Dead-Time Compensation for the First-Order Dead-Time Processes: Towards a Broader Overview

Abstract

The article reviews the results of a number of recent papers dealing with the revision of the simplest approaches to the control of first-order time-delayed systems. The concise introductory review is extended by an analysis of two discrete-time approaches to dead-time compensation control of stable, integrating, and unstable first-order dead-time processes including simple diagnostics of the model used and focusing on the possibility of simplified but reliable plant modelling. The first approach, based on the first historically known dead-time compensator (DTC) with possible dead-beat performance, is based on the reconstruction of the actual process variables and the compensation of input disturbances by an extended state observer (ESO). Such solutions play an important role both in a disturbance observer (DOB) based control and in an active disturbance rejection control (ADRC). The second approach considered comes from the Smith predictor with two degrees of freedom, which combines feedforward control with output disturbance reconstruction and compensation by the parallel plant model. It is shown that these two approaches offer advantageous properties in the case of actuator limitations, in contrast to the commonly used PID controllers. However, when applied to integrating and unstable first-order systems, the unconstrained and possibly unobservable output disturbance signal of the second solution must be eliminated from the control loop, due to the hidden structural instability of the Smith predictor-like solutions. The modified solutions, usually referred to as filtered Smith predictor (FSP), then no longer provide a disturbance signal and thus no longer fully fit into the concept of Industry 4.0, which is focused on further optimization, predictive maintenance in dynamic systems, diagnosis, fault detection and fault identification of dynamic processes and forms the basis for the digitalization of smart production. Nevertheless, the detailed analysis of the elimination of the unstable disturbance response mode is also worth mentioning in terms of other possible solutions. The application of both approaches to the control of a thermal process shows almost equivalent quality, but with different dependencies on the tuning parameters used. It is confirmed that a more detailed identification of the controlled process and the resulting higher complexity of the control algorithms does not necessarily lead to an increase in the resulting quality of the transients, which underlines the importance of the simplified plant modelling for practice.

The Regulation of an Electric Oven and an Inverted Pendulum

“…C s d dt T s = q − q g − q r C g d dt T g = q g C r d dt T r = q r − q a (3) Considering Equations ( 1) and ( 2), the differential equations that describe the mathematical model of the electric oven are as follows: C r (4) where q is the thermal power, R is the coefficient of thermal resistivity, T is the temperature, the subscript g is the product to be heated (aluminum), the subscript s is the oven, the subscript r is the insulation, the subscript a is the air of the environment,u is the supply of electric potential, k is the thermal conductivity, and C is the thermal capacitance. The values of the constants can be seen in Table 1.…”

“…There are several kinds of controls: proportional integral derivative (PID) controls are studied in [1,2], model-based controls are discussed in [3,4], and disturbance rejection controls are designed in [5,6]. For these controls, there are two types of objective-tracking, which involves the following of a time-varying set point, and regulation, which involves the following of a constant set point.…”

Reference Model Control of the Time Delayed Double Integrator

“…Therefore, it will be useful to start clarifying the increased tuning complexity by explaining particular tuning steps, preferably from the simplest tasks. To illustrate the use of the RM-DTC design and practical problems associated with its application, we will consider the thermal process control discussed already in [31], [60], [64]. The choice of this process is motivated by several aspects -from a physical point of view, it is a highly nonlinear and time-variable higher-order process posing a challenge for robust control -only due to the fact that the concept of a nominal dynamics is strongly questionable.…”

“…Parameters of the plant model identified in the vicinity of the selected operating point and applied in works [31], [64] can be given as…”

“…SP represents the best known structure for the control of time-delayed systems by combining the advantage of an independent design of dynamic feedforward control and of disturbance reconstruction and compensation. However, the use of integrating process models in SP leads to unobservable and unconstrained output disturbances [30], [31]. Moreover, equivalent output disturbances may increase beyond all limits in the presence of constant input disturbances [32].…”