Hybrid control of a double tank system

Malmborg, Jörgen; Eker, Johan

doi:10.1109/cca.1997.627515

Cited by 29 publications

(14 citation statements)

References 4 publications

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“…Theorem 1: with the developed nonlinear adaptive backstepping sliding-mode controller (III-A) and a stable sliding surface (19), the reaching condition σσ < 0 is satisfied. Thus, all components of z(t), z 1 and z 2 , are exponentially convergent to the origin.…”

Section: B Stability Analysismentioning

confidence: 92%

“…Firstly, In [19], a hybrid control design was presented for the state-coupled, two-tank system, which consisted of a switching between a PID controller and a bang-bang type, time-optimal controller. Using the quadruple-tank process as a benchmark, Astrom, Johansson and Wang [2] designed decoupled PI controllers for general two-by-two systems.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive backstepping sliding mode control of hydraulic system with nonlinear unknown parameters

Benayache

Chrifi‐Alaoui

Bussy

2010

18th Mediterranean Conference on Control and Automation, MED'10

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The paper proposes an adaptive backstepping sliding mode control method for a hydraulic system with nonlinear unknown parameters, which enter the system equations in a nonlinear way. Backstepping sliding-mode method of system always assume that the parameters are certain and known. But in practical hydraulic system, the parameters are unknown and change. However, the upper bound of the lumped uncertainty is difficult to obtain in advance of practical applications. Therefore, an adaptive law is derived to adapt the value of the lumped uncertainty in real time, and an adaptive backstepping sliding-mode control law is the result. The experimental results show that the nonlinear control algorithm, together with the adaptation scheme, gives a good performance for the specified tracking task in the presence of nonlinear unknown parameters.

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Section: B Stability Analysismentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Adaptive backstepping sliding mode control of hydraulic system with nonlinear unknown parameters

Benayache

Chrifi‐Alaoui

Bussy

2010

18th Mediterranean Conference on Control and Automation, MED'10

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“…The problem of controlling two interconnected tanks using hybrid control appeared in [15]. The authors of [16] applied switching time optimization to obtain the optimal inputs.…”

Section: Double-tank Systemmentioning

confidence: 99%

Second-Order Switching Time Optimization for Switched Dynamical Systems

Stellato

Ober‐Blöbaum

Goulart

2017

IEEE Trans. Automat. Contr.

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Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear and nonlinear systems. A novel second-order optimization algorithm is introduced where, at each iteration, the dynamics are linearized over an underlying time grid to compute the cost function, the gradient and the Hessian efficiently. With the proposed method, the most expensive operations at each iteration are shared between the cost function and its derivatives, thereby greatly reducing the computational burden. We implemented the algorithm in the Julia package SwitchTimeOpt allowing the user to easily solve switching time optimization problems. In the case of linear dynamics, many operations can be further simplified and benchmarks show that our approach is able to provide optimal solutions in just a few ms. In the case of nonlinear dynamics, two examples show that our method provides optimal solutions with up to two orders of magnitude time reductions over state-of-the-art approaches.

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“…Applications of differential automata by others can be found in (e.g.) [2][3][4][5]. The modeling of hybrid systems has also developed along different lines, as shown in [6][7][8][9][10].…”

Section: Differential Automatamentioning

confidence: 99%

Generic asymptotic error estimates for the numerical simulation of hybrid systems

Tavernini

2009

Nonlinear Analysis: Hybrid Systems

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Hybrid control of a double tank system

Cited by 29 publications

References 4 publications

Adaptive backstepping sliding mode control of hydraulic system with nonlinear unknown parameters

Adaptive backstepping sliding mode control of hydraulic system with nonlinear unknown parameters

Second-Order Switching Time Optimization for Switched Dynamical Systems

Generic asymptotic error estimates for the numerical simulation of hybrid systems

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