Theoretical Foundation of MPC

Khaled, Nassim; Pattel, Bibin

doi:10.1016/b978-0-12-813918-9.00002-2

Cited by 7 publications

(11 citation statements)

References 2 publications

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“…In this work, the embedded solver of the Matlab MPC toolbox was chosen [26,27]. To compensate for the control delay due to the digital implementation, a one-step state prediction is applied before the QP solver is called [28].…”

Section: Quadratic Optimization Problemmentioning

confidence: 99%

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors Considering Current and Torque Constraints

Brosch

Wallscheid

Böcker

2023

IEEE Trans. Power Electron.

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In various permanent magnet synchronous motor (PMSM) drive applications the torque dynamics are an important performance criterion. Here, time-optimal control (TOC) methods can be utilized to achieve highest control dynamics. Applying state-of-the-art TOC methods leads to unintended overcurrents and torque over-and undershoots during transient operation.To prevent these unintended control characteristics while still achieving TOC performance the time-optimal model predictive control (TO-MPC) is proposed in this work. The TO-MPC contains a reference pre-rotation (RPR) and a continuous control set model predictive flux control (CCS-MPFC). By applying Pontryagin's maximum principle, the TOC solution trajectories for states and inputs of the PMSM are determined neglecting current and torque limits. With the TOC solution, a flux linkage reference for the CCS-MPFC is calculated that corresponds to a pre-rotation of the operating point in the stator-fixed coordinate system. This pre-rotated flux linkage reference is reached in minimum time without overcurrents and torque over-as well as undershoots by incorporating current and torque limits as timevarying softened state constraints into the CCS-MPFC. Simulative and experimental investigations for linearly and nonlinearly magnetized PMSMs in the whole speed and torque range show that, compared to state-of-the-art TOC methods, overcurrents and torque over-as well as undershoots are prevented by the proposed TO-MPC.

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Section: Quadratic Optimization Problemmentioning

confidence: 99%

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors Considering Current and Torque Constraints

Brosch

Wallscheid

Böcker

2023

IEEE Trans. Power Electron.

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“…To solve the QP with linear inequality constraints (10), any standard QP solver can be utilized. In this work, the embedded solver of the Matlab MPC toolbox [34,35] was chosen. To compensate the control delay due to the digital implementation, a one-step prediction is executed before the QP solver is called.…”

Section: H Continuous-control-set Model Predictive Flux Controlmentioning

confidence: 99%

“…This is due to the varying required number of iteration steps for the utilized embedded active-set solver, cf. [34,35], to find the optimum of the QP (10). In simulations and experiments it has been observed that not more than 11 iterations are required to find the optimum [7].…”

Section: Experimental Investigationmentioning

confidence: 99%

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors in the Whole Speed and Modulation Range Considering Current and Torque Constraints

Brosch¹,

Wallscheid²,

Böcker³

2023

Preprint

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<p>Improving control dynamics and enabling maximum torque and power conversion for a given electrical drive are important target quantities of drive control algorithms. To utilize the electrical drive to its maximum extent during transient and steady-state operation, a time-optimal continuous-control-set model predictive flux control (CCS-MPFC) for permanent magnet synchronous motors (PMSM) is proposed. This scheme considers torque and current limits as softened state constraints in the CCS-MPFC’s optimization problem to prevent transient overcurrents as well as torque over- and undershoots during time-optimal operating point changes. Furthermore, the overmodulation range including six-step operation can be entered seamlessly to ensure maximum power conversion at high speeds. Fastest transients within the whole modulation range are enabled by a time-optimal harmonic reference generator (TO-HRG). Here, the flux reference of the CCS-MPFC is complemented with a harmonic content that enables operation in the overmodulation region. Further, the reference is pre-rotated during transient operation to attain time-optimal control performance. Extensive simulative as well as experimental investigations for linearly and nonlinearly magnetized PMSMs show that, compared to state-of-the-art methods, time-optimal control performance in the whole modulation range without transient overcurrents as well as torque over- and undershoots can be achieved by the proposed control method.</p>

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“…Second, in the optimizer’s cost functional algorithm, the current controller utilizes just output reference tracking and modifications in manipulated variables. Generally, MPC can control the process with these two cost functions satisfactorily . These cost functions are resolved via an online optimization approach to deliver the trajectory of the controller output.…”

Section: Development Of Online Safety Control Using Mpcmentioning

confidence: 99%

“…Generally, MPC can control the process with these two cost functions satisfactorily. 45 These cost functions are resolved via an online optimization approach to deliver the trajectory of the controller output. The selection of the process model type is the primary factor that distinguishes nonlinear MPC (NMPC) from linear MPC (LMPC).…”

Section: Development Of Online Safety Control Using Mpcmentioning

confidence: 99%

Nonlinear Control of Fouling in Polyethylene Reactors

et al. 2022

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Fouling formation in reactor vessels poses a serious threat to the safe operation of the industrial low-density polyethylene (LDPE) polymerization. Fouling also degrades the polymer quality and causes productivity loss to some extent. In this work, neural Wiener model predictive control (NWMPC) is introduced to address the fouling concern. In addition, a soft sensor model is used to activate the fouling−defouling (F−D) mechanism when the fouling surpasses the thickness limit to prevent vessel overheating. NWMPC is proven to be fast, stable, and robust under various control scenarios. The use of a soft sensor model in conjunction with NWMPC enables the online monitoring and controlling of the F−D processes. When comparison is made with a state space (SSMPC) utilizing only the linear block, NWMPC is found to be able to control the LDPE grade with quicker grade transition and lower resource consumption.

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Theoretical Foundation of MPC

Cited by 7 publications

References 2 publications

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors Considering Current and Torque Constraints

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors Considering Current and Torque Constraints

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors in the Whole Speed and Modulation Range Considering Current and Torque Constraints

Nonlinear Control of Fouling in Polyethylene Reactors

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