# A Set of Active Disturbance Rejection Controllers Based on Integrator Plus Dead-Time Models +
###### Abstract  
The paper develops and investigates a novel set of constrained-output robust controllers with selectable response smoothing degree designed for an integrator-plus-dead-time (IPDT) plant model. The input-output response of the IPDT system is internally approximated by several time-delayed, possibly higher-order plant models of increasing complexity. Since they all contain a single integrator, the presented approach can be considered as a generalization of active disturbance rejection control (ADRC). Due to the input/output model used, the controller commissioning can be based on a simplified process modeling, similar to the one proposed by [PERSON] and [PERSON]. This allows it to be compared with several alternative controllers commonly used in practice. Its main advantage is simplicity, since it uses only two identified process parameters, even when dealing with more complex systems with distributed parameters. The proposed set of controllers with increasing complexity includes the stabilizing proportional (P), proportional-derivative (PD), or proportional-derivative-acceleration (PDA) controllers. These controllers can be complemented by extended state observers (ESO) for the reconstruction of all required state variables and non-measurable input disturbances, which also cover imperfections of a simplified plant modeling. A holistic performance evaluation on a laboratory heat transfer plant shows interesting results from the point of view of the optimal least sensitive solution with smooth input and output. ADRC; temperature control; performance optimization Article  
A Set of Active Disturbance Rejection Controllers Based on Integrator Plus Dead-Time Models +
Footnote †: _Applied_  
M.M. by disturbance-observer-based integral action introduced to reconstruct and compensate input disturbances. At the same time, the considered structures have been used to illustrate the core ideas behind the commonly used, but usually not sufficiently clarified, ADRC structures. Since with each simplification we get closer to oversimplification, the method should be presented clearly enough and should be compatible to other alternative control designs [21], especially those tending to higher-order controllers [22] with a more effective noise attenuation. In principle, ADRC uses the state observer and the controller designed in the state-space. The ADRC is based on the extended state observer (ESO). In addition to the reconstruction of the state of the considered system, it also reconstructs the overall input disturbance, which is the result of external disturbances and model inaccuracies. The work of [23] has already brought the first such solutions using the approaches used today in ADRC and disturbance-observer based control. Unlike PID controllers, which do not consider the exact reconstruction of disturbances and pay for it with the emergence of windup-effect, resistance to control signal limitations is one of the basic advantages of systems with reconstruction of input or output disturbances. Use of the simplest integrative models represents another dominant feature of ADRC. Simplified modeling of systems simplifies their identification as well as the design and implementation of controllers. Modeling inaccuracies are taken into account in the reconstructed disturbance and compensated by the increased robustness of the obtained solutions. ADRC was introduced by [PERSON] [24] and further developed by [PERSON] [25; 26] and his collaborators extensively. However, the basic advantages of the simplifications on which the ADRC is based have been used by a number of other authors, not to mention only [PERSON] and [PERSON] and their method for experimental setup of controllers [27]. This paper focuses on aspects related to time delays that are always present, while showing the possibilities of using higher-order controllers.