Robust Model Predictive Control of a Nonlinear System with Known Scheduling Variable and Uncertain Gain

Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

doi:10.3182/20120620-3-dk-2025.00107

Cited by 10 publications

(7 citation statements)

References 9 publications

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“…Rotor rotational speed Generated power Tower top acceleration Measured collective pitch Hub height wind speed vector (22) More details about this controller can be found in [21].…”

Section: Methodsmentioning

confidence: 99%

“…Having the LPV model of the system we proceed to compute state predictions using the approach proposed in [21]. In our method the predicted state is a function of the current state x k , the control inputs u n , as well as the scheduling variable Γ n = γ k+1 , γ k+2 , .…”

Section: A Problem Formulationmentioning

confidence: 99%

“…After computing the state predictions as functions of control inputs, it is straightforward to write down the optimization problem similar to a linear MPC problem as a quadratic program, more details can be found in [21].…”

Section: A Problem Formulationmentioning

confidence: 99%

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An MPC approach to individual pitch control of wind turbines using uncertain LIDAR measurements

Mirzaei

Soltani

Poulsen

et al. 2013

2013 European Control Conference (ECC)

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“…Rotor rotational speed Generated power Tower top acceleration Measured collective pitch Hub height wind speed vector (22) More details about this controller can be found in [21].…”

Section: Methodsmentioning

confidence: 99%

Section: A Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

An MPC approach to individual pitch control of wind turbines using uncertain LIDAR measurements

Mirzaei

Soltani

Poulsen

et al. 2013

2013 European Control Conference (ECC)

Self Cite

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show abstract

“…After computing the state predictions as functions of control inputs, we can write down the optimization problem similar to a linear MPC problem as a quadratic program, more details can be found in [20].…”

Section: A Problem Formulationmentioning

confidence: 99%

Model predictive control of wind turbines using uncertain LIDAR measurements

Mirzaei

Soltani

Poulsen

et al. 2013

2013 American Control Conference

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Abstract-The problem of Model predictive control (MPC) of wind turbines using uncertain LIDAR (LIght Detection And Ranging) measurements is considered. A nonlinear dynamical model of the wind turbine is obtained. We linearize the obtained nonlinear model for different operating points, which are determined by the effective wind speed on the rotor disc. We take the wind speed as a scheduling variable. The wind speed is measurable ahead of the turbine using LIDARs, therefore, the scheduling variable is known for the entire prediction horizon. By taking the advantage of having future values of the scheduling variable, we simplify state prediction for the MPC. Consequently, the control problem of the nonlinear system is simplified into a quadratic programming. We consider uncertainty in the wind propagation time, which is the traveling time of wind from the LIDAR measurement point to the rotor. An algorithm based on wind speed estimation and measurements from the LIDAR is devised to find an estimate of the delay and compensate for it before it is used in the controller. Comparisons between the MPC with error compensation, the MPC without error compensation and an MPC with re-linearization at each sample point based on wind speed estimation are given. It is shown that with appropriate signal processing techniques, LIDAR measurements improve the performance of the wind turbine controller.

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“…is method is applicable already in numerous domains in industry [6] as regulation and control. Generally, real processes are nonlinear, complex, and uncertain [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

2020

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An enhanced method able to perform accurate stability of constrained uncertain systems is presented. The main objective of this method is to compute a sequence of feedback control laws which stabilizes the closed-loop system. The proposed approach is based on robust model predictive control (RMPC) and enhanced maximized sets algorithm (EMSA), which are applied to improve the performance of the closed-loop system and achieve less conservative results. In fact, the proposed approach is split into two parts. The first is a method of enhanced maximized ellipsoidal invariant sets (EMES) based on a semidefinite programming problem. The second is an enhanced maximized polyhedral set (EMPS) which consists of appending new vertices to their convex hull to minimize the distance between each new vertex and the polyhedral set vertices to ensure state constraints. Simulation results on two examples, an uncertain nonisothermal CSTR and an angular positioning system, demonstrate the effectiveness of the proposed methodology when compared to other works related to a similar subject. According to the performance evaluation, we recorded higher feedback gain provided by smallest maximized invariant sets compared to recently studied methods, which shows the best region of stability. Therefore, the proposed algorithm can achieve less conservative results.

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Robust Model Predictive Control of a Nonlinear System with Known Scheduling Variable and Uncertain Gain

Cited by 10 publications

References 9 publications

An MPC approach to individual pitch control of wind turbines using uncertain LIDAR measurements

An MPC approach to individual pitch control of wind turbines using uncertain LIDAR measurements

Model predictive control of wind turbines using uncertain LIDAR measurements

Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

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