Backstepping control of flexible joint manipulator based on hyperbolic tangent function with control input and rate constraints

Wang, Lijun; Shi, Qiuyue; Liu, Jinkun; Zhang, Dan

doi:10.1002/asjc.2006

Cited by 20 publications

(13 citation statements)

References 30 publications

(42 reference statements)

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“…We know that the solution to this equation is always feasible. We can assert that there is a feasible solution which satisfies both linear and nonlinear equation for a controllable system, as given in (20). Therefore, the state equation is rewritten as…”

Section: Step 2: State Constraint Handlingmentioning

confidence: 99%

“…The partially continuous structure of system constraints makes the mathematical calculations difficult. It is possible to express constraints with smooth and differentiable functions instead of inequalities [20]. By using these so-called saturation-like functions, it is possible to revise the dynamic equations of the system and obtain equality constrained structures for MPC.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An algebraic and suboptimal solution of constrained model predictive control via tangent hyperbolic function

Dursun

Taşçıkaraoğlu

Üstoğlu

2020

Asian Journal of Control

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In this paper, we propose a novel method to solve the model predictive control (MPC) problem for linear time-invariant (LTI) systems with input and output constraints. We establish an algebraic control rule to solve the MPC problem to overcome the computational time of online optimization methods. For this purpose, we express system constraints as a continuous function through the tangent-hyperbolic function, hence the optimization problem is reformulated.There are two steps for the solution of the optimization problem. In the first step, the optimal control signal is determined by the use of the necessary condition for optimality, assuming that there is only input constraint. In the latter, the solution obtained in the first step is revised to keep the system states in a feasible region. It is shown that the solution is suboptimal. The proposed solution method is simulated for three different sample systems, and the results are compared with the classical MPC, which show that the new algebraic method dramatically reduces the computational time of MPC.

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Section: Step 2: State Constraint Handlingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An algebraic and suboptimal solution of constrained model predictive control via tangent hyperbolic function

Dursun

Taşçıkaraoğlu

Üstoğlu

2020

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…To address the output constraint or input saturation, many researchers have proposed diverse solutions June 26, 2021 DRAFT in recent years [23]- [30]. To list some examples, in [24], [26], a saturation function was employed to describe the mathematical model of input saturation.…”

Section: Introductionmentioning

confidence: 99%

“…To list some examples, in [24], [26], a saturation function was employed to describe the mathematical model of input saturation. In [27], the dead zone nonlinearity was applied to replace the saturation nonlinearity in multi-agent systems, and the hyperbolic tangent function was applied to the control law design of a flexible manipulator with input and rate constraints [30], which can effectively solve the problem that the sharp corner of saturation function was not differentiable. In [31], [32], the constrained system was transformed into the unconstrained case using the system transformation technique and the system remained to be stable.…”

Section: Introductionmentioning

confidence: 99%

“…Since the backstepping control is able to handle diverse nonlinearities during the design [37]- [42], it has become a common design aid for the control of various nonlinear systems [30], [43]- [46]. The main idea is to split the high-order system into several subsystems, and then use Lyapunov method to design the appropriate virtual control law for each subsystem to achieve the overall control object, but the biggest problem is that "term explosion" will occur in the process of frequent derivation, which makes the control law design difficult.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Finite-time Dynamic Surface Neural Network Control of an Uncertain Robot with Output Constraint and Input Saturation

Zhang

Peng

Zhao

2021

Preprint

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In this study, a finite-time dynamic surface neural network control is developed for an uncertain n-link robot subject to input saturation and output constraints. First, a barrier Lyapunov function and a hyperbolic tangent function are applied to solve the system constraints using a dynamic surface control. Subsequently, a radial basis function neural network is utilized to handle system uncertainties. Then, a finite-time filter is employed in the design to achieve the fast convergence and a Nussbaum function is employed to optimize the design process. Finally, the simulation results show that the dynamic tracking error is proved to converging to zero, and the proposed control method is effective and never violates the constraints.

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Speed control strategy of dual flexible servo system considering time‐varying parameters for flexible manipulator with an axially translating arm

Shang

Yin

et al. 2022

Asian Journal of Control

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Many factors lead to fluctuations of output speed in the motor side during the movement processes in a flexible manipulator with an axially translating arm. These factors include the time‐varying characteristics of manipulator parameters, external disturbance, and flexibility in the manipulator. The vibration of flexible manipulators is strengthened by fluctuations of output speed, which seriously affects the motion accuracy. Therefore, a variable parameters proportional–integral (PI) control strategy based on disturbance observer is adopted to reduce fluctuations of output speed in a dual flexible servo system. First, the dynamic model of the dual flexible servo system is established by the assumed mode method. Then, the variable parameters PI control strategy is applied to the servo system, and the controller parameters in different conditions are selected by pole placement strategies. Finally, numerical simulations and control experiments of the servo system are carried out. The results show that the control strategy using the variable parameters and disturbance observer could reduce fluctuations of output speed and improve the motion accuracy of flexible manipulators.

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Backstepping control of flexible joint manipulator based on hyperbolic tangent function with control input and rate constraints

Cited by 20 publications

References 30 publications

An algebraic and suboptimal solution of constrained model predictive control via tangent hyperbolic function

An algebraic and suboptimal solution of constrained model predictive control via tangent hyperbolic function

Adaptive Finite-time Dynamic Surface Neural Network Control of an Uncertain Robot with Output Constraint and Input Saturation

Speed control strategy of dual flexible servo system considering time‐varying parameters for flexible manipulator with an axially translating arm

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