Move blocked model predictive control with improved optimality using semi-explicit approach for applying time-varying blocking structure

Son, Seung Hyun; Oh, Tae Hoon; Kim, Jong Woo; Lee, Jong Min

doi:10.1016/j.jprocont.2020.04.002

Cited by 20 publications

(8 citation statements)

References 24 publications

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“…As a first motivational example, let us consider the ball plate system from [27, 28] modified to a nonlinear version as given in [29]. The system is then represented by the following nonlinear state space:

\begin{eqnarray} \underbrace{\def\eqcellsep{&}\begin{bmatrix} \dot{x}_1\\[6pt] \dot{x}_2\\[6pt] \dot{x}_3\\[6pt] \dot{x}_4 \end{bmatrix}}_{\dot{x}}=\underbrace{\def\eqcellsep{&}\begin{bmatrix} x_2\\[6pt] -700\sin (x_3)\\[6pt] x_4\\[6pt] 33.18x_4+3.7921 u \end{bmatrix}}_{f(x,u)}, \end{eqnarray}

where

x_1=p

x_2=\dot{p}

x_3=\theta

and

x_4=\dot{\theta }

.…”

Section: Example 1: the Nonlinear Ball Plate Systemmentioning

confidence: 99%

“…Consider now the optimisation of this system subject to the same penalisation weights as in [27, 28], that is, a state‐error penalisation weight

q_{k+i}=diag([6,0.1,500,100])\ \forall i=[1,N_p]

, and an input‐error penalisation weight of

r_{k+i}=diag([1])\ \forall i=[0,N_p-1]

. Although one could optionally use the infinite horizon terminal weight (

q_{k+N_p}=P_N

) as in [27, 28] to embed the secondary/terminal “dual‐mode”, this is not required to observe the benefits that result from the application of the proposed approach. Moreover, the system was subject to the following input and position constraints:

\begin{eqnarray} -20\le p\le 20\ (cm),\end{eqnarray}

\begin{eqnarray} -10\le u \le 10\ (V).

…”

Section: Example 1: the Nonlinear Ball Plate Systemmentioning

confidence: 99%

See 1 more Smart Citation

An efficient condensing algorithm for fast closed loop dual‐mode nonlinear model predictive control

Villarreal

Rossiter

Tsourdos

2022

IET Control Theory & Appl

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This paper presents a novel computationally efficient Closed Loop Dual-Mode Nonlinear Model Predictive Control scheme that uses closed loop models for condensing-based multiple-shooting frameworks which result in numerically robust optimisations. The proposed approach uses Time-Varying gains obtained from solving the Time-Varying Discrete Algebraic Ricatti Equation to embed feedback around the multiple-shooting trajectory, and proves the equivalence of the solution with the standard approach, thus resulting in the exact same stability, recursive feasibility and convergence properties. Moreover, the paper proposes an efficient algorithm based on an extension of the well-known O(N 2 p ) condensing algorithm, which can be used within the so-called Real-Time Iteration Scheme to achieve real-time performance. Simulations of a nonlinear ball-plate system, as well as of an inverted pendulum, and its extension -the triple inverted pendulum, are presented along the paper to demonstrate the advantages along with some disadvantages, focusing on the numerical conditioning, the disturbance rejection properties, and the computational performance.

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\begin{eqnarray} \underbrace{\def\eqcellsep{&}\begin{bmatrix} \dot{x}_1\\[6pt] \dot{x}_2\\[6pt] \dot{x}_3\\[6pt] \dot{x}_4 \end{bmatrix}}_{\dot{x}}=\underbrace{\def\eqcellsep{&}\begin{bmatrix} x_2\\[6pt] -700\sin (x_3)\\[6pt] x_4\\[6pt] 33.18x_4+3.7921 u \end{bmatrix}}_{f(x,u)}, \end{eqnarray}

where

x_1=p

x_2=\dot{p}

x_3=\theta

and

x_4=\dot{\theta }

.…”

Section: Example 1: the Nonlinear Ball Plate Systemmentioning

confidence: 99%

“…Consider now the optimisation of this system subject to the same penalisation weights as in [27, 28], that is, a state‐error penalisation weight

q_{k+i}=diag([6,0.1,500,100])\ \forall i=[1,N_p]

, and an input‐error penalisation weight of

r_{k+i}=diag([1])\ \forall i=[0,N_p-1]

. Although one could optionally use the infinite horizon terminal weight (

q_{k+N_p}=P_N

\begin{eqnarray} -20\le p\le 20\ (cm),\end{eqnarray}

\begin{eqnarray} -10\le u \le 10\ (V).

…”

Section: Example 1: the Nonlinear Ball Plate Systemmentioning

confidence: 99%

An efficient condensing algorithm for fast closed loop dual‐mode nonlinear model predictive control

Villarreal

Rossiter

Tsourdos

2022

IET Control Theory & Appl

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show abstract

“…A key advantage of utilizing these model identification techniques, based on Koopman operator theory, is the availability of linear predictors for nonlinear systems. This allows the application of well‐established linear MPC schemes 39,40 to develop Koopman‐based model predictive control (KMPC) scheme 41,42 . Furthermore, Abhinav and Kwon 43 proposed a Koopman Lyapunov‐based model predictive control (KLMPC) that integrates EDMD and Lyapunov‐based MPC scheme to ensure the feasibility and stability of a control system, whose mathematically rigorous stability analysis is studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Application of offset‐free Koopman‐based model predictive control to a batch pulp digester

2021

Self Cite

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This work presents the application of a Koopman operator approach to a batch pulp digester. To manufacture paper products with desired properties, it is essential to consider both macroscopic and microscopic attributes of pulp. However, the complexity of multiscale dynamics of pulping processes hinders proper control system design. Therefore, we utilize extended dynamic mode decomposition (EDMD), which is based on Koopman operator theory, to derive a global linear representation of a pulp digester. Then, we design an offset‐free Koopman‐based model predictive control (KMPC) system to regulate the Kappa number and cell wall thickness (CWT) of fibers at a batch pulp digester while compensating for the influence of plant‐model mismatch and disturbance during operation. The numerical experiments demonstrate that the linear state‐space model, obtained via EDMD, properly predicts the behavior of a batch pulp digester, and the designed offset‐free KMPC system successfully drives the Kappa number and CWT to set‐point values.

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“…Model-based control strategies manipulate a system based on the prediction of the future state of a process using a known model. Model predictive control (MPC) which derives a finite-horizon optimal solution in a receding horizon manner is one of the most representative model-based approaches (Mayne, Rawlings, Rao and Scokaert, 2000;Kim, Park, Jung, Kim, Kim and Lee, 2018;Son, Oh, Kim and Lee, 2020d;Son, Park, Oh, Kim and Lee, 2020e). MPC can effectively derive a reliable solution based on the model, but the performance of MPC is directly related to the prediction accuracy of the model.…”

Section: Introductionmentioning

confidence: 99%

Model-plant mismatch learning offset-free model predictive control

Son,

Kim,

et al. 2020

Preprint

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We propose model-plant mismatch learning offset-free model predictive control (MPC), which learns and applies the intrinsic model-plant mismatch, to effectively exploit the advantages of model-based and data-driven control strategies and overcome the limitations of each approach. In this study, the model-plant mismatch map on steady-state manifold in the controlled variable space is approximated via a general regression neural network from the steady-state data for each setpoint. Though the learned model-plant mismatch map can provide the information at the equilibrium point (i.e., setpoint), it cannot provide model-plant mismatch information during the transient state. Moreover, the intrinsic model-plant mismatch can vary due to system characteristics changes during operation. Therefore, we additionally apply a supplementary disturbance variable which is updated from the disturbance estimator based on the nominal offset-free MPC scheme. Then, the combined disturbance signal is applied to the target problem and finite-horizon optimal control problem of offset-free MPC to improve the prediction accuracy and closed-loop performance of the controller. By this, we can exploit both the learned model-plant mismatch information and the stabilizing property of the nominal disturbance estimator approach. The closed-loop simulation results demonstrate that the developed scheme can properly learn the intrinsic model-plant mismatch and efficiently improve the model-plant mismatch compensating performance in offset-free MPC. Moreover, we examine the robust asymptotic stability of the developed offset-free MPC scheme, which is known to be difficult to analyze in nominal offset-free MPC, by exploiting the learned model-plant mismatch information.

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Move blocked model predictive control with improved optimality using semi-explicit approach for applying time-varying blocking structure

Cited by 20 publications

References 24 publications

An efficient condensing algorithm for fast closed loop dual‐mode nonlinear model predictive control

An efficient condensing algorithm for fast closed loop dual‐mode nonlinear model predictive control

Application of offset‐free Koopman‐based model predictive control to a batch pulp digester

Model-plant mismatch learning offset-free model predictive control

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