Adaptation Dead Zone Research Articles

Locomotion Control of a Hydraulically Actuated Hexapod Robot by Robust Adaptive Fuzzy Control with Self-Tuned Adaptation Gain and Dead Zone Fuzzy Pre-compensation

Hydraulically actuated robotic mechanisms are becoming popular for field robotic applications for their compact design and large output power. However, they exhibit nonlinearity, parameter variation and flattery delay in the response. This flattery delay, which often causes poor trajectory tracking performance of the robot, is possibly caused by the dead zone of the proportional electromagnetic control valves and the delay associated with oil flow. In this investigation, we have proposed a trajectory tracking control system for hydraulically actuated robotic mechanism that diminishes the flattery delay in the output response. The proposed controller consists of a robust adaptive fuzzy controller with self-tuned adaptation gain in the feedback loop to cope with the parameter variation and disturbances and a one-step-ahead fuzzy controller in the feed-forward loop for hydraulic dead zone pre-compensation. The adaptation law of the feedback controller has been designed by Lyapunov synthesis method and its adaptation rate is varied by fuzzy self-tuning. The variable adaptation rate helps to improve the tracking performance without sacrificing the stability. The proposed control technique has been applied for locomotion control of a hydraulically actuated hexapod robot under independent joint control framework. For tracking performance of the proposed controller has also been compared with classical PID controller, LQG state feedback controller and static fuzzy controller. The experimental results exhibit a very accurate foot trajectory tracking with very small tracking error with the proposed controller.

On the adaptive control of a class of SISO dynamic hybrid systems

This paper deals with the problem of synthesizing a robust adaptive controller for a specific class of single-input single-output (SISO) time-invariant hybrid controlled object (plant) which can operate under bounded disturbances and/or unmodeled dynamics. The hybrid plant dealt with is composed of two coupled subsystems, one of them being of continuous-time type while the other is digital. The estimation algorithm is of a continuous-time nature since the plant parameter estimates are updated for all time. The adaptive scheme is pole-placement based and it is of indirect type since the controller parameters are re-updated at all time based on the calculated plant parameter estimates. An input–output model is first directly obtained from a state-space description which involves filtered signals for the hybrid plant from an initial state-space description. Such a model is simultaneously driven by the standard continuous-time input plus an extra signal. The extra input is composed for all time of a signal which involves the contribution of the input and output over a finite number of preceding sampling instants plus a driving signal which involves the contribution of the weighted integral of the continuous-time input on a set of preceding sampling intervals. Such a driving signal is due to the existing couplings between the continuous-time and digital substates of the hybrid plant. A relative adaptation dead zone is used in the parameter estimation scheme whose role is the robust adaptive stabilization in the presence of uncertainties. The hybrid nature of the system becomes apparent since the plant is simultaneously driven by the continuous time input plus its samples at sampling instants. As a result, its input–output differential equation has forcing terms generated by the system description at sampling instants.

Robustly stable multiestimation scheme for adaptive control andidentification with model reduction issues

A discrete pole‐placement‐based and multiestimation‐based adaptive control scheme involving a relative adaptation dead zone is presented for a plant with known poles and unknown zeros. The basic usefulness of the proposed multiestimation scheme is related to the use of a set of models of reduced order associated with the multiestimation scheme instead of a high‐order one. Depending on the frequency spectrum characteristics of the input and on the estimates evolution, the multiestimation scheme selects on‐line the most appropriate model and its related estimation scheme in order to improve the identification and control performances. Robust closed‐loop stability is proved even in the presence of unmodeled dynamics of sufficiently small sizes as it has been confirmed by simulation results. The scheme chooses in real time the estimator/controller associated with a particular reduced model possessing the best performance according to an identification performance index by implementing a switching rule between estimators. The switching rule is subject to a minimum residence time at each identifier/adaptive controller parameterization for closed‐loop stabilization purposes. A conceptually simple higher‐level supervisor, based on heuristic updating rules which estimate on‐line the weights of the switching rule between estimation schemes, is discussed.

Adaptive control of single‐input single‐output hybrid systems possessing interacting discrete‐ and continuous‐time dynamics

This paper deals with the problem of synthesizing a robust adaptive controller for a specific class of single‐input single‐output (SISO) time‐invariant hybrid controlled object (plant) which can operate under bounded disturbances and/or unmodeled dynamics. The hybrid plant dealt with is composed of two coupled subsystems, one of them being of continuous‐time type while the other is digital. As a result there are also mixed continuous‐time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete‐time and continuous‐time forcing terms and on generalized difference equations associated with discretized and digital signals. The estimation algorithm is of a continuous‐time nature since the plant parameter estimates are updated for all time. It also incorporates a relative adaptation dead‐zone as a robust stabilization mechanism which prevents against instability in the presence of a common class of unmodeled dynamics and bounded noise.

Robust adaptive control of discrete nominally stabilizable plants

This paper presents an indirect pole-placement based adaptive control scheme for discrete linear time-invariant non-necessarily inversely stable and stabilizable systems. The scheme is a pole-placement type without requiring the plant inverse stability assumption. The control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal, given by an arbitrary stable filter, under a bounded tracking error while ensuring robust closed-loop stability. The adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and, possibly, bounded disturbances, are proved without assuming the controllability of the modeled plant. A normalized least-squares algorithm with a relative adaptation dead-zone and ‘a posteriori’ modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit. Such a property is crucial to solve the stable pole-placement problem. On the other hand, the relative adaptation dead-zone is included for robustness purposes under unmodeled dynamics and, possibly, bounded disturbances.

Robust adaptive control of dynamic hybrid systems

Deals with the problem of synthesizing a robust adaptive controller for a class of single-input single-output time-invariant hybrid plant which can operate under bounded disturbances and/or unmodelled dynamics. The hybrid plant dealt with is composed of two subsystems one being of continuous-time type while the other is digital. The system is simultaneously driven by the standard continuous-time input plus an extra signal. A relative adaptation dead zone is used in the parameter estimation scheme whose role is the robust adaptive stabilization in the presence of uncertainties.

Robust adaptive regulation of potentially inversely unstable first-order hybrid systems

This paper presents a robust adaptive stabilization scheme for a class of hybrid time-invariant linear system involving both continuous and discrete signals. The continuous subsystem and the discrete one are both of first-order. The usual assumptions of inverse stability of the plant and knowledge of the high-frequency gain are not required for this first-order hybrid system. The design philosophy used relies on the separation of the continuous and discrete dynamics by generating two additive terms to build the control action. The estimation scheme is unified in the sense that both continuous and discrete estimated parameters are generated from the same adaptation error. The controllability of the nominally estimated plant model is maintained by using an hysteresis switching function under the controllability of the nominal plant. This allows relaxing the usual assumption of stability of the plant inverse. Also, an adaptation dead zone is used for robust stabilization by using a known overbounding function of the contribution of the unmodelled dynamics.

Robust adaptive stabilization of time-invariant first-order hybrid systems with covariance resetting

This paper presents a robust adaptive stabilization scheme for a class of nominally controllable first-order hybrid time-invariant linear systems which involve both continuous and discrete signals. The usual assumptions of inverse stability of the plant and knowledge of the high-frequency gain are not required. The design philosophy used relies on the separation of the contributions to the output of the continuous and discrete dynamics through the generation of two additive signals to build the overall control action. The estimation scheme is unified in the sense that both continuous and discrete updated parameters are generated from the same adaptation error. The controllability of the nominally estimated plant model is maintained by using an hysteresis switching function under the controllability of the nominal plant. This allows relaxing the usual assumption of stability of the plant inverse. Also, an adaptation dead zone is used for robust stabilization by using a known overbounding function of the contribution of the unmodelled dynamics.

Robust Adaptive Tracking with Pole Placement of First-Order Potentially Inversely Unstable Continuous-Time Systems

This note presents an indirect adaptive control scheme applicable to nominally con- trollable non-necessarily inversely stable first-order continuous linear time-invariant systems with unmodelled dynamics. The control objective is to achieve a bounded tracking-error between the system output and a reference signal . A least-squares algorithm with normalization is used to es- timate the plant parameters by using two additional design tools, namely: 1) a modification of the parameter estimates and2) a relative adaptation dead-zone . The modification is based on the properties of the inverse of the least-squares covariance matrix and it uses an hysteresis switching function. In this way, the non-singularity of the controllability matrix of the estimated model of the plant is ensured. The relative dead-zone is used to turn off the adaptation process when an absolute augmented error is smaller than the value of an available overbounding function of the unmodelled dynamics contribution plus, eventually, bounded noise.