Application of time-series methods to disturbance estimation in predictive control problems

Abstract

Disturbance effect is a very important issue to be analyzed and considered in any control problem. Models representing the disturbance effect on the process variable are usually obtained for this purpose. These models are useful to design, for instance, classical feedforward compensators. However, when predictive control strategies are being used, no only the model capturing the disturbance effect is necessary, but that future estimations of the disturbances would be also extremely useful to get advance in the prediction capabilities. Measurable disturbances can be represented as time-series data and processed in order to estimate future variations. Therefore, this paper is focused on studying how well-known time-series methods can be used to obtain disturbance forecasts in order to be taken into account in predictive control algorithms. The methods used here have two main objectives: to detect the nature and properties of any variable represented as time-series data, and second, to forecast future behavior based on acquired data series. An example using the solar radiation measured from an industrial greenhouse is presented to show how these future estimations can be obtained.

Application of Predictive Feedforward Compensator to Microalgae Production in a Raceway Reactor: A Simulation Study

“…It was shown that an improved disturbance compensator can be obtained by setting the error in the feedback structure equal to zero. This assumption can be confirmed by the GPC control law provided in Equation (8). Taking into account that the set point is set to w(j) = y(t) for j = t + d + 1, .…”

“…In previous works, [8,9,24], a study of different forecasting techniques was performed in order to extend the functionality of the MPC approach. The availability of the future signal values are used to improve the prediction mechanism accuracy, which results in better performance of the MPC controller [9].…”

“…The one sampling instance ahead prediction is obtained byx k+1 = S k + b k and the m− sampling periods forecast is obtained usignx k+m = S k + mb k . The initial values for S k and b k were set to S k = x 1 and b k = (x 1 + x 2 + x 3 )/3 as recommended in [8,9]. Moreover, the values for φ and γ ∈ (0, 1) can be obtained via optimization techniques as described in [8].…”

“…, t + d + N, and the system is in a steady state, then u p = ∆u(t − 1) = 0. Equation (8) representing control law results in:…”

Measurable Disturbances Compensation: Analysis and Tuning of Feedforward Techniques for Dead-Time Processes

“…In industrial processes, the basic control structure consists of a feedback controller, since it is capable of providing reference tracking, while reducing the influence of plant-model mismatch and compensating for process disturbances [1,5]. It is usual that the control system only focuses on one of the listed related to the incorporation of future disturbance information [20,21]. The MPC feedback and feedforward co-design procedure results in a tradeoff, where the controller tuning procedure is carried out taking into account the most important aspects.…”