Both comparative simulations and experiment between the proposed control scheme and other conventional algorithms are verified on a 3-DOF serial hydraulic manipulator, subjected to the payload variations in free motion, to evaluate the effectiveness of the proposed methodology. During this process, position-based impedance control (PB-IC) is preferred as the key point to achieve the power regulation and system stability under the influence of the sensor error.
Introduction
- Overview
- Research objectives
- Limitations
- Dissertation outline
In [26], the author combined the DO and ESO to simultaneously address the influence of matched and mismatched uncertainties of the EHS. Since the main concern of this thesis is the applicability of the proposed control strategy for actual implementation, the advanced control structure is very simple based on basic sliding mode control and backstepping technique with disturbance estimator and fuzzy logic control.
Mathematical preliminaries
Introduction
Mathematic
- Vector and matrices analysis
- Vectors and matrices differential calculus
- Vector and matrix norms
- Vector norms
- Matrix norms
- Eigen value of square matrix
- Inequalities
- Young’s inequality
- Rayleigh inequality
- Lipschitz functions
The square matrix PRn n is non-singular (or invertible) if and only if Q Rn n such that. Considering a square matrix PRm n , the matrix norm induced by the p-norm of vector xRn is defined as.
Lyapunov stability theory
- Stability concepts for autonomous systems
- Stability concepts for non-autonomous systems
- Lyapunov stability theorems
- Lyapunov stability using Barbalat’s lemma
It is also noteworthy to point out that since the behavior of the autonomous systems is independent of the initial time, all the stability properties of an autonomous system are uniform. The concepts of stability for non-autonomous systems are very similar to the autonomous systems.
![Figure 2-1 Concept of stability illustrations: curve 1 - asymptotically stable, curve 2 - marginally stable, curve 3 – unstable [69]](https://thumb-ap.123doks.com/thumbv2/123dokinfo/10358443.0/31.892.357.588.481.699/figure-concept-stability-illustrations-asymptotically-stable-marginally-unstable.webp)
Dynamics of n-DOF Serial Hydraulic Manipulator Including Actuator Dynamics
- Introduction
- Problem formulation of n-DOF serial manipulator system
- Mechanical structure of n-DOF serial hydraulic manipulator
- Dynamics of n-DOF serial hydraulic manipulator
- Problem formulation Electro-hydraulic system
- Importance of the electro-hydraulic system
- Electro-hydraulic system dynamics modeling
- Comprehensive dynamics of the n-DOF serial hydraulic manipulator system
- Adaptive backstepping sliding mode control for n-DOF serial hydraulic manipulator 23
Δ Δ Δ , then the term, η1 is chosen to be greater than the upper bound of the estimated error, i.e. 1imisfit i,. From Equation (3.32), the derivative of the Lyapunov function V1 is semi-negative if the error e3 converges to zero.
Verification of n-DOF Serial Hydraulic Manipulator in Free Motion
Introduction
Structure of the 3-DOF Serial hydraulic manipulator
Adaptive fuzzy backstepping sliding mode control with disturbance observer
- Generalized momentum observer for force disturbance
- Model-based disturbance observer
- Disturbance estimator-based generalized momentum observer technique
- General momentum and observer matrix gain design
- Adaptive backstepping sliding mode control with GMO
- Adaptive Fuzzy BSMC with GMO
- Controller gains initialization
- Neural network sliding mode control
- The Constraint of the Updating Law
From equation (4.53), the derivative of the Lyapunov function V1* is semi-negative if the error converges to zero. The control law is designed such that the strong terms can cover the upper bound of the estimated error. The general scheme of the proposed AFBSMC Disturbance Observer (DOAFBSMC) methodology is illustrated in Figure 4-4.
According to the portrait phase of the sliding mode control presented in Yuri et al. Tracking error e(t) and its rate of change è(t) are considered as two nodal inputs of the NN. The first weights to be set are the gains for each e(t) and ė(t) that specify the slope of the sliding surface.
The hidden layer is represented using three nodes determined from the sliding surface that is the output of the input layer. After updating the controller gain, the slope of the sliding surface is then adjusted due to the backpropagation process to satisfy the performance. In order to reduce the convergence time, the update law for the slope of the sliding surface is then adjusted so that the equivalent slope increases and reaches the optimal value:.
Numerical simulations
- Case study 1
- Case study 2
- Case study 3
Improbably, in the FFDOAFBSMC, the estimated disturbance load torque is not fed back to the controller as designed; then the fuzzy logic mechanism assigns their estimated values as inputs to adjust the gains of the robust term to compensate the estimated error that cannot be practically obtained. The desired trajectory of the three joints is assumed to be sawtooth profile created by insert forming. The tracking performance and tracking error of the three joints are described in Figures 4-13 and 4-14, respectively.
The role of the proposed controller is validated at the time the external payload is applied. The tracking performance and tracking error of the three joints are described in Figure 4-17 and Figure 4-18, respectively. The track performance and the track error of the three joints are described in Figure 4-21 and Figure 4-22, respectively.
The estimated load torques are depicted in Figure 4-25, and Figure 4-26 shows the control input signals for the three links. As can be seen in Figures and 4-19 corresponding to the three case studies, the torque load can be observed and its profile is similar to that of the payload. Here, only the magnitude of the torque load is considered, because none of the values of the torque load are negative or positive, they all affect the tracking performance of the system.
Experiments
- Experimental test bench setup
- Experimental Results
- Case study 1
- Case study 2
- Case study 3
The tracking performance and tracking error of the three joints are described in Figure 4-28 and Figure 4-29, respectively. The desired trajectory is set as the same sinusoidal signal as the first case study, but has a 5 kg external load attached to it. The tracking performance and tracking error of the three joints are shown in Figure 4-30 and Figure 4-31, respectively.
The step signal is applied instead of using the smooth signal as in the above two case studies or the sawtooth profile as in the simulation. The tracking performance and tracking error of the system is shown in Figure 4-32 and Figure 4-33, respectively. As can be seen in the three case studies shown in Figure 4-28 to Figure 4-33, especially in the second and third cases, the performance of the three nodes is quite similar to the simulations, . in which the errors when using DOAFBSMC are the smallest compared to that of FFDOAFBSMC) and conventional ABSMC.
The error of the third joint under load and no load is quite similar. This can be explained by the fact that the short length of the third joint is less affected by the load. But due to the length in the second link and the torque of the dynamic coupling between the third and second link, the error of the second link is slightly larger than in the absence of load.
Discussions
Fault estimation and Fault-tolerant Control for n-DOF serial Hydraulic Manipulator in
- Introduction
- System modeling and Problem formulation
- Structure of the impedance control
- System modeling with sensor faults
- A novel robust fault estimation based extended state observer
- Development of adaptive fuzzy backstepping sliding mode control based on fault-
- Numerical simulation
- Setup scenario
- Simulation results
- Conclusion
The sensor errors, in another aspect, can be considered as extended states of the controlled system. The physical interaction between the end effector of the robot manipulator and environment is represented in Figure 5-2. Considering the system behavior under the influence of sensor errors, the dynamics of the 3-DOF serial hydraulic manipulator including actuators in constrained framework is expanded as.
Under the influence of sensor errors, the robust observer based on the extended state observer (ESO) is designed to estimate the state of the system as. Calculation of the end effect estimate ˆXa is calculated from the system state xˆ1 to the forward kinematic si. Then, the objective is to investigate the behavior of the 2-DOF serial manipulator subject to encoder and force sensor errors.
The position tracking performance and state estimation of the two links are depicted in Figure 5-5. In the second case study, the effectiveness of the active FTC is verified in the constrained framework. To address the influence of the sensor errors, the error estimation algorithm based on ESO was designed to detect and estimate the measured and actual joint angle and force the defective signals.
Control strategy for Safety Operation with Contact-loss for n-DOF serial Hydraulic
- Introduction
- Modified position-based impedance control with virtual energy tank
- Contact-loss consideration-based virtual energy tank and passivity control
- Modification of trajectory
- Force sensorless-based extended state observer (ESO)
- Whole system stability analysis
- Numerical simulation results
- Scenario for verification and setting parameters
- Simulated results
- Conclusion
To fully demonstrate a safe motion when contact is lost, a new trajectory must be designed to smooth the motion of the end effector. A shaping function ρ is introduced to create a smooth transition between force and impedance control; thus ensuring a smooth transition in the operation of the position of the end effector. Our goal is to show the response of the system when using the contact loss impedance algorithm.
In addition, the end effector of the KIRO robot must exert a constant force of 100 N on the wall. The tracking effort and energy variable response are shown in Figure 6-13 and Figure 7-14. As can be seen in Figures 6-13 and 6-14, the tracking performance of the end effector changes under the undulating frame, no matter how different the force control gain values are.
In general, larger values of the force control gains generate more accurate, faster and smoother response of the end effector when loss of contact occurs. As can be seen in Figure 6-15, different values of power control gains at the time of contact loss result in different responses of the end effector. The loss of contact is likely to occur in the case of constrained motion when the end effector of the manipulator moves out of the constrained frame.
Conclusion and future work
Conclusions
Unlike previous works that proposed error estimation and fault-tolerant control focusing on free-motion position sensor error, this work considered the impact of sensor errors on both encoder and force sensor errors subject to impedance control in a limited framework. First, a PB-IC was performed, where the sensor errors were initialized by the lag of the measured joint angle and force signals. The simulation results obtained through simulations on a 3-DOF hydraulic manipulator showed that the active FTC can accurately estimate the error of the measured joint angle and force signals and the aligned and unaligned uncertainties.
The proposed control scheme proved its effectiveness; In addition to the occurrence of sensor failure, however, the safety operation of the system exposed to shocks or sudden loss of contact in limited settings should be considered. The passive stability of the method was evidently proved using another Lyapunov theorem considering the virtual energy tank variable and passive variables. Comparative simulations were carefully implemented on the 6-DOF KIRO robot to evaluate the superior efficiency of the proposed control scheme with conventional PB-IC.
Generalized a typically highly nonlinear system and purposefully derived system dynamics with the influence of uncoordinated and coherent disturbances. Proposed a robust error estimation based on ESO to solve the sensor error problem under limited motion. Contact loss considered for safe operation based on virtual energy reservoir and passive control concepts.
Future works and developments
Forward kinetic and Jacobian matrix
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