(299e) Disturbance Modeling for Model Predictive Control Using Neural Networks

The use of model predictive control (MPC) for an industrial deployment requires two types
of models. First, an actuator-to-sensor model that predicts the plant measurements based on the
manipulated control inputs. This model is usually obtained by a black-box or grey-box system
identification procedure applied on process data. Second, a disturbance model that is used to make
feedforward predictions of disturbances or estimate the plant-model mismatch and disturbances
from measurements in real-time. The predictions using both these models are used online in an
optimization problem to determine the actuator movements.

The choice of the disturbance model depends on the control objective. For a setpoint tracking
MPC application, this model is chosen to be integrators at a minimum to maintain zero offset in the
controlled outputs (Pannocchia and Rawlings, 2003). Additional disturbance models can be used
along with the integrators to make feedforward predictions of disturbances and achieve improved
closed-loop performance with the MPC controller. Over the past decade, the improvement in data
acquisition and sensing technology in various industries provides additional information in form of
auxiliary measurements to develop more accurate disturbance models. Examples of these types of
measurements include images in crystallization processes (Qu et al., 2006; Wang et al., 2008), and
features such as time-of-day, time-of-year for heat disturbance modeling in heating, ventilation, and
air-conditioning (HVAC) applications. The current industrial approach for developing feedforward
disturbance models is to use classical nonlinear regression techniques with some hand-engineered
features designed based on the auxiliary measurements as the predictor variables. Neural networks
can be used to upgrade this industrial disturbance modeling approach and provide an accurate and
convenient method to exploit information from the auxiliary measurements. In this talk, we present
a systematic framework for feedforward disturbance modeling in MPC using neural networks and
demonstrate improvement in closed-loop performances via several case studies.

To start, we first demonstrate the application of our proposed system identification procedure
via simulation studies on a HVAC example. The unmeasured heat generated due to the occupants
in commercial buildings is the primary disturbance and its forecast is required in the real-time
optimization layer (Patel et al., 2016) for industrial deployment. The model identification process
goes as follows. We first perform the usual system identification experiments and use the collected data
to identify a grey-box model. We then use the estimated model to determine a residual signal on
historical closed-loop operational data. A neural network is then trained on this residual signal
with the auxiliary measurements as inputs to the network. We use the identified grey-box and the
neural network in the MPC controller and compare the closed-loop performance with a traditional
feedforward disturbance modeling approach. We highlight that the use of neural networks even
as the disturbance model introduces state estimation challenges due to the nonlinear function
represented by neural networks. This challenge can be addressed with moving horizon estimation
and with the use of advanced nonlinear optimization solvers.

Finally, we move on to challenging system identification problems. We present one case study in
which classical nonlinear regression techniques for feedforward disturbance modeling can result in
poor closed-loop performance. We proceed with the identification procedure as discussed previously
and train a neural network on the residual signal obtained using an identified grey-box model. The
primary difficulty with any hybrid grey-box and data-driven process modeling approach is the
appropriate segregation of the two types of models. We report the data requirements for building
the models to obtain good closed-loop performance and present a comparison with the standard
disturbance modeling approach

References -

G. Pannocchia and J. B. Rawlings. Disturbance models for offset-free MPC control. AIChE J., 49
(2):426-437, 2003.

N. R. Patel, M. J. Risbeck, J. B. Rawlings, M. J. Wenzel, and R. D. Turney. Distributed economic
model predictive control for large-scale building temperature regulation. In American Control
Conference, pages 895-900, Boston, MA, July 6-8, 2016.

H. Qu, M. Louhi-Kultanen, and J. Kallas. In-line image analysis on the effects of additives in batch
cooling crystallization. J. Cryst. Growth, 289:286-294, 2006.

X. Z. Wang, K. J. Roberts, and C. Ma. Crystal growth measurement using 2d and 3d imaging and
the perspectives for shape control. Chemical Engineering Science, 63(5):1173-1184, 2008.