Abstract
This study revealed the system of a lower limb exoskeleton created for knee rehabilitation. The exoskeleton has been extensively used in rehabilitation robotic device research, but its practical applicability is limited due to its high nonlinearity and uncertain behavior. As a result, the control technique is critical in increasing the efficacy of rehabilitation devices. For the rehabilitation and help of a patient with a lower-limb condition, a sliding mode control (SMC) with proportional derivative (PD) control approach are used as parallel loops. Active disturbances rejection control (ADRC) is used by these controllers to cancel any external influences. To overcome the degradation of disturbance rejection and robustness caused by a failure to fully adjust for the entire disturbance, a (SMC) loop was introduced to the control regulation. By assessing performance indices related to the estimated inaccuracy, the results demonstrate the effectiveness of the suggested controller. Simulink is used for simulation and analysis.
1 Introduction
Exoskeletons are a type of mechanical robot that can help people and improve their physical capabilities, such as enhancing soldier strength, supporting the elderly in walking, and healing patients with limb injuries. It has attracted a lot of attention in recent years [1, 2]. The lower leg is the weakest of the limb joints in humans. It facilitates in human movement by supporting body weight, absorbing impact stress, and assisting lower limb swing [3]. Over the past few decades, different control techniques have been researched to increase the accuracy of joint motion control for exoskeletons. In [4, 5] used a feedback and feed forward proportional–integral–derivative (PID) controller for monitoring the limb exoskeleton's desirable output. Despite its ease of implementation, the usage of PID control is limited by the convergence analysis and coefficients adjustment. Soft computing approaches such as fuzzy sets and artificial neural networks have been investigated in recent years (ANNs). For exoskeletons, a fuzzy controller with a bang-bang controller has been proposed [6]. In [7] the rehabilitation robot developed an adaptive self-organizing fuzzy controller. In [8] it was demonstrated how to achieve accurate control performance using ANN-based model predictive control (MPC) methods. Despite the ability to approximate nonlinear properties, real-time performance is constrained, and all of these control applications are limited. System uncertainties, such as exogenous disruptions, unmodeled dynamics, and parameter perturbations, have a significant impact on the performance of a control system. The development of the any controller that attempts to fulfill these objectives while also assuring disturbance rejection and strong tracking performance in the face of huge uncertainty is complicated. As a result, anti-disturbance approaches using both external- and internal-loop controllers and estimators have been widely employed [9]. The ADRC controller was first proposed in [10], which offers many benefits. The industry's rapid adoption of ADRC over the past three decades is evidence of the technology's value in position control and other application fields [11–15]. Regarding the biomechanics of the exoskeleton, (SMC) may be an appropriate solution due to its robustness to both internal and external system uncertainties [16–18]. To achieve optimal performance, SMC parameters should be chosen carefully. Genetic Algorithm GA [19], particle swarm optimization (PSO) [20], and Grey-wolf optimization [21] are examples of common optimization methods that are given and used in exoskeleton devices. Algorithm for ant colony optimization [22] was also used. GA is easy to use and capable of finding global optima, which can be used to improve the structure of optimization systems [23]. In this research, a hybrid proposed control technique that combines optimal SMC and PD compensation is presented.
The contributions of this study can be highlighted by the following points:
This study has proposed an expanded ADRC by adding a second SMC-LESO in combination with a PD controller LESO to produce a multilayered LESO. It is particularly efficient to use numerous LESOs within that ADRC framework when dealing with highly unpredictable nonlinear systems.
The controlled system's stability and global convergence properties have been verified according to Lyapunov's second approach
By choosing the best gains for the observer and sliding surface of the SMC technique the chattering phenomenon is minimized.
The rest of this paper is laid out as follows. In the second part, the particular human exoskeleton under investigation is described. The proposed control strategy is clearly described in Section 3. The fourth part incorporates simulations and analysis of results utilizing the proposed approach. In the concluding section, conclusions are formed.
2 Exoskeleton mathematical representation
3 Proposed controller
Only the bandwidth
If one chooses the bandwidth of observer
4 Simulation results and discussion
This part uses numerical simulations to validate the effectiveness of the designed controller. MATLAB's Simulink can be used to carry out the simulation results. Table 1 lists the important parameters of the human-exoskeleton system [24] as well as the control parameters.
Shows all system variables with observer tuning parameters
Parameter | Value |
Inertia ( | |
Solid Friction Coefficient (A) | 1 |
Viscous Friction Coefficient (B) | 0.9 |
Gravity Torque ( | |
Sliding Surface Coefficient | 0.015 |
Switching controller gain | 7.53 |
Proportional gain | 600 |
Derivative gain | 49 |
Observer gain | 288 |
Observer gain | 28,812 |
Observer gain | 941,192 |
Five categories of indices are taken into account to evaluate the performances of the controlled system in terms of error and control effort. These are the Integral of Absolute magnitude of Error (IAE), Integral Square Error (ISE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Integral Absolute control signal (IAU) were chosen as performance indices for comparison [9, 24, 30].To prove the advantages and superiority of the proposed SMC + PDADRC (Eq. (14)) over SMCADRC (Eq. (14) with
- ASimulation Results with Nominal case
The track effectiveness of the suggested methodology is examined and compared to the SMCADRC and PDADRC approaches in the nominal case (
Measures of effectiveness for three controllers with nominal case
Indices | PDADRC | SMCADRC | SMC + PDADRC |
R.M.S.E (rad) | 0.0038 | 0.0023 | 0.0017 |
IAE (rad) | 0.0310 | 0.0121 | 0.0019 |
ISE (rad) | 0.00014 | 0.00005 | 0.00002 |
MAE (rad) | 0.0031 | 0.0012 | 0.0001 |
IAU (N.m) | 28.63 | 100 | 79.58 |
- BSimulation Results with constant load disturbance case
A second simulation is run with a constant disturbance of 0.5 N.m. at time t = 2 s to test the performance of all controllers with payload condition. Figure 6 depicts the performance of the three controllers (Real vs. Desired output). Figure 7 shows the difference in knee position between the desired and actual settings for the same controllers. The SMC + PDADRC can adapt for load disturbances fast and return to the ideal trajectory in less time than the PDADRC and SMCADRC (0.35 s). When a load disturbance is added, the SMC + PDADRC technique exhibits reduced oscillation, but the PDADRC and SMCADRC methods exhibit larger oscillation while maintaining a steady tracking trajectory. Under the aforementioned simulated conditions, SMC + PDADRC is always stable and has the best tracking accuracy. As a result, the proposed method is more robust to variations in load weight. Figure 8 shows the torque control efforts for three controllers. The SMCADRC and SMC + PDADRC demand more torque and have a higher index (IAU) than the PD-ADRC. Table 3 contains a list of all performance indices. The results show that as the system nears steady state, the proposed sliding gain Eq. (13) converges to near zero, preventing chattering.
Measures of effectiveness for three controllers with constant load disturbance case
Indices | PDADRC | SMCADRC | SMC + PDADRC |
R.M.S.E (rad) | 0.0584 | 0.0568 | 0.0547 |
IAE (rad) | 0.1226 | 0.1111 | 0.1073 |
ISE (rad) | 0.0339 | 0.0321 | 0.0298 |
MAE (rad) | 0.0123 | 0.0112 | 0.0108 |
IAU (N.m) | 25.11 | 99.94 | 79.17 |
- CSimulation Results with noise disturbance case
In fact, when a knee trajectory traveling along a predefined path encounters a sudden shock disturbance, such as the human effect (
Measures of effectiveness for three controllers with noise disturbance case
Indices | PDADRC | SMCADRC | SMC + PDADRC |
R.M.S.E (rad) | 0.0067 | 0.0064 | 0.0028 |
IAE (rad) | 0.0388 | 0.0276 | 0.0124 |
ISE (rad) | 0.00044 | 0.00041 | 0.00030 |
MAE (rad) | 0.0039 | 0.0028 | 0.0012 |
IAU (N.m) | 31.92 | 100 | 80.03 |
5 Conclusions
A SMC + PDADRC approach is proposed in this paper for controlling a single knee joint rehabilitation exoskeleton. Several experiments have been conducted in the actual exoskeleton system, including angle trajectory tracking under various conditions, initially the nominal case, and then various external disturbances. The results suggest that the revised approach can track the angle of the knee joint well. The mistakes of SMC + PDADRC are greatly decreased when compared to the original PDADRC and SMCADRC in various instances, with MAE reductions of more than 69% and RMSE reductions of more than 58% in these calculations for the worst scenario (noise disturbance). The position transient can swiftly recover to normal and accomplish accurate tracking when exposed to external disturbances. In general, all controller approaches demonstrate stability as measured by the error trajectory. As a result, for exoskeletons with changing payloads or disturbances, the objectives for reliability and perturbation elimination cannot be satisfied by PD-type control laws. In order to overcome the loss of disturbance rejection and robustness caused by a failure to fully adjust for the whole disturbance, a sliding mode term is introduced to the control rule. The fundamental disadvantage of SMC is chattering, which is eliminated in this study by finding the optimal coefficients of (
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