Offset-free model predictive control: a study of different formulations with further results

This paper presents discussions on offset-free model predictive control (MPC) methods for linear discrete-time systems in the presence of deterministic system disturbances. The general approach is based on the use of a disturbance model and an observer to estimate the disturbance states. The recent development in offset-free MPC has established the equivalence of the velocity form (without output delay) to a specific choice of the disturbance model and observer. In this note, it was shown that this particular disturbance model and observer is not necessarily equivalent to the velocity form with output delay. Nevertheless, it was shown that the velocity form with output delay is equivalent to a different choice of the disturbance model and observer. An import of this result is that the velocity forms (with and without delayed output) belong to the same general approach - disturbance model and observer. Furthermore, areas that may be considered in future researches are also highlighted

Disturbance modeling and state estimation for offset-free predictive control with state-space process models

Disturbance modeling and design of state estimators for offset-free Model Predictive Control (MPC) with linear state-space process models is considered in the paper for deterministic constant-type external and internal disturbances (modeling errors). The application and importance of constant state disturbance prediction in the state-space MPC controller design is presented. In the case with a measured state, this leads to the control structure without disturbance state observers. In the case with an unmeasured state, a new, simpler MPC controller-observer structure is proposed, with observation of a pure process state only. The structure is not only simpler, but also with less restrictive applicability conditions than the conventional approach with extended process-and-disturbances state estimation. Theoretical analysis of the proposed structure is provided. The design approach is also applied to the case with an augmented state-space model in complete velocity form. The results are illustrated on a 2×2 example process problem

Disturbance modeling and state estimation for offset-free predictive control with state-space process models

Disturbance modeling and design of state estimators for offset-free Model Predictive Control (MPC) with linear state-space process models is considered in the paper for deterministic constant-type external and internal disturbances (modeling errors). The application and importance of constant state disturbance prediction in the state-space MPC controller design is presented. In the case with a measured state, this leads to the control structure without disturbance state observers. In the case with an unmeasured state, a new, simpler MPC controller-observer structure is proposed, with observation of a pure process state only. The structure is not only simpler, but also with less restrictive applicability conditions than the conventional approach with extended process-and-disturbances state estimation. Theoretical analysis of the proposed structure is provided. The design approach is also applied to the case with an augmented state-space model in complete velocity form. The results are illustrated on a 2×2 example process problem

Disturbance models for offset-free nonlinear predictive control

Offset-free model predictive control refers to a class of control algorithms able to track asymptotically constant reference signals despite the presence of unmeasured, nonzero mean disturbances acting on the process and/or plant model mismatch. Generally, in these formulations the nominal model of the plant is augmented with integrating disturbances, i.e. with a properly designed disturbance model, and state and disturbance are estimated from output measurements. To date the vast majority of offset-free MPC applications are based on linear models, however, since process dynamics are generally inherently nonlinear, these may perform poorly or even fail in some situations. Better results can be achieved by making use of nonlinear formulations and hence of nonlinear model predictive control (NMPC) technology. However, the obstacles associated with implementing NMPC frameworks are nontrivial. In this work the offset-free tracking problem with nonlinear models is addressed. Firstly some basic concepts related to the observability of nonlinear systems and state estimation are reviewed, focusing on the digital filtering and putting a strong accent on the role of the disturbance model. Thus, a class of disturbance models in which the integrated term is added to model parameters is presented together with an efficient and practical strategy for its design and subsequent implementation in offset-free NMPC frameworks

Controladores preditivos filtrados utilizando otimização multiobjetivo para garantir offset-free e robustez

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2017.A tese tem como objetivo estudar e desenvolver controladores preditivos do tipo GMV (Generalized Minimum Variance) e GPC (Generalized Predictive Controller), ampliando a família de projetos e a aplicabilidade destes controladores, para eliminar o offset (erro de regime permanente), rejeitar perturbações e assegurar rastreamento de referência e robustez. A proposta apresenta um novo formalismo matemático aos projetos dos controladores GMV e GPC, aplicado a sistemas monovariáveis e multivariáveis, empregando o modelo do processo e a função custo na forma posicional e inserindo um filtro de ponderação polinomial e integral na referência e saída do processo, alcançando projetos de controladores denominados Indirect Filtered Positional GMV (I-FPGMV) e Filtered Positional GPC (FPGPC). Para o projeto do controlador I-FPGMV, dois controladores adicionais são implementados, um utilizando-se a abordagem adaptativa (Direct FPGMV) e o outro hibridizado com a síntese do controlador PID. Para o FPGPC, é apresentada uma metodologia de projeto para processos multivariáveis e a hibridização do FPGPC com o controlador PID e com uma estrutura IMC filtrada (Filtered Internal Model Control - F-IMC). Adicionalmente, em ambos os controladores, I-FPGMV e FPGPC, uma estrutura de malha de controle é sugerida para mitigar problemas de saturação no sinal de controle. Ademais, os controladores I-FPGMV e FPGPC são combinados com a técnica de controle repetitivo para tratar referências e/ou perturbações periódicas, fornecendo dois projetos alternativos de controladores denominados Repetitive I-FPGMV (RI-FPGMV) e Adaptive Repetitive FPGPC (AR-FPGPC). Em seguida, é proposto um projeto de controle para lidar com perturbações conhecidas ou desconhecidas e mensuráveis ou não mensuráveis, combinando o FPGPC, hibridizado com a estrutura F-IMC e a ação de controle feedforward adaptativa, alcançando uma estrutura de malha de controle denominada Adaptive Feedback/Feedforward F-IMC (AFF-FIMC). Por fim, aspectos de robustez são incorporados nos polinômios de projetos dos controladores propostos, por meio de uma implementação que envolve as definições da função sensitividade e da integral do erro absoluto (Integrated Absolute Error - IAE), para a sintonia ?ótima? dos parâmetros do filtro, utilizando otimização multiobjetivo baseada em algoritmo genético. Simulações numéricas e ensaios práticos são aplicados para avaliar os projetos dos controladores propostos.Abstract : The thesis aims to study and develop predictive controllers of the kind GMV (Generalized Minimum Variance) and GPC (Generalized Predictive Controller), thereby extending the design family and the applicability of these controllers to eliminate offset (steady-state error), disturbance rejection and ensure reference tracking and robustness. The proposal presents a new mathematical formalism to the designs of the GMV and GPC controllers, applied to monovariable and multivariable systems, using both process model and cost function in the positional form and inserting an integral polynomial weighting filter for the setpoint and output of the process, thus achieving controller designs called Indirect Filtered Positional GMV (I-FPGMV) and Filtered Positional GPC (FPGPC). For the I-FPGMV controller design, two additional controllers are implemented, one using the adaptive approach (Direct FPGMV) and another hybridized with the PID controller synthesis. For the FPGPC, a design methodology to multivariable processes and for the hybridization of the FPGPC with the PID controller and with a Filtered Internal Model Control (F-IMC) structure is presented. Additionally, using both I-FPGMV and FPGPC controllers, a control loop structure is suggested to mitigate saturation problems in the control signal. In addition, the I-FPGMV and FPGPC controllers are combined with the repetitive control technique to handle periodic references and/or disturbances, providing two alternative controller designs called Repetitive I-FPGMV (RI-FPGMV) and Adaptive Repetitive FPGPC (AR-FPGPC). Afterwards, a control design is proposed to deal with known or unknown and measurable or non-measurable disturbances, combining the FPGPC, hybridized with the F-IMC structure, and the adaptive feedforward control action, achieving a control loop structure called Adaptive Feedback/Feedforward Filtered IMC (AFF-FIMC). Finally, robustness aspects are incorporated into the design polynomials of the proposed controllers, through an implementation involving the definitions of sensitivity function and integrated absolute error (IAE), for the optimal tuning of the filter parameters, using multiobjective optimization based on genetic algorithm. Numerical simulations and practical essays are applied to evaluate the proposed designs