Reference Model Control of the Time Delayed Double Integrator

Abstract

This paper illustrates the reference model-based dead-time compensator (RM-DTC) recently developed for first-order time-delayed systems using a real-time example, and extends this novel approach for a time-delayed double integrator system. RM-DTC enables fully decoupled setpoint tracking and disturbance reconstruction and compensation. The overall structure of RM-DTC includes feedforward control using either a transfer function based implementation or the primary loop which produces a filtered inverse of the model transfer function. The setpoint feedforward is complemented by a disturbanceobserver-based input disturbance reconstruction that also uses the filtered inverse of the plant model. The reference models of setpoint and input disturbance feedforward control allow the introduction of a stabilising PD controller without compromising the nominally independent dynamics of setpoint tracking and disturbance rejection. The main advantage of retaining the full functionality of disturbance reconstruction in RM-DTC is that it enables monitoring and diagnostics of the controlled process, which is important in terms of full automation of running processes representing the fundamental goal of the Industry 4.0 campaign. This surpasses the approaches based on internal model control, which have been modified for unstable systems to achieve internal stability by eliminating the reconstructed disturbance signal from the control loop. The excellent properties of RM -DTCs are illustrated by simulation and real-time control of thermal process.

Performance Portrait Method: An Intelligent PID Controller Design Based on a Database of Relevant Systems Behaviors

“…From the point of view of the universal applicability of the results achieved by means of individual models, ultra-local integral models [ 38 , 56 ] have proved to be important since the first known method [ 57 ] for setting controllers. Although over time it has become possible to achieve a significant improvement in the dynamic properties of the circuit with more complex structures (as, for example, [ 58 ]), due to their simplicity, PID controllers still maintain an exceptional place in practice. As mentioned in Section 2 , in [ 33 , 34 , 35 , 44 ], and in many other ADRC [ 31 , 32 ] or MFC publications [ 29 , 30 ], the use of ultra-local models to approximate different dynamical processes is an important robust control tool in which the system’s internal feedback is included in an equivalent disturbance compensated by an integral action of the controller.…”

“…Regarding the development trends in the field of automatic control, we should note the increase in open solutions, in which the designer does not have to rely on a relatively narrow offer of industrially manufactured controllers with a relatively fixed structure, but implements its own solution using a far more universal base of programmable embedded controllers. This is also related to the development of ever new regulators and structures [ 58 , 60 ], which significantly push the boundaries of achievable circuit characteristics. It follows from this statement that the PPM will also need to be developed for the design of additional controllers with more advanced and efficient disturbance observers.…”

Series PIDA Controller Design for IPDT Processes

“…To illustrate the performance of the proposed PIDA schemes in practice, the same thermo-opto-mechanical system (TOM1A system) as in [14] is used. This process has already been used to test several well-known types of disturbance observer (DOB) under the classical state-space approach, the simplified version based on IPDT models in the ADRC approach, the polynomial approach using inverse process models, and to test the new version of the disturbance reference model control [14,40,[48][49][50][51]. Since each of these DOBs can be combined with higher-order stabilizing controller, and there are too many possible combinations, we decided not to compare all the mentioned approaches within the scope of this paper.…”

“…The thermal process, consisting of a heat source (light bulb), a temperature sensor (Pt1000) and a cooling fan, was approximated by the following IPDT model: K sp = 0.01, T dp = 0.3, similar to that used, for example, in [48,51]. By approximating the fastest possible temperature rise, we meet the requirements derived from the robust stability analysis in [52].…”

A unified design approach for control integrating processes with time delay

“…The controllers were obtained using analytical rules based on curve fitting techniques [ 26 ]. Huba et al extended the reference model-based dead-time compensator for double integrator with time delay system, the control performance is excellent although the method is complicated [ 27 ].…”