Series PIDA Controller Design for IPDT Processes

Abstract

This paper discusses optimal design of the series proportional–integral–derivative–accelerative (PIDA) controller for integral-plus-dead-time (IPDT) plants. The article starts with the design of disturbance reconstruction and compensation based on proportional-derivative-accelerative (PDA) stabilizing controllers. It shows that by introducing positive feedback by a low-pass filter from the (limited) output of the stabilizing PDA controller, one gets disturbance observer (DOB) for the reconstruction and compensation of input disturbances. Thereby, the DOB functionality is based on evaluating steady-state controller output. This DOB interpretation is in full agreement with the results of the analysis of the optimal setting of the stabilizing PDA controller and of its expanded PIDA version with positive feedback from the controller output. By using the multiple real dominant pole (MRDP) method, it confirms that the low-pass filter time constant in positive feedback must be much longer than the dominant time constant of the stabilized loop. This paper also shows that the constrained PIDA controller with the MRDP setting leads to transient responses with input and output overshoots. Experimentally, such a constrained series PIDA controller can be shown as equivalent to a constrained MRDP tuned parallel PIDA controller in anti-windup connection using conditional integration. Next, the article explores the possibility of removing overshoots of the output and input of the process achieved for MRDP tuning by interchanging the parameters of the controller transfer function, which was proven as very effective in the case of the series PID controller. It shows that such a modification of the controller can only be implemented approximately, when the factorization of the controller numerator, which gives complex conjugate zeros, will be replaced by a double real zero. Neglecting the imaginary part and specifying the feedback time constant with a smaller approximative time constant results in the removal of overshoots, but the resulting dynamics will not be faster than for the previously mentioned solutions. A significant improvement in the closed-loop performance can finally be achieved by the optimal setting of the constrained series PIDA controller calculated using the performance portrait method. This article also points out the terminologically incorrect designation of the proposed structure as series PIDA controller, because it does not contain any explicit integral action. Instead, it proposes a more thorough revision of the interpretation of controllers based on automatic reset from the controller output, which do not contain any integrator, but at the same time represent the core of the most used industrial automation. In the end, constrained structures using automatic reset of the stabilizing controller output can ensure a higher performance of transient responses than the usually preferred solutions based on parallel controllers with integral action that, in order to respect the control signal limitation, must be supplemented with anti-windup circuitry. The excellent properties of the constrained series PIDA controller are demonstrated by an example of controlling a thermal process and proven by the circle criterion of absolute stability.

Parametrization and Optimal Tuning of Constrained Series PIDA Controller for IPDT Models

“…Several recent works have shown that it is possible to design higher order constrained controllers. These structures combine stabilizing controllers (using higher-order derivatives) with automatic reset, guaranteeing disturbance reconstruction and compensation of disturbances [26,27,35]. Automatic-reset and hyper-reset (pre-act)-based controllers were invented before the World War II, although they have largely disappeared from the literature due to the dominance of linear control theory.…”

“…Due to the interpretations by linear control theory, even the series controllers are not well understood in practice. As a result, users are not aware of the role of disturbance observers in automatic reset controllers, although it is important for optimal controller tuning and constrained system control (see also [26,27,35,39]). Recently, clarification of some key conceptual differences between series and parallel controllers with higher-order derivatives has enabled substantial progress in the design of constrained controllers for the simplest processes that can be adequately approximated by the first-order models with dead time.…”

“…can form a series PIDA controller by introducing a positive feedback loop including a low-pass filter with a time constant T i (see, e.g., [26,27,35])…”

“…However, outside the range of proportional control, the automatic reset behaves completely differently from the parallel PIDA controller with an explicit integrator. In order to prevent the redundant integration of an explicit integrator from causing the controller windup, various antiwindup measures must be applied [26,40]. On the other hand, some authors discuss anti-windup measures [32,41] also for series PI and PID controllers, although they have inherent anti-windup protection.…”

“…Thereby, the series structure was chosen regarding its acceptance in industrial control systems. The MRDP method presented in [26][27][28][29] showed that the series PI and PID controllers can be extended to the whole family of constrained controllers with higher-order derivatives. In this way, we can create an alternative to the higher order PID controllers that realize fractional order PID control [23].…”