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Additional steps are preferred for systems that show a high degree a nonlinearity or when there is little additional expense to obtain the data. The following code generates data at multiple input levels and with varying different step time intervals.

## Model Predictive Control – Institute for Dynamic Systems and Control | ETH Zurich

The cooling jacket temperature is not raised above K to avoid reactor instability in open loop. There are many methods to develop a controller model. For linear MPC, there are many options to obtain a controller model through identification methods.

For nonlinear MPC, the nonlinear simulator equations can be used to develop the controller. This section demonstrates how to obtain a linear model for the MPC application using the step test data generated in the prior section.

### Introduction

Dynamic Optimization. Syllabus Schedule. Tc - Tc0 MV tuning m. In recent years it has also been used in power system balancing models [1] and in power electronics [2]. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from Linear-Quadratic Regulator LQR.

Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability.

MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry. The models used in MPC are generally intended to represent the behavior of complex dynamical systems. The additional complexity of the MPC control algorithm is not generally needed to provide adequate control of simple systems, which are often controlled well by generic PID controllers. Common dynamic characteristics that are difficult for PID controllers include large time delays and high-order dynamics.

MPC models predict the change in the dependent variables of the modeled system that will be caused by changes in the independent variables. In a chemical process, independent variables that can be adjusted by the controller are often either the setpoints of regulatory PID controllers pressure, flow, temperature, etc. Independent variables that cannot be adjusted by the controller are used as disturbances. Dependent variables in these processes are other measurements that represent either control objectives or process constraints. MPC uses the current plant measurements, the current dynamic state of the process, the MPC models, and the process variable targets and limits to calculate future changes in the dependent variables.

These changes are calculated to hold the dependent variables close to target while honoring constraints on both independent and dependent variables. The MPC typically sends out only the first change in each independent variable to be implemented, and repeats the calculation when the next change is required. While many real processes are not linear, they can often be considered to be approximately linear over a small operating range.

Linear MPC approaches are used in the majority of applications with the feedback mechanism of the MPC compensating for prediction errors due to structural mismatch between the model and the process. In model predictive controllers that consist only of linear models, the superposition principle of linear algebra enables the effect of changes in multiple independent variables to be added together to predict the response of the dependent variables. This simplifies the control problem to a series of direct matrix algebra calculations that are fast and robust. When linear models are not sufficiently accurate to represent the real process nonlinearities, several approaches can be used.

The process can be controlled with nonlinear MPC that uses a nonlinear model directly in the control application.

### Stochastic model predictive control for tracking linear systems

The nonlinear model may be in the form of an empirical data fit e. The nonlinear model may be linearized to derive a Kalman filter or specify a model for linear MPC. An algorithmic study by El-Gherwi, Budman, and El Kamel shows that utilizing a dual-mode approach can provide significant reduction in online computations while maintaining comparative performance to a non-altered implementation.