Variable-Structure Control Design of Switched Systems With an Application to a DC–DC Power Converter

Cardim, Rodrigo; Teixeira, Marcelo Carvalho Minhoto; Assunção, Edvaldo; Covacic, Márcio Roberto

doi:10.1109/tie.2009.2026381

Cited by 102 publications

(52 citation statements)

References 33 publications

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“…Switched systems have attracted the attention of the scientific community in the last decades because of their high potential for practical applications, as for instance, in power electronics [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

“…Hence, the control goals consist in determining a set of attainable equilibrium points and a switching rule that guides any trajectory of the system, starting from an arbitrary initial condition, to the desired equilibrium, which can not be shared by any of the subsystems. The literature presents some results about stabilisation based on optimal control, see [2,16,17], and on Lyapunov method approach, see [1,3,[18][19][20][21][22][23][24][25], where [19,25] deal with sampled-data implementation. Most of them, as for instance, [3,18] are based on a quadratic Lyapunov function and show that the existence of a stable convex combination of the subsystems state-space matrices is a sufficient condition for global asymptotic stability.…”

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confidence: 99%

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State feedback ℋ _∞ control design of continuous‐time switched affine systems

Deaecto

Santos

2015

IET Control Theory & Applications

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This study deals with state feedback H ∞ control design of continuous-time switched affine systems. The main purpose is to design a set of state feedback gains together with a switching function assuring global asymptotic stability of a desired equilibrium point. The equilibrium point belongs to a set of attainable ones to be determined. Moreover, the control design must take into account a pre-specified upper bound to the L 2 gain from the external input to the controlled output. Two different switching functions are proposed and discussed. The first one depends only on the state and the other depends also on the external input. The results are compared with recent ones available in the literature to date, as for instance, those based on a max-type Lyapunov function and those commonly used to assure practical stability. Numerical examples illustrate the theoretical results and are used for comparisons. IntroductionSwitched systems have attracted the attention of the scientific community in the last decades because of their high potential for practical applications, as for instance, in power electronics [1-3].They represent a subclass of hybrid systems characterised by having a switching rule that selects at each instant of time one of the available subsystems. This switching rule can be arbitrary, see [4], or a control variable that must be designed in order to assure stability and good performance for the overall system. Another possible control technique is based on sliding mode control, as it has been proposed in [5]. For switched linear systems, the literature presents several important results concerning the control design of a switching rule based on state feedback [6, 7] and on output feedback [8,9]. One interesting characteristic is that the switching strategy can assure global asymptotic stability even if all subsystems are unstable. Moreover, the recent paper [10] shows that, even if all subsystems are stable, a consistent switching rule can enhance the global performance when compared with that of each isolated subsystem. The articles [11][12][13] and the books [14,15] are surveys on this topic. Switched affine systems are more involved since they present several equilibrium points composing a region on the state space. Hence, the control goals consist in determining a set of attainable equilibrium points and a switching rule that guides any trajectory of the system, starting from an arbitrary initial condition, to the desired equilibrium, which can not be shared by any of the subsystems. The literature presents some results about stabilisation based on optimal control, see [2,16,17], and on Lyapunov method approach, see [1,3,[18][19][20][21][22][23][24][25], where [19,25] deal with sampled-data implementation. Most of them, as for instance, [3,18] are based on a quadratic Lyapunov function and show that the existence of a stable convex combination of the subsystems state-space matrices is a sufficient condition for global asymptotic stability. Another recent technique is based on a max-type Lyapunov ...

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

State feedback ℋ _∞ control design of continuous‐time switched affine systems

Deaecto

Santos

2015

IET Control Theory & Applications

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“…Infinite frequency is the ideal operating frequency of SMC. However, switching frequencies of power converters must be restricted within a practical range [3]- [5].…”

Section: Introductionmentioning

confidence: 99%

PWM-Based Sliding Mode Controller for Three-Level Full-Bridge DC-DC Converter that Eliminates Static Output Voltage Error

Liu¹,

Xiao²,

Ma³

et al. 2015

Journal of Power Electronics

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This paper proposes a pulse width modulation (PWM)-based sliding mode controller (SMC) for a full-bridge DC-DC converter that can eliminate static output voltage error. Hysteretic SMC in DC-DC converter does not have a fixed switching frequency, and applying hysteretic SMC to full-bridge converters is difficult. Fixed-frequency SMC, which is also called PWM-based SMC, based on equivalent control overcomes these shortcomings. However, the controller order reduction in equivalent control in PWM-based SMC causes static output voltage error. To resolve this issue, an integral item is added to the PWM-based SMC. Sliding mode coefficients are designed by applying a standard second-order system to the sliding mode surface. The effect of adding an integral item on the controller is analyzed, and an integral coefficient design method is proposed. Experiment results on a three-level full-bridge DC-DC converter verify the control scheme and design method proposed in this paper.

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“…Nonlinear control concepts such as passivity or flatness are exploited in [3], [7], while [4] present fuzzy controllers which deal with the nonlinearities of the converter. Model predictive methods are shown in [5] while synthesis methods based on optimization algorithms and LMIs are shown in [6], [8]- [12].…”

Section: Introductionmentioning

confidence: 99%

Robust gain-scheduled control of dc-dc converters: An LMI approach

Olalla

Queinnec

Leyva

2011

2011 IEEE International Conference on Control Applications (CCA)

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This paper deals with the modeling of nonlinear and time-varying dc-dc converters in linear parameter variant (LPV) form. Such LPV models are employed to derive synthesis conditions in order to obtain robust gain-scheduled controllers in a systematic form, thanks to a linear convex formulation. The proposed synthesis algorithm allows taking into account uncertainties of the system and common specifications of power converters, such as settling time, overshoot and disturbance rejection. The LPV formulation allows to obtain improved robustness and performance properties, as compared to previous time-invariant synthesis approaches. The results are verified by boost dc-dc converter simulations.

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Variable-Structure Control Design of Switched Systems With an Application to a DC–DC Power Converter

Cited by 102 publications

References 33 publications

State feedback ℋ _∞ control design of continuous‐time switched affine systems

State feedback ℋ _∞ control design of continuous‐time switched affine systems

PWM-Based Sliding Mode Controller for Three-Level Full-Bridge DC-DC Converter that Eliminates Static Output Voltage Error

Robust gain-scheduled control of dc-dc converters: An LMI approach

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Variable-Structure Control Design of Switched Systems With an Application to a DC–DC Power Converter

Cited by 102 publications

References 33 publications

State feedback ℋ ∞ control design of continuous‐time switched affine systems

State feedback ℋ ∞ control design of continuous‐time switched affine systems

PWM-Based Sliding Mode Controller for Three-Level Full-Bridge DC-DC Converter that Eliminates Static Output Voltage Error

Robust gain-scheduled control of dc-dc converters: An LMI approach

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State feedback ℋ _∞ control design of continuous‐time switched affine systems

State feedback ℋ _∞ control design of continuous‐time switched affine systems