Auto-tuning PID using loop-shaping ideas

Gaikwad, S.V.; Dash, S.; Stein, G.

doi:10.1109/cca.1999.806712

Cited by 6 publications

(6 citation statements)

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“…Two of the most relevant techniques are relay feedback (Hagglund and Astrom, 1985), and set point relay (Luo et al, 1998). Some recent findings in this area are iterative tuning with cost minimization (Akerblad et al, 2000) and Auto-tuning of PID using Loop-shaping ideas (Gaikwad et al, 1999). These techniques do not provide solution for on-line controller improvement in an automated way for nonlinear processes.…”

Section: Auto-tuningmentioning

confidence: 97%

Design and implementation of a fuzzy supervisor for on-line compensation of nonlinearities: An instability avoidance module

Sanjuán

Kandel

Smith

2006

Engineering Applications of Artificial Intelligence

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Section: Auto-tuningmentioning

confidence: 97%

Design and implementation of a fuzzy supervisor for on-line compensation of nonlinearities: An instability avoidance module

Sanjuán

Kandel

Smith

2006

Engineering Applications of Artificial Intelligence

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“…This approach relies on a brilliant observation, due to G. Stein, that the loop transfer function can be directly optimized to approximate a prescribed target, based on input-output data alone [28,29]. It inherently makes use of a natural frequency weighting by the target loop sensitivity and can be used independent of input signal saturation, but requires the a priori knowledge of a nearly feasible target loop.…”

Section: Direct Identification Of the Pid Controller Parametersmentioning

confidence: 99%

“…One particular design point of view that has emerged and has been well-received in applications [20] is the delivery of multiple tunings, e.g., on a Pareto optimal curve, that allow the user to select among different performance-robustness metrics. A typical implementation of this idea involves high-level tuning parameters, such as closed-loop bandwidth, damping, etc., and the use of simulation to visualize the performance of the tuning with the identified model.…”

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confidence: 99%

Identification for PID Control

Tsakalis

Dash

2012

PID Control in the Third Millennium

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Proportional-Integral-Derivative (PID) controllers are still the most common control algorithms used in the process industry. PID is a reduced complexity controller that provides the bare essentials for control: an integrator for low-frequency disturbance attenuation, and two-zeros-worth of phase lead for stabilization and phase margin adjustment. Practical experience shows that its tuning can be accomplished with very little information about the plant from the point of view of standard design techniques. This celebrated feature carefully underplays the fact that as a limited degree of freedom controller, the PID may be unsuccessful in controlling arbitrary plants and the tuning techniques may become progressively more complicated as the class of plants is expanded. For example, it is quite straightforward to show that PID controllers can always stabilize a single integrator and that they cannot stabilize a chain of three integrators. Furthermore, techniques that have a well established track record for the typical process control application, e.g., a heating process, are shown to fail when the plant contains flexible modes, e.g., a pendulum with flexible shaft. It is in these cases where PID control must ultimately escape the back-of-the-envelope calculations and the nearly-model-free framework. The most popular controller can now utilize the most recent computational methods and design understanding. The benefits are in the hardware simplicity, including anti-windups and fast execution times, and ease of scheduling.Many methods for PID tuning are found in the literature, and [1] is an excellent introduction. Typical examples include an analytic derivation of the tuning, based on

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“…Following , the development of an online direct adaptive algorithm that approximates the off‐line FLS solution begins with the transformation of the error operator minimization into an error signal minimization. Such a transformation essentially aims to utilize the plant input–output data instead of its transfer function (or any other model) in order to solve the optimization problem .…”

Section: The Scripthmathclass-rel∞/fb Adaptation Algorithm For Pid Tumentioning

confidence: 99%

“…Next, the reparametrization of the same loop‐shaping objective described in establishes a linear model relationship for the PID parameters, allowing for their direct update with a variety of estimation algorithms, such as least squares (LS). In particular, when this parametrization is combined with the FB idea of , we obtain an adaptation algorithm that approximates the constrained minimization of the operator norm of the error system rather than the energy of the error itself.…”

Section: Introductionmentioning

confidence: 99%

Approximate loop shaping in PID parameter adaptation

Tsakalis

Dash

2012

Adaptive Control & Signal

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This paper discusses the use of H-infinity approximation for the online adaptation of PID controller parameters. For a frequency loop-shaping control objective, it is possible to adapt the PID parameters directly with linear model estimation algorithms. Standard least squares algorithms are common solutions for this problem, but their estimates exhibit a well-known strong dependence on the properties of the excitation. This drawback becomes more pronounced for systems where the modeling mismatch is large, as is frequently the case in PID control. In an alternative formulation of the estimation problem, we use a filter-bank to decompose the error signal to different components and minimize approximately the H-infinity norm of the sensitivity-weighted error operator. This approach results in a more consistent estimate of the optimal PID parameters, at the expense of higher excitation requirements. It also allows for the computation of a 'health indicator' to describe the confidence in the estimated parameters. The practical implication of this observation is that PIDs can be tuned more reliably, even in cases of large mismatch between the target and the feasible loop shapes. It also suggests a general theme where a min-max optimization of an operator error provides an advantage over signal error optimization. The key aspects of the algorithm are illustrated by numerical examples.APPROXIMATE H 1 LOOP SHAPING 137 ‡ Note that, although parsimony is not a strict requirement in adaptive control (e.g., over-parametrized controllers), the robustness of such schemes is questionable at best. § Situations of insufficient excitation are not of interest here, because we have shown that they are prone to large parameter misadjustment and adaptation bursting in the pre-sense of arbitrarily small disturbances [25].Notice that, because of the special PID structure, the estimation error has the familiar linear-in-theparameters formnew cost functional is quadratic in Â kC1 and can be written as follows, regardless of the update method for Â k142 K. S. TSAKALIS AND S. DASHwhere S and P are the gradient and Hessian of the functional J and can be computed recursivelyThe descent direction is now computed by solvingwhere I is the set of indices for which the partial costs are 'close' to the maximum, for example, within 10%. This is carried out to prevent the subsequent line search from producing zero step size caused by the non-smooth boundary of the constraints (other computations of a descent direction are also possible). It is the use of the expression (5) that this computation is fairly simple and can be performed by finding the unconstrained solution and then projecting on the constraint set. Finally, given the descent direction Â kC1 , we compute the step size by solving the line-search problem opt D arg min

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Auto-tuning PID using loop-shaping ideas

Cited by 6 publications

References 0 publications

Design and implementation of a fuzzy supervisor for on-line compensation of nonlinearities: An instability avoidance module

Design and implementation of a fuzzy supervisor for on-line compensation of nonlinearities: An instability avoidance module

Identification for PID Control

Approximate loop shaping in PID parameter adaptation

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