Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes

Huba, Mikuláš; Bisták, Pavol; Vrančić, Damir

doi:10.3390/math11010030

Cited by 7 publications

(8 citation statements)

References 39 publications

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“…For T e = T dp (center, Figure 3), the control signal of the PD 7 7 R controller shows some spikes thanks to the "aggressive" setting. This shows that the tuning parameter T em of the individual PD m n R controller cannot be arbitrarily small with regard to the stability of closed loops (previously analyzed for an IPDT system and m ∈ [0, 2] in [28]).…”

Section: Closed-loop Responses Based On the Ipdt Model Of The Sopdtuz...mentioning

confidence: 82%

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

Bistak,

Huba,

Vrancic

2024

Applied Sciences

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The proposed practice-oriented controller design (POCD) aims at stabilizing the system, reconstructing and compensating for disturbances while achieving fast and smooth step responses. This is achieved through a simple approach to process identification and controller tuning that takes into account control signal constraints and measurement noise. The proposed method utilizes POCD by eliminating the influence of the unstable zero dynamics of the inverse-response processes, which limits the achievable performance. It extends the previous work on PI and PID controllers to higher-order (HO) automatic reset controllers (ARCs) with low-pass filters. It is also extended according to POCD requirements while maintaining the simplified process model. The final result is an extremely simple design for a constrained controller that provides sufficiently smooth and robust responses to a wide family of HO-ARCs with odd derivatives, designed using integral plus dead time (IPDT) models and tuned by the multiple real dominant pole method (MRDP) and the circle criterion of absolute stability. The proposed design can be considered as a generalization of the Ziegler and Nichols step response method for inverse response processes and HO-ARCs.

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Section: Closed-loop Responses Based On the Ipdt Model Of The Sopdtuz...mentioning

confidence: 82%

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

Bistak,

Huba,

Vrancic

2024

Applied Sciences

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“…The "nominal" IPDT system is denoted by omitting the subscripts p in (8). Despite the very simple model, for precise overtuned approximations (see e.g., [43]), PIDA controllers derived from an IPDT model (8) can provide excellent performance for a much wider range of processes possibly of higher order.…”

Section: Process Approximation By Ipdt Modelmentioning

confidence: 99%

“…The original approach of Ziegler and Nichols uses the tangent line passing through the inflection point of the measured process response. However, due to the poor numerical properties of such an approach and the robust stability analysis in [43], the following approximation…”

Section: Step Response Based Approximation Of Stable Process By Ipdt ...mentioning

confidence: 99%

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

Huba,

Bistak,

Vrancic

2023

Mathematics

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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.

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“…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]. When controlled by an embedded Arduino-Due controller, the process can be represented by a simple block in the Matlab/Simulink programming environment with a sampling period greater than T s = 15 ms. To highlight the differences between each of the considered modifications of the PIDA controller, which increase with the value of T d , the process delay was artificially increased by 0.7 s using a Simulink time delay block, so that the values T dp = 1s; K sp = 0.01; T e = 0.6s (41) were taken into account in the design.…”

Section: Real-time Temperature Controlmentioning

confidence: 99%

Series PIDA Controller Design for IPDT Processes

2023

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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.

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Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes

Cited by 7 publications

References 39 publications

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

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

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

Series PIDA Controller Design for IPDT Processes

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