A Comparison of LQR and MPC Control Algorithms of an Inverted Pendulum

Jezierski, A.; Możaryn, Jakub; Suski, Damian

doi:10.1007/978-3-319-60699-6_8

Cited by 10 publications

(5 citation statements)

References 3 publications

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“…Some works are focused on the evaluation of the performances of these optimal controllers, mainly in simulation and sometimes also experimentally. In [25] the study was performed on a simulated model of an inverted pendulum, and it has been shown that the LQR algorithm works better for stabilization problems and disturbance rejection, while the MPC controller is more suitable for the trajectory tracking task. In [26], two optimal control techniques such as LQR and SDRE, have been applied to a double inverted pendulum on a cart and these were investigated and compared.…”

Section: Related Workmentioning

confidence: 99%

Execution Time of Optimal Controls in Hard Real Time, a Minimal Execution Time Solution for Nonlinear SDRE

et al. 2020

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Many engineering fields, such as automotive, aerospace, and the emerging challenges towards industry 4.0, have to deal with Real-Time (RT) or Hard Real Time (HRT) systems, where temporal constraints must be fulfilled, to avoid critical behaviours or unacceptable system failures. For this reason, estimation of code's Worst-Case Execution Time (WCET) has received lots attention because in RT systems a fundamental requirement is to guarantee at least a temporal upper bound of the code execution for avoiding any drawbacks. However, until now there is no approved method to compute extremely tight WCET. Nowadays, indeed, HRT requirements are solved via hardware, using multi-cores embedded boards that allow the computation of the deterministic Execution Time (ET). The availability of these embedded architectures has encouraged the designers to look towards more computationally demanding optimal control techniques for RT scenarios, and to compare and analyze performances also evaluating a tight WCET. However, this area still lacks deep investigations. This paper has the intent of analysing results regarding the choice between three of the most established optimal controls (LQR, MPC, SDRE), providing the first link between WCET analysis and control algorithms performances. Moreover, this work shows how it is also possible to obtain a minimal ET solution for the nonlinear SDRE controller. The results might be useful for future implementations and for coping with Industry 4.0 emerging challenges. Furthermore, this approach can be useful in control system engineering field, especially in the design stage for RT or HRT systems, where temporal bounds have to be fulfilled jointly with all the other application's specifications.

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Section: Related Workmentioning

confidence: 99%

Execution Time of Optimal Controls in Hard Real Time, a Minimal Execution Time Solution for Nonlinear SDRE

et al. 2020

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“…LQR is designed with a cost function that allows the optimal control by means of control inputs and internal states. 31 Superior to LQR, MPC has the property of rolling optimization and the ability to handle constraints, solving problems with state and control input constraints, and obtaining an optimized control volume under multiple constraints. 32 For the formation control in an environment with alleyway mutation, a difficult problem may be that frequent formation switching will bring the instability to the velocities of individual robots, resulting in a lack of stability and accuracy of formation.…”

Section: Introductionmentioning

confidence: 99%

Adaptive obstacle avoidance control strategy for a formation under a narrow alleyway environment

Yue

Shangguan

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article develops an effective adaptive obstacle avoidance control strategy containing formation decision mechanism and a model predictive control–based formation controller for a multi-robot system working in a narrow alleyway environment. First, a decision mechanism containing two obstacle avoidance methods, homogeneous deformation and heterogeneous deformation, is established to provide a flexible choice for the formation to pass through the obstacle area, taking into account the formation safety and environment constraint. Furthermore, a formation bank is preset, and a performance evaluation system containing structural deformation, convergence speed, and energy consumption is established to help determine the best obstacle avoidance configuration. Then, a model predictive control–based formation controller with the leader–follower approach is utilized to realize the configuration switching and keeping. In the end, the simulation results verify the effectiveness of the proposed control strategy.

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“…LQG refers to infinite horizon optimization, and the algorithms are much simpler and deal with disturbance rejection better, while MPC refers to finite-horizon optimization and the algorithms are more complex and necessary to perform more complicated calculations online. However, MPC shows better trajectory tracking and considerably smoother control action changes [8].…”

Section: Introductionmentioning

confidence: 99%

Model Predictive Control for Autonomous Driving Vehicles

et al. 2021

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The field of autonomous driving vehicles is growing and expanding rapidly. However, the control systems for autonomous driving vehicles still pose challenges, since vehicle speed and steering angle are always subject to strict constraints in vehicle dynamics. The optimal control action for vehicle speed and steering angular velocity can be obtained from the online objective function, subject to the dynamic constraints of the vehicle’s physical limitations, the environmental conditions, and the surrounding obstacles. This paper presents the design of a nonlinear model predictive controller subject to hard and softened constraints. Nonlinear model predictive control subject to softened constraints provides a higher probability of the controller finding the optimal control actions and maintaining system stability. Different parameters of the nonlinear model predictive controller are simulated and analyzed. Results show that nonlinear model predictive control with softened constraints can considerably improve the ability of autonomous driving vehicles to track exactly on different trajectories.

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A Comparison of LQR and MPC Control Algorithms of an Inverted Pendulum

Cited by 10 publications

References 3 publications

Execution Time of Optimal Controls in Hard Real Time, a Minimal Execution Time Solution for Nonlinear SDRE

Execution Time of Optimal Controls in Hard Real Time, a Minimal Execution Time Solution for Nonlinear SDRE

Adaptive obstacle avoidance control strategy for a formation under a narrow alleyway environment

Model Predictive Control for Autonomous Driving Vehicles

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