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Publication# Design of an H infinity controller for the Delta robot: experimental results

Abstract

This paper deals with an efficient implementation of an H multi-variable controller on the three degrees of freedom (DOF) parallel robot namely the Delta robot'. The H controller is designed by the mixed sensitivity approach in which the sensitivity function matrix S and the complementary sensitivity function matrix T are taken into account. For this purpose, a nonlinear analytical dynamic state model is developed and a tangent linearization procedure is used to obtain a multi-variable linear model around a functional point. Real-time experiments were performed to compare the centralized H controller with a classical decentralized Proportional Integral Derivative (PID) controller. Experimental tracking results show that the performances of the PID compared to those of the H decrease when the movement dynamic is increased. At high dynamic (12Ge), it is shown that the maximum tracking error and the error around the stop positions of the H are, respectively, 80 and 60% of the PID. The experiments of the load variation have proven that the H is more robust than the PID. The steady-state root mean square error of the H is less than 60% of the one obtained using the PID controller.

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Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.

Proportional–integral–derivative controller

A proportional–integral–derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control. A PID controller continuously calculates an error value as the difference between a desired setpoint (SP) and a measured process variable (PV) and applies a correction based on proportional, integral, and derivative terms (denoted P, I, and D respectively), hence the name.

Closed-loop controller

A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g., voltage applied to an electric motor) have an effect on the process outputs (e.g., speed or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop.

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