Showing papers by "Ye-Hwa Chen published in 2018"

A Fuzzy Approach for Optimal Robust Control Design of an Automotive Electronic Throttle System

Abstract: In this paper, we propose a fuzzy approach for optimal robust control design of an automotive electronic throttle (ET) system. Compared with the conventional ET control systems, we establish the fuzzy dynamical model of the ET system with parameter uncertainties, nonlinearities, and external disturbances, which may be nonlinear, (possibly fast) time varying. These uncertainties are assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. A robust control that is deterministic and is not the usual if–then rules-based control is presented to guarantee the controlled system to achieve the deterministic performance: uniform boundedness and uniform ultimate boundedness. Furthermore, a fuzzy-based system performance index including average fuzzy system performance and control cost is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved by minimizing the fuzzy-based performance index. With this optimal robust control, the performance of the fuzzy ET system is both deterministically guaranteed and fuzzily optimized.

Optimal Robust Control Design for Constrained Uncertain Systems: A Fuzzy-Set Theoretic Approach

Abstract: The control design problem for a class of constrained uncertain systems is considered in this paper. The uncertainty in the system, including unknown system parameters and external disturbance, is nonlinear and time-varying. The bound of the uncertainty is described via a fuzzy set. The states of the system are constrained to be bounded. A one-to-one state transformation is proposed to convert the bounded state constrained system into the unconstrained system. A new robust control scheme is then proposed for the transformed system, which is in deterministic form and not fuzzy if–then rule based. By fuzzy description of the uncertainty bound, the optimal design of the control gain is proposed, which minimizes a fuzzy performance index associated with both the fuzzy system performance and the control effort. The analytic solution to the optimization problem is demonstrated to always exist and be unique. The resulting control can guarantee uniform boundedness and uniform ultimate boundedness of the uncertain system, while minimizing the fuzzy-based performance index. In addition, the state constraint can be always guaranteed.

Adaptive robust control methodology for active roll control system with uncertainty

Abstract: The active roll control system (ARCS) can impose anti-roll moment quickly to prevent the vehicle rolling when the vehicle generates the roll tendency and effectively enhance the vehicle dynamic performance without sacrificing the ride comfort. In the dynamic model of the ARCS, the sprung mass of the vehicle is considered to be the uncertain parameter, which is (possibly) fast-varying. However, what we know about the uncertainty is just that it is bounded. Furthermore, the bound is unknown. The target roll angle is regarded as the constraint when the vehicle equipped with the ARCS is running under a given case. Taking the parameter uncertainty and possible initial condition deviation from the constraint into account, an adaptive robust control scheme based on the Udwadia and Kalaba’s approach is proposed to drive the ARCS to follow the pre-specified constraint approximately. The adaptive law is of leakage type which can adjust itself based on the tracking error. Numerical simulation shows that by using the adaptive robust control scheme, the error between the actual roll angle and the desired roll angle converges to zero quickly in 0.3 s from initial error 0.287 deg, and the final error is of the order of $$10^{-7}$$ . Thus, the control design renders the ARCS practically stable and achieves constraints following maneuvering.

Adaptive robust control for dual avoidance–arrival performance for uncertain mechanical systems

Abstract: An unprecedented dual avoidance–arrival problem is addressed for uncertain mechanical systems. The concerned system uncertainty is (possibly fast) time-varying but within an unknown bound. The objective is to design a control to simultaneously guarantee two seemingly opposite system performance: avoidance (with respect to a region) and arrival (with respect to another region). This is formulated as an approximate constraint-following control problem, in which formulation, the desired constraint is creatively divided into two categories as the avoidance constraint and the arrival constraint. An adaptive robust control is then put forward under the consideration of the system uncertainty. It is proved that, with the proposed control input, the avoidance constraint is completely followed and the arrival constraint is closely followed; hence, the dual avoidance–arrival problem is carried out.

Adaptive robust constrained state control for non-linear maglev vehicle with guaranteed bounded airgap

Abstract: The authors propose an adaptive robust control approach for the levitation control of non-linear maglev vehicle with state constraint. The system contains non-linear and (possibly) time-varying uncertainty, which is supposed to be bounded. In order to prevent the undesirable collision, the airgap between suspended chassis and guideway should be restrained in a specified range for safety concerns. Furthermore, the maglev vehicle does not satisfy the (global) matching condition. The authors propose a three-step state transformation approach to transform the maglev vehicle to an interconnected uncertain system. After that, the robust control is proposed based on the transformed system, and the adaptive law is constructed to emulate the total system uncertainty. The adaptive robust control is able to ensure the system performance (uniform boundedness and the uniform ultimate boundedness) of uncertain maglev vehicle. In addition, the airgap can be confined within the specified range.

Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications

Abstract: There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations.

Robust Approximate Constraint‐Following Control for Autonomous Vehicle Platoon Systems

Abstract: We consider an autonomous vehicle platoon system consisting of N+1 vehicles in the presence of modeling uncertainty. The uncertainty may be due to parameter variations, aerodynamics, external disturbances, etc., which is nonlinear and time-varying. Subject to the collision avoidance consideration, the original state is one-sided restricted. To resolve this restriction, we propose a state transformation to convert the bounded state into a globally unbounded state. Furthermore, motivated by the properties of artificial swarm systems, we incorporate the swarm system performance into the platoon system by treating it as a d'Alembert's constraint. By the Udwadia and Kalaba's approach, we obtain the analytic (closed-form) expression of the constraint force. Based on this, a class of robust controls for each vehicle (except the leading vehicle) is proposed to drive the platoon system to follow the ideal swarm model. Four major system performances are accomplished: (i) compact vehicle formation, (ii) collision avoidance, (iii) stable platoon system formation, (iv) global behavior.

Guaranteeing Uniform Ultimate Boundedness for Uncertain Systems Free of Matching Condition

Abstract: A fuzzy-based optimal approach to robust control design is proposed for interconnected uncertain systems with mismatching conditions, which were previously unavailable. The interconnected system contains uncertainty, which may include initial conditions, unknown system parameters and input disturbance. The uncertainty bound lies within a prescribed fuzzy set. The system does not satisfy the matching condition. The robust control design in this paper consists of a control scheme design and control gain optimization. A new robust control scheme is first proposed, whose structure is deterministic and not if–then fuzzy rule based. The control gain design problem is then formulated as constrained optimization by fuzzy description of the uncertainty bound, which minimizes the fuzzy system performance and the control effort. It is shown that the global solution to this optimization problem always exists and is unique. The closed-form solution and closed-form minimum cost are presented. The resulting control is able to render the system performance in twofold. First, it guarantees uniform boundedness and uniform ultimate boundedness regardless of the actual value of uncertainty. Second, it minimizes a fuzzy-based performance index. The novelty of this research is a new and carefully orchestrated effort in blending several creative methods and tools; including simultaneous state transformation and control design, dual deterministic and fuzzy features of the performance index, and raised control order; into an integrated framework, resulting in a tractable design problem.

A constraint-following control for uncertain mechanical systems: given force coupled with constraint force

Abstract: A novel constraint-following control for uncertain mechanical systems is proposed. In mechanical systems, certain given forces may arise due to the constraint forces, which means the given forces are coupled with the constraint forces. By using the second-order form of the constraints, the given forces are decoupled explicitly. The uncertainty of the mechanical system is time-varying and bounded. But its bound is unknown. A series of adaptive parameters are invoked to estimate the bound information of the uncertainty in virtue of state feedback. Based on the estimated bound information, a robust control is designed to render the mechanical system an approximate constraint-following. The system performance under the control is guaranteed as uniform boundedness and uniform ultimate boundedness.

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

Abstract: A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within p...

Optimal fuzzy adaptive control for uncertain flexible joint manipulator based on D -operation

Abstract: A fuzzy approach to the optimal control design for a kind of uncertain flexible joint manipulator is proposed. The system contains mismatched uncertainty which is described by fuzzy set theory and is assumed to be bounded. By implanting a fictitious control and transforming the system with new state variables, an adaptive robust controller is designed to guarantee the uniform boundedness and uniform ultimate boundedness of the transformed system. The proposed control is only based on the existence of the uncertainty bound and is not if-then heuristic rules-based. Furthermore, the performance of the original system is also proven theoretically. By applying D -operation, the optimal design problem associated with the control can then be solved by minimising a constrained performance index. The performance index, which is based on the fuzzy information, includes average fuzzy system performance and control effort. The resulting control design is systematic and is able to assure the deterministic performance as well as the fuzzy performance. An illustrative example is given to demonstrate the authors' conclusions.

Robust Constraint Following Stabilization for Mechanical Manipulators Containing Uncertainty: An Adaptive $\varphi$ Approach

Abstract: The constraint following stabilization problem of aerospace mechanical manipulators containing uncertainty is investigated. Due to the inevitable modeling error and external disturbance, there always exists uncertainty. To guarantee that the mechanical system follows prescribed constraints (holonomic or non-holonomic), two classes of adaptive robust controls are proposed. The system performance is represented based on a $\varphi $ -measure. The control scheme consists of two parts: the nominal control part and the adaptive robust control part. By the Udwadia–Kalaba theory, the nominal control is proposed to force the nominal mechanical system to meet the constraints. Furthermore, the adaptive robust control is proposed to address the uncertainty issue, while the adaptation law is proposed to estimate the bounding information of the uncertainty. Under the control, the system is guaranteed to follow the constraint regardless of the uncertainty.

Optimal design for robust control parameter for active roll control system: a fuzzy approach:

Abstract: In this paper, we investigate the dynamical model of an active roll control system (ARCS) which can impose an anti-roll moment quickly by active actuators to prevent a vehicle rolling when the vehi...

Bivariate Optimization for Control Design of Interconnected Uncertain Nonlinear Systems: A Fuzzy Set-Theoretic Approach

Abstract: A new fuzzy set-theoretic approach to the control design of interconnected uncertain nonlinear system is proposed. The uncertainty of the system is nonlinear and (possible) fast time-varying, which may be due to unknown parameter and input disturbance. The uncertainty bound can be described via a fuzzy set. In this paper, the control design consists of the control scheme design and control gain optimization. Under a state transformation, a new robust control scheme in deterministic form is proposed for the interconnected system, which is not fuzzy if-then rule-based. The optimal design of the control gain is then proposed via the fuzzy description of the uncertainty bound, which is formulated as a bivariate constrained optimization problem by minimizing a fuzzy-based performance index. We show that the globally unique solution to this optimization problem always exists. The closed-form (i.e., analytic) solution and the corresponding minimum value of the performance index are also presented. The resulting control is able to render the system performance in twofold. First, it guarantees uniform boundedness and uniform ultimate boundedness of the system regardless of the actual value of uncertainty. Second, it minimizes the fuzzy-based performance index associated with both the fuzzy system performance and the control cost.

Canonical Generalized Inversion Form of Kane’s Equations of Motion for Constrained Mechanical Systems

Abstract: The canonical generalized inversion dynamical equations of motion for ideally constrained discrete mechanical systems are introduced in the framework of Kane’s method. The canonical equations of motion employ the acceleration form of constraints and the Moore-Penrose generalized inversion-based Greville formula for general solutions of linear systems of algebraic equations. Moreover, the canonical equations of motion are explicit and nonminimal (full order) in the acceleration variables, and their derivation ismadewithout appealing to the principle of virtual work or to Lagrange multipliers. The geometry of constrained motion is revealed by the canonical equations of motion in a clear and intuitive manner by partitioning the canonical accelerations’ column matrix into two portions: a portion that drives the mechanical system to abide by the constraints and a portion that generates the momentum balance dynamics of the mechanical system. Some geometrical perspectives of the canonical equations of motion are illustrated via vectorial geometric visualization, which leads to verifying the Gauss’ principle of least constraints and its Udwadia-Kalaba interpretation.