PID controller tuning by frequency loop-shaping: application to diffusion furnace temperature control

Grassi, E.; Tsakalis, K.

doi:10.1109/87.865857

Cited by 72 publications

(40 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this section we will see how our design fares with the continuous time PID tuner described in [4]. We will also compare our results with two other methods.…”

Section: Comparison Among Tuning Methodsmentioning

confidence: 96%

“…Despite the recent advancements in control theory that allows for design and Although Ziegler-Nichols is widely popular due its computational simplicity and almost no requirement of a priori knowledge of the plant, it gives up on flexibility of conditions on the plant for a successful implementation and also has a lack of proper tuning "knobs" [4]. While all the above mentioned methods work under specific circumstances, none of them provide enough degrees of freedom for the operator to be able to adjust the parameters to improve on performance based on their judgment and expertise.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Our work derives its roots mostly from the research done in [4]. However, in this work the loop-shaping has been done in comparison to a Glover-McFarlane ℋ ∞ controller [14] instead of an LQR controller.…”

Section: More Recent Work Done By Tsakalis Et Al [11] [4] [12] [13] Umentioning

confidence: 99%

“…The only problem that remains to be solved is to find a good target LTF. In [4], the loop transfer function was selected by first designing an LQR controller for the plant then incorporating it into L. However, in this work, we will be selecting the loop based on an ℋ ∞ controller designed for the plant.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

See 3 more Smart Citations

Discrete-Time PID Controller Tuning Using Frequency Loop-Shaping.

Ashfaque

Tsakalis

2012

IFAC Proceedings Volumes

View full text Add to dashboard Cite

i ABSTRACT Proportional-Integral-Derivative (PID) controllers are a versatile category of controllers that are commonly used in the industry as control systems due to the ease of their implementation and low cost. One problem that continues to intrigue control designers is the matter of finding a good combination of the three parameters -P, I and D of these controllers so that system stability and optimum performance is achieved. Also, a certain amount of robustness to the process is expected from the PID controllers. In the past, many different methods for tuning PID parameters have been developed. Some notable techniques are the ZieglerNichols, Cohen-Coon, Astrom methods etc. For all these techniques, a simple limitation remained with the fact that for a particular system, there can be only one set of tuned parameters; i.e. there are no degrees of freedom involved to readjust the parameters for a given system to achieve, for instance, higher bandwidth. Another limitation in most cases is where a controller is designed in continuous time then converted into discrete-time for computer implementation. The drawback of this method is that some robustness due to phase and gain margin is lost in the process.In this work a method of tuning PID controllers using a loop-shaping approach has been developed where the bandwidth of the system can be chosen within an

show abstract

“…In this section we will see how our design fares with the continuous time PID tuner described in [4]. We will also compare our results with two other methods.…”

Section: Comparison Among Tuning Methodsmentioning

confidence: 96%

Section: Literature Reviewmentioning

confidence: 99%

Section: More Recent Work Done By Tsakalis Et Al [11] [4] [12] [13] Umentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

See 2 more Smart Citations

Discrete-Time PID Controller Tuning Using Frequency Loop-Shaping.

Ashfaque

Tsakalis

2012

IFAC Proceedings Volumes

View full text Add to dashboard Cite

show abstract

“…Sensitivity and complementary sensitivity peaks are used as design objectives for FOPI controllers in Chen et al [17]. Other mixed H 2 /H ∞ loop shaping approaches of PID controller tuning can be found in [18][19][20]. The fundamental improvement of the present work over the above discussed literatures is that it is the first attempt to look at the merits of FOPID controllers vis-à-vis PID controllers, with different range of integrodifferential orders for comparing the trade-offs between several mixed H 2 /H ∞ design objectives.…”

Section: Conflicting Objectives In Loop Shaping Approachmentioning

confidence: 99%

On the Mixed <inline-formula><tex-math notation="TeX">${{\rm H}_2}/{{\rm H}_\infty }$</tex-math></inline-formula> Loop-Shaping Tradeoffs in Fractional-Order Control of the AVR System

Das

Pan

2014

IEEE Trans. Ind. Inf.

View full text Add to dashboard Cite

I. INTRODUCTIONPPLICATION of fractional calculus based control system designs have gained impetus in recent times due to the flexibility and effectiveness that can be gained through such methodologies [1][2]. These controllers use the FO integrodifferential operators as extra tuning knobs which can be tuned to meet additional design constraints and provide additional robustness to the design [3][4]. Merging the concepts of computational intelligence techniques with FO control designs are also being recently explored with encouraging results [5].However applications of fractional order controllers for electrical power and energy systems are still largely unexplored. A few studies have been done for the application of the FOPID controller to the design of the AVR in a power system. In [6][7], the FOPID parameters are tuned for an AVR system with swarm based optimization algorithms which show better time domain performance over that with conventional PID structure. In [8] a multi-objective formalism has been Manuscript received November 17, 2013; revised February 18, 2014 developed and the time domain performance trade-offs of various design objectives have been investigated. The obtained results are mixed, with the PID performing better under some objectives and the FOPID performing better at others. However, all these investigations suffer from a common problem. The objective functions are framed in time domain and the evolutionary algorithms minimize some time domain performance index. Therefore, the obtained results give no indication of other important design focuses like robust stability, disturbance rejection capability etc. To alleviate these issues, the problems in power system control can be framed in frequency domain and the system performance can be expressed in terms of system norms which need to be minimized or maximized. In [9], the FOPID design for an AVR system has been done in frequency domain. The conflicting objectives being maximization of phase margin (for better oscillation damping) and gain crossover frequency (for higher speed of operation) are studied by coupling them with multi-objective evolutionary algorithms. In this paper, we extend this concept to an exhaustive set of frequency domain design criteria for the AVR system and show the achievable set of performances with the FOPID controller structure.The rest of the paper is organized as follows. Section II briefly introduces the theoretical background of the problem with the basics of FO control using system norms. Section III shows the design trade-offs for several combinations of conflicting objectives and compares the best compromise solutions for each controller structure. The paper ends with the conclusion as section IV. II. THEORETICAL BACKGROUND OF FRACTIONAL ORDER CONTROL DESIGN FOR AVR SYSTEM A. Fractional Calculus Based Control SystemsFractional calculus extends the common notion of integer order integration or differentiation to any arbitrary real number. B. AVR System and Controller StructureIn the conventional AVR loop in...

show abstract

Approximate loop shaping in PID parameter adaptation

Tsakalis

Dash

2012

Adaptive Control & Signal

View full text Add to dashboard Cite

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

show abstract

PID controller tuning by frequency loop-shaping: application to diffusion furnace temperature control

Cited by 72 publications

References 14 publications

Discrete-Time PID Controller Tuning Using Frequency Loop-Shaping.

Discrete-Time PID Controller Tuning Using Frequency Loop-Shaping.

On the Mixed <inline-formula><tex-math notation="TeX">${{\rm H}_2}/{{\rm H}_\infty }$</tex-math></inline-formula> Loop-Shaping Tradeoffs in Fractional-Order Control of the AVR System

Approximate loop shaping in PID parameter adaptation

Contact Info

Product

Resources

About