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

Abstract

The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) process models. The controller output constraints are taken into account by inserting the smallest numerator time constant of the controller transfer function into the positive feedback loop representing the automatic reset (integral) term. In the series realization of the proportional–integral–derivative–acceleration (PIDA) controller (and other controllers with even derivative degree), the time constant mentioned is complex, so only the real part of the time constant has been used so far. Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. In this article, the impact of the tuning parameter on the overall dynamics of the control loop is studied by simulation. In addition, an evaluation of the stability of the closed-loop control system is performed using the circle criterion in the frequency domain. The analysis has shown that the approximation of the complex zero by its real part and modulus leads to a near optimal response to the set point tracking. The disturbance rejection can be significantly improved by increasing the tuning parameter by nearly 50%. In general, the tuning parameter can be used to find a compromise between servo and regulatory control. The robustness and applicability of the proposed controller is evaluated using a time-delayed process with first-order dominant dynamics when the actual transfer function is much more complicated than the IPDT model. A comparison of the proposed MRDP-PIDA controller with series PI, PID and PIDA controllers based on a modified SIMC method has shown that the MRDP-PIDA controller performs better than the SIMC method, although the SIMC uses a more complex process model.

Practice-Oriented Controller Design for an Inverse-Response Process: Heuristic Optimization versus Model-Based Approach

“…This represents a special case of HO-ARC, which was considered in [17] for m ∈ Z + , m ∈ [0, 5]. The separate treatment of even and odd values of m in the constrained control case is based on the requirement to achieve conditions for absolute stability by factorizing the zeros of the controller transfer function derived using the multiple real dominant pole (MRDP) method (see, e.g., [18], which deals with the case m = 2, and [24], which presents a particular solution for m = 4).…”

“…This can be done using the circle criterion of absolute stability [9,32,33]. Here, the PD m n R controller from Figure 1 must be converted into the standard non-linear form, which expresses deviations from a required steady state and is composed of the saturation nonlinearity and the associated linear loop blocks [17,18]…”

“…The use of HO-ARCs on IPDT models in [17,18] has shown that their MRDP design for odd m directly satisfies the conditions for absolute stability. However, for m > 1, this is only true for suitably chosen T e .…”

“…Several recently published papers (see, e.g., [17,18]) have shown that the essential idea of these historical and still-existing in industry automatic reset controllers (ARCs) is the use of a positive feedback from the controller output (see Figure 1). The problem is that the implementation has been neglected for a long time.…”