistent benchmark between a selection of software tools that have been recently developed. The code that was used for the simulations is publicly available for readers that wish to reproduce the results or test the benchmarked solvers on their own nonlinear MPC applications.

Rate-Based Model Predictive Control of Diesel Engines

The paper presents the results of a rate-based model predictive controller development for diesel engine air path control. The objective is to regulate the intake manifold pressure and EGR rate estimate to the specified set-points by coordinated control of the Variable Geometry Turbine (VGT), EGR valve, and EGR throttle. The approach utilizes rate-based reduced order linear models and Model Predictive Control (MPC). Potential benefits of using a rate-based approach versus conventional MPC methods are illustrated. Most notably, it is found that using a rate-based approach greatly extends the operating range of a single linear MPC controller on the nonlinear model. The performance of the rate-based MPC controller versus conventional MPC approaches subject to input and state constraints while following the specified set-points is evaluated using nonlinear model simulations. Strategies to reduce the computational complexity of explicit MPC are exemplified.

Dynamic modeling and linear model predictive control of gas pipeline networks

A linear model predictive control (LMPC) strategy is developed for large-scale gas pipeline networks. A nonlinear dynamic model of a representative pipeline is derived from mass balances and the Virial equation of state. Because the full-order model is illconditioned, reduced-order models are constructed using time-scale decomposition arguments. The first reduced-order model is used to represent the plant in closed-loop simulations. The dimension of this model is reduced further to obtain the linear model used for LMPC design. The LMPC controller is formulated to regulate certain pipeline pressures by manipulating production setpoints of cryogenic air separation plants. Both input and output variables are subject to operational constraints. Three methods for handling output constraint infeasibilities are investigated. # 2001 Elsevier Science Ltd. All rights reserved.

Nonlinear Model Predictive Control of pH Neutralisation Using Wiener Models

A Wiener model is used within a model predictive control (MPC) scheme. The method is applied to a pH neutralisation process and its performance is compared to linear MPC and PID controllers.