Jairo Terra Moura

Sliding Mode Control With Sliding Perturbation Observer

This work introduces a new robust motion control algorithm using partial state feedback for a class of nonlinear systems in the presence of modelling uncertainties and external disturbances. The effects of these uncertainties are combined into a single quantity called perturbation. The major contribution of this work comes as the development and design of a robust observer for the state and the perturbation which is integrated into a Variable Structure Controller (VSC) structure. The proposed observer combines the procedures of Sliding Observers (Slotine et al, 1987) with the idea of Perturbation Estimation (Elmali and Olgac, 1992). The result is what is called Sliding Perturbation Observer (SPO). The VSC follows the philosophy of Sliding Mode Control (SMC) (Slotine and Sastry, 1983). This combination of controller/observer gives rise to the new routine called Sliding Mode Control with Sliding Perturbation Observer (SMCSPO). The stability analysis shows how the algorithm parameters are scheduled in order to assure the sliding modes of both controller and observer. A simplified form of the general design procedure is also presented in order to ease the practical applications of SMCSPO. Simulations are presented for a two-link manipulator to verify the proposed approach. Experimental validation of the methodology is also performed on a PUMA 560 robot. A superior control performance is obtained over some full state feedback techniques such as SMC and Computed Torque Method.

A comparative study on simulations vs. experiments of SMCPE

Sliding mode control with perturbation estimation (SMCPE) is a robust trajectory control strategy for coordinated multiple axes motion generators. The control strategy assures the pursuit of desired trajectories of multiple axes within a determined proximity despite the presence of modeling and disturbance uncertainties. The great majority of robust control studies assume that these uncertainties exhibit known upper bounds. The fundamental contribution of SMCPE is that the modeling uncertainties and disturbances do not have to be bounded by a priori known extremes, instead they are estimated in real time. This estimation is done by properly utilizing the feedback from the present position and velocity sensing, also the past control decisions. This paper presents simulation and experimental results for a 2-link SCARA type manipulator using SMCPE. The experiments were performed in ALARM laboratory at the University of Connecticut. The simulations reproduce the experimental results. If and when they do, they can be further used to study the effect of parametric variations on the performance of the control.

Tracking control of a rotating flexible beam using modified frequency-shaped sliding mode control

The purpose of this study is to improve a robust control strategy using frequency-shaped sliding surfaces. The control objective is the trajectory tracking of a flexible beam attached to a rigid hub. A compensator is introduced in sliding mode through a frequency-shaped performance index with prescribed degree of stability. This procedure yields desirably fast trajectory tracking without exciting the unmodelled dynamics (UD). It also offers a methodology to resolve this trade-off. Simulation results show that regarding the excitation of UD, the proposed control structure exhibits superior characteristics among peer sliding mode strategies.

Frequency-shaped sliding modes: analysis and experiments

A recent improvement over a motion control algorithm, sliding mode control with perturbation estimation, is considered in this paper. It enforces the nonlinear system to follow a desired trajectory despite the presence of modeling uncertainties and disturbances. This robustness feature is introduced by a control which may excite resonances of the system, especially those of high frequency. A complementary procedure, frequency shaping, is utilized in order to attenuate these controller introduced excitations. The combined control algorithm offers a couple of attractive features, such as suppression of high-frequency dynamics (including those which are unmodeled), as well as maintaining a desired level of tracking ability for the original uncertain system. The highlight of this work is to bring an equivalent conventional sliding surface to the frequency-shaped one. It is shown that such a strategy exists and can be found as a function of the initial conditions of the dynamics. This optimal conventional sliding surface is found by minimizing a quadratic cost over the trajectory tracking errors. The results of this study are experimentally verified using a single degree of freedom robot with a flexible appendage which represents the unmodeled dynamics.

Implementation of sliding mode control using the concept of perturbation

This work presents further improvements on a class of non-linear robust motion controllers, namely Sliding Mode Control (SMC) and Sliding Mode Control with Perturbation Estimation (SMCPE). Typically, the SMC methodology requires a priori knowledge of the uncertainty upper bounds for the system dynamics. It may be a difficult task to accomplish, and sometimes even impossible, due to the complexity in identifying the individual dynamic uncertainties. This work utilizes a perturbation analysis to remedy this hardship. SMCPE, on the other hand, requires the upper bounds of perturbation estimation errors, instead of the uncertainties themselves. We present an enhancement on this process also, by evaluating these bounds based on the given hardware limitations at hand. The contributions of this work appear at two points: (a) new guidelines to obtain uncertainty knowledge, (b) new feedback gain selection strategy to assure robustness without being overly conservative. All critical steps, such as robustness and stability, are rigorously proven. Practicality is the major objective in this new formulation. The claims are verified through experiments on a three-axes industrial manipulator. It is shown that the controller does not have to know more than the hardware specs of the sensory and actuation devices in order to assure robustness of the two control routines. This makes control design process much easier to complete.

Robust Lyapunov control with perturbation estimation

This paper presents an approach for motion control of nonlinear systems with modeling uncertainties which are called perturbations. These perturbations are estimated online as a compensating mechanism against the unknown terms. The starting point is a Lyapunov function that is dependent only on the joint tracking errors. Then a robust Lyapunov control is found such that the tracking errors are minimized, and ultimately confined to a prescribed manifold. The robustness against uncertain dynamics is treated in length. The convergence is assured outside the manifold in order to form a reaching phase from the initial state towards the manifold. An advantage of the method over the conventional sliding mode control is that it is not necessary to have a prior knowledge of modeling uncertainties and disturbance upper bounds. However, it is necessary to determine and assure an upper bound for the estimation errors. Parametric selections for the controller are suggested to obtain the desired tracking performance. Simulation results are presented for a two-link manipulator.

Sliding Mode Control with Perturbation Estimation (SMCPE) and frequency shaped sliding surfaces

Sliding Mode Control with Perturbation Estimation (SMCPE) is a recent control routine which steers uncertain dynamic systems with disturbances to follow a desired trajectory. It eliminates the conventional requirement for the knowledge of uncertainty upper bound. A perturbation estimation scheme provides a tool for robustness. This text offers an additional robustizing mechanism: selection of time-varying sliding functions utilizing frequency shaping techniques. Frequency shaping together with sliding mode control introduces a behavior for selectively penalizing tracking errors at certain frequency ranges. This combination provides two advantages concurrently: (a) It filters out certain frequency components of the perturbations therefore eliminating the possible excitation on the unmodelled dynamics, and (b) it drives the state to the desired trajectory despite perturbations. The crucial point is that a priori knowledge of the perturbation upper bound is not necessary to eliminate the perturbation effects at the designated frequencies. Numerical examples prove the effectiveness of this novel scheme.

Application of optimal trajectory algorithms to a solar-panel handling industrial manipulator: A case study

Several algorithms have been proposed in the last 25 years on the problem of generating time-optimal trajectories for robot manipulators along specified paths. This article describes an application of an optimal trajectory algorithm to an industrial manipulator used in the transfer of solar panel substrates between process modules. These manipulators operate in a vacuum environment and have constraints on substrate accelerations as well as available motor torques. The article shows that a trajectory profile optimized for both substrate acceleration and motor torques can reduce substrate transport time by 25 percent over the commonly used “S-curve” based algorithms.