PI control of discrete linear repetitive processes

Sulikowski, Bartłomiej; Gałkowski, Krzysztof; Rogers, Eric; Owens, D.H.

doi:10.1016/j.automatica.2006.01.012

Cited by 27 publications

(16 citation statements)

References 5 publications

(4 reference statements)

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“…The control law here does not require an observer to reconstruct the current pass state vector (most of the currently available control law design methods assume direct access to all entries in the current pass state vector). Previous work Sulikowski, Gałkowski, Rogers, and Owens (2006) has considered the design of PI control laws for discrete linear repetitive processes but the results here do not follow by substitution, i.e. simple rearrangement of these previous results.…”

Section: Pi Controlmentioning

confidence: 84%

PI output feedback control of differential linear repetitive processes

2008

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Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass-to-pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws. These are for the sub-class of so-called differential linear repetitive processes which arise in applications areas such as iterative learning control. They show how a form of proportional-integral (PI) control based only on process outputs can be designed to give stability plus performance and disturbance rejection.

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Section: Pi Controlmentioning

confidence: 84%

PI output feedback control of differential linear repetitive processes

2008

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“…To accomplish this we use a combination of state and output feedback. As discussed in [14], an appropriate choice for such a 2D control law is the following:…”

Section: B Augmented Error Model With Integral Informationmentioning

confidence: 99%

“…Following [14], we integrate the error information propagating across the cycles. This integral information can be defined with the help of a new variable:…”

Section: B Augmented Error Model With Integral Informationmentioning

confidence: 99%

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Repetitive Model Predictive Control using Linear Matrix Inequalities

Tiwari

Kothare

2008

2008 American Control Conference

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Repetitive systems can be characterized by two time variables, namely, the finite time within each repeating cycle and the cycle index, each embodying a distinct connotation of time. Conventional optimal control theory does not explicitly account for this two dimensional (2D) description of repetitive systems. We propose a new formulation for control of repetitive systems using Model Predictive Control (MPC) that explicitly incorporates a 2D representation of the system. The proposed formulation uses a 2D Lyapunov function and the stability requirements are established along each time dimension of the system. The resulting controller synthesis problem is expressed in convex form using Linear Matrix Inequalities (LMIs). The approach allows explicit incorporation of input/output constraints in the controller design. Two examples illustrate the applicability of the proposed approach.

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“…Recently, the 2-D modeling theory is also frequently applied as an analysis tool to some control problems, e.g., iterative learning control [3], repetitive process control [4] and PI control of discrete linear repetitive processes [5], etc. In [6], the problem of stability and l 1 -gain analysis for positive 2D T-S fuzzy state-delayed systems in the second FM model has also been investigated.…”

Section: Introductionmentioning

confidence: 99%