# A Robust \(H_{\infty}\) Application for Motor-Link Control Systems of Industrial Manipulators
## 2 \(H_{\infty}\) Control Approach Basics
### The Closed-Loop Control Architecture  
The accuracy of the movements performed by a robotic arm is estimated by means of the analysis of velocity and position measurements of each axis of the kinematic chain. A typical industrial manipulator has 6 DOFs. The most common control architectures can be regrouped as follows:  
* In the first case, the manipulator is considered as a unique multi-DOF system and a completely centralized controller is implemented. * In the second case, six independent controllers, each one linked to a single axis of the structure, are developed. In the end, they are synchronized to let them operate as a single one. This paper is focused on the second kind of control architecture, dealing with a single axis of a 6 DOF manipulator, considered as a single DOF system. Since industrial manipulators are generally not equipped with link gyroscopes, the control is realized at the motor side but with the purpose of reaching satisfying performances for the link motion. The control architecture is composed by two nested loops (Figure 2), in order to split up the overall complex motion control problem into two smaller ones, according to the \"divide et impera\" technique: the inner one is a velocity loop, in which a velocity controller is applied based on the motor velocity feedback, whereas the outer one is a position loop, in which a position controller based on the motor position feedback is applied to the velocity-controlled system. It is worth to be noted that the control architecture in Figure 2 includes neither a current loop nor any feed-forward term. With reference to the actual control software architecture of industrial robots, the current loop is assumed to be directly included in the servo-system implemented on board, i.e., the APOCOS by B&R for COMAU robots (Figure 3), whereas the velocity and position loops (and in general any specific control scheme adopted) are implemented in the Aut  
Figure 2: Closed-Loop architecture. In this kind of control architecture, feed-forward terms are not always strictly required, thanks to the good behavior offered by the system when controlling a base industrial arm axis in a specific inertia condition, such as in the considered case. In particular:  
1. A velocity feed-forward is generally used to synchronize all the axes of the manipulator. It is computed starting from a prefixed delay that the controllers of all the mechanical bodies of the structures have to meet. Such a term has not been included in the considered scheme for the sake of simplicity, since the goal here is to prove the effectiveness of the \(H_{\infty}\) control applied to a single axis of the robot, working as if it were its only component. 2. An acceleration feed-forward term could be added to compensate a possible unacceptable overshoot; in addition, it is a powerful instrument to make the step response invariant in the presence of varying load inertia conditions. The considered case is relative to the analysis of the behavior of a robot moving in a single inertia condition, and as it will be shown in the remainder of the paper, no high overshoot occurs requiring an additional damping action. The adoption of the \(H_{\infty}\) approach in the design of both controllers will enhance the stability robustness of the controlled system because possible limits or weakness of the inner system can be overcome by the outer one. In Figure 2, \(G_{pm}(s)\) is the plant model used for the velocity loop.