Controlling mechanical systems with backlash—a survey

Nordin, Mattias; Gutman, Per‐Olof

doi:10.1016/s0005-1098(02)00047-x

Cited by 404 publications

(268 citation statements)

References 37 publications

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“…For many applications, such nonlinear operators affect the inputs of control systems (see e.g. [17], [19]). The negligence of such nonlinearities during the control design or the stability analysis can lead to an important degradation of the closed-loop performance or even to the loss of stability (see, in particular, [19]).…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Stabilization of Systems With Input Backlash

Tarbouriech

Queinnec

Prieur

2014

IEEE Trans. Automat. Contr.

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Abstract-This paper deals with the stability analysis and stabilization of linear systems with backlash in the input. Uniform ultimate boundedness stability and stabilization problems are tackled allowing to characterize suitable regions of the state space in which the closedloop trajectories can be captured. In the state feedback control design, computational oriented solutions are derived to solve suboptimal convex optimization problems able to give a constructive solution.

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Section: Introductionmentioning

confidence: 99%

Stability Analysis and Stabilization of Systems With Input Backlash

Tarbouriech

Queinnec

Prieur

2014

IEEE Trans. Automat. Contr.

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“…Given ◊ rotating masses, the model contains n = 7 + 2◊ dimensions. The hybrid behavior of the drivetrain originates from backlash [42], which is caused by a physical gap between two components that are normally touching, such as gears. When the rotating components switch direction, for a short time they temporarily disconnect, and the system is said to be in the dead zone.…”

Section: Discussionmentioning

confidence: 99%

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Bak

Bogomolov

Althoff

2017

Lecture Notes in Computer Science

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Abstract.A promising technique for the formal verification of embedded and cyber-physical systems is flow-pipe construction, which creates a sequence of regions covering all reachable states over time. Flow-pipe construction methods can check whether specifications are met for all states, rather than just testing using a finite and incomplete set of simulation traces. A fundamental challenge when using flow-pipe construction on high-dimensional systems is the cost of geometric operations, such as intersection and convex hull. We address this challenge by showing that it is often possible to remove the need to perform high-dimensional geometric operations by combining two model transformations, direct time-triggered conversion and dynamics scaling. Further, we prove the overapproximation error in the conversion can be made arbitrarily small. Finally, we show that our transformation-based approach enables the analysis of a drivetrain system with up to 51 dimensions.

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“…2 shows the optimal value of k i according to the design problem (25) as function of α = α S = α T for the uncertain processes presented in (24). These figures illustrate how allowing for a higher probability of constraint violation (by increasing the value of α) can significantly improve the level of performance in terms of maximizing k i .…”

Section: Processes With Different Normalized Time Delaymentioning

confidence: 99%

“…These two transfer functions represent the paths from plant input and disturbance, respectively, to plant output. The reader is referred to [25] for a more detailed description of this model. The following numerical values, taken from [25], are used in this example: Although the disturbance acts on the output through P d , minimization of the corresponding IE is equivalent to maximization of k i :…”

Section: Plant With Large Number Of Uncertain Coefficientsmentioning

confidence: 99%

Robust PID design by chance-constrained optimization

Mercader

Soltesz

Baños

2017

Journal of the Franklin Institute

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A method for synthesizing proportional-integral-derivative (PID) controllers for process models with probabilistic parametric uncertainty is presented. The proposed method constitutes a stochastic extension to the well-studied maximization of integral gain optimization (MIGO) approach, i.e., maximization of integral gain under constraints on the H∞-norm of relevant closed-loop transfer functions. The underlying chance-constrained optimization problem is solved using a gradient-based algorithm once it has been approximated by a deterministic optimization problem. The approximate solution is then probabilistically verified using randomized algorithms (RAs). The proposed method is demonstrated through several realistic synthesis examples.

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Controlling mechanical systems with backlash—a survey

Cited by 404 publications

References 37 publications

Stability Analysis and Stabilization of Systems With Input Backlash

Stability Analysis and Stabilization of Systems With Input Backlash

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Robust PID design by chance-constrained optimization

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