Output feedback controller synthesis for piecewise-affine systems with multiple equilibria

Rodrigues, Luís; Hassibi, Arjang; How, Jonathan P.

doi:10.1109/acc.2000.879508

Cited by 54 publications

(50 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most of the work, e.g. [2], [3], [4], [5] focuses on the stabilization of the system dynamics, meaning that regulation problems are considered, whereas tracking control problems have been given less attention in literature, as recognized by [6]. Also in [7], regulation problems are considered.…”

Section: Introductionmentioning

confidence: 99%

Tracking control for piecewise linear systems using an error space approach: A case-study in sheet control

Bukkems¹,

Heemels

Molengraft

et al. 2008

2008 American Control Conference

View full text Add to dashboard Cite

Abstract-This paper presents the design of tracking controllers for piecewise linear systems, with application to sheet control in a printer paper path. The approach that we will take is based upon an error space approach, which is derived from linear systems theory. We will show that due to the discontinuity in the piecewise linear system, the resulting model in error space consists of both flow conditions, describing the dynamics in each regime, and jump conditions, describing the error dynamics at the switching boundaries. Two types of controllers are proposed that result in either full or partial linearization of the closed-loop error dynamics. To show the effectiveness of the control design approach in practice, the sheet controllers are implemented on an experimental paper path setup.

show abstract

Section: Introductionmentioning

confidence: 99%

Tracking control for piecewise linear systems using an error space approach: A case-study in sheet control

Bukkems¹,

Heemels

Molengraft

et al. 2008

2008 American Control Conference

View full text Add to dashboard Cite

show abstract

“…To enforce continuity of the control inputs at the boundaries one can include actuator dynamics into the plant. The order of the system dynamics will then increase for each input [19]. Nevertheless, continuity of the control input is not a considerable issue for PWM converters.…”

Section: B the Current Loop Controller Designmentioning

confidence: 99%

“…4) Find the corresponding augmented plant matrices in (13). 5) Solve the LMI optimization problem constructed by (17) through (19) using an appropriate solver. The output feedback controller for each cell (14) is obtained as a result of the optimization problem.…”

Section: B the Current Loop Controller Designmentioning

confidence: 99%

Piecewise Affine Control Design for Power Factor Correction Rectifiers

Tahami

Poshtkouhi²,

Ahmadian³

2011

Journal of Power Electronics

View full text Add to dashboard Cite

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method.

show abstract

“…In fact, it was shown in [Rodrigues et al, 2000] that an LQG controller can be designed for each region R i to yield the controller parameters K i , L i and A c i . The parameter m i is obtained from the solution of the equation…”

Section: Remark 11mentioning

confidence: 99%

“…Except when otherwise discussed, the iterative solution algorithms were initialized using a patched LQR or LQG, as described in Remark 11 [Rodrigues et al, 2000]. For all examples with nonlinear plant dynamics, the algorithm in [Rodrigues and How, 2001] was used to approximate these dynamics with a piecewise-affine model.…”

Section: Examplesmentioning

confidence: 99%

Observer-based control of piecewise-affine systems

Rodrigues¹,

How²

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)

Self Cite

View full text Add to dashboard Cite

This paper presents a new synthesis method for both state and dynamic output feedback control of a class of hybrid systems called piecewise-affine (PWA) systems. The synthesis procedure delivers stabilizing controllers that can be proven to give either asymptotic or exponential convergence rates. The synthesis method builds on existing PWA stability analysis tools by transforming the design into a closed-loop analysis problem wherein the controller parameters are unknown. More specifically, the proposed technique formulates the search for a piecewise-quadratic control Lyapunov function and a piecewise-affine control law as an optimization problem subject to linear constraints and a bilinear matrix inequality. The linear constraints in the synthesis guarantee that sliding modes are not generated at the switching. The resulting optimization problem is known to be N P hard, but suboptimal solutions can be obtained using the three iterative algorithms presented in the paper. The new synthesis technique allows controllers to be designed with a specified structure, such as a combined regulator and observer. The observers in these controllers then enable switching based on state estimates rather than on measured outputs. The overall design approach, including a comparison of the synthesis algorithms and the performance of the resulting controllers, is clearly demonstrated in four simulation examples.

show abstract

Output feedback controller synthesis for piecewise-affine systems with multiple equilibria

Cited by 54 publications

References 7 publications

Tracking control for piecewise linear systems using an error space approach: A case-study in sheet control

Tracking control for piecewise linear systems using an error space approach: A case-study in sheet control

Piecewise Affine Control Design for Power Factor Correction Rectifiers

Observer-based control of piecewise-affine systems

Contact Info

Product

Resources

About