机械系统的互联阻尼配置无源控制方法
On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems
摘要：
互联阻尼配置无源性控制（IDA-PBC）是一种很好的方法来稳定的机械系统的哈密顿形式。本文对IDA-PBC方法进行了几点改进。IDA-PBC的传统形式的斜对称互连子矩阵示出具有一定的冗余度的自由度的数量大于大于两个，包含不必要的组件，不有助于动态的系统。为了完全消除这种冗余，二次陀螺力的使用提出的反对称互连子矩阵的地方。通过消除匹配偏微分方程中的陀螺力，减少了IDA-PBC中匹配偏微分方程的数目，简化了匹配偏微分方程的结构。此外，易于验证的标准提供了李雅普诺夫/指数镇定IDA-PBC的所有线性控制哈密顿系统与任意程度的欠驱动和所有非线性控制哈密顿系统与一个程度的欠驱动。给出了IDA-PBC的一般设计过程，并举例说明。讨论了新IDA-PBC方法与受控拉格朗日方法的对偶性。本文使IDA-PBC方法与受控拉格朗日方法一样强大。
英文摘要：
Interconnection and damping assignment passivity-based control (IDA-PBC) is an excellent method to stabilize mechanical systems in the Hamiltonian formalism. In this paper, several improvements are made on the IDA-PBC method. The skew-symmetric interconnection submatrix in the conventional form of IDA-PBC is shown to have some redundancy for systems with the number of degrees of freedom greater than two, containing unnecessary components that do not contribute to the dynamics. To completely remove this redundancy, the use of quadratic gyroscopic forces is proposed in place of the skew-symmetric interconnection submatrix. Reduction of the number of matching partial differential equations in IDA-PBC and simplification of the structure of the matching partial differential equations are achieved by eliminating the gyroscopic force from the matching partial differential equations. In addition, easily verifiable criteria are provided for Lyapunov/exponential stabilizability by IDA-PBC for all linear controlled Hamiltonian systems with arbitrary degrees of underactuation and for all nonlinear controlled Hamiltonian systems with one degree of underactuation. A general design procedure for IDA-PBC is given and illustrated with examples. The duality of the new IDA-PBC method to the method of controlled Lagrangians is discussed. This paper renders the IDA-PBC method as powerful as the controlled Lagrangian method.
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