The main goal of the paper is to test the Embedded Model Control (EMC) design and implementation on a typical underactuated apparatus, like the Furuta pendulum, by comparing experimental results with a Linear Quadratic Regulator (LQR). EMC can be considered as a disturbance rejection control strategy, since the state predictor is extended to explicitly include disturbance dynamics, in charge of predicting the uncertainty to be rejected by control law. Essential in EMC design is the separation between controllable and not controllable dynamics, a task which allows us to find the controllable channel of underactuated systems from the low-dimensional command to the whole system degrees of freedom (DF). Pursuing this objective, a rather generic method is shown, which is applicable to other underactuated systems. The result is a very simple controllable dynamics from the single pendulum command to pendulum DF arranged in a single series of controllable integrators. The neglected feedback channels, including the unstable gravity feedback, are treated as unknown thus posing a challenge to disturbance prediction and closed loop stability. Typical in EMC, closed loop eigenvalues are chosen to guarantee stability, a pre-requisite to performance. Experimental results point out effectiveness and advantage, with respect to LQR, of design and implementation under adverse conditions, due to a disturbance pulse, in which command saturates.

本文的主要目标是通过将实验结果与线性二次调节器 (LQR) 进行比较，在典型的欠驱动装置（如古田摆）上测试嵌入式模型控制 (EMC) 设计和实现。EMC 可以被认为是一种干扰抑制控制策略，因为状态预测器被扩展为明确包含干扰动力学，负责预测控制律拒绝的不确定性。EMC 设计中必不可少的是可控和不可控动力学之间的分离，这项任务使我们能够找到欠驱动系统从低维命令到整个系统自由度 (DF) 的可控通道。为了实现这一目标，展示了一种相当通用的方法，该方法适用于其他欠驱动系统。结果是一个非常简单的可控动态，从单摆命令到摆在单个系列可控积分器中的 DF。被忽视的反馈通道，包括不稳定的重力反馈，被视为未知的，从而对扰动预测和闭环稳定性提出了挑战。在 EMC 中，通常选择闭环特征值来保证稳定性，这是性能的先决条件。实验结果表明，在不利条件下，由于干扰脉冲，指令饱和，设计和实施相对于 LQR 的有效性和优势。被视为未知，从而对干扰预测和闭环稳定性构成挑战。在 EMC 中，通常选择闭环特征值来保证稳定性，这是性能的先决条件。实验结果表明，在不利条件下，由于干扰脉冲，指令饱和，设计和实施相对于 LQR 的有效性和优势。被视为未知，从而对干扰预测和闭环稳定性构成挑战。在 EMC 中，通常选择闭环特征值来保证稳定性，这是性能的先决条件。实验结果表明，在不利条件下，由于干扰脉冲，指令饱和，设计和实施相对于 LQR 的有效性和优势。