Lyapunov-function-based design of fuzzy logic controllers and itsapplication on combining controllers

This paper presents the design of fuzzy logic controllers (FLCs) for nonlinear systems with guaranteed closed-loop stability and its application on combining controllers. The design is based on heuristic fuzzy rules. Although each rule in the FLC refers to a stable closed-loop subsystem, the overall system stability cannot be guaranteed when all these rules are applied together. In this paper, it is proved that if each subsystem is stable in the sense of Lyapunov (ISL) under a common Lyapunov function, the overall system is also stable ISL. Since no fuzzy plant model is involved, the number of subsystems generated is relatively small, and the common Lyapunov function can be found more easily. To probe further, an application of this design approach to an inverted pendulum system that combines a sliding-mode controller (SMC) and a state feedback controller (SFC) is reported. Each rule in this FLC has an SMC or an SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. The stability of the whole system is guaranteed by the proposed design approach. More importantly, the controller thus designed can keep the advantages and remove the disadvantages of the two conventional controllers     

New hybrid fuzzy controller for direct torque control induction motor drives

A new hybrid fuzzy controller for direct torque control (DTC) induction motor drives is presented in this paper. The newly developed hybrid fuzzy control law consists of proportional-integral (PI) control at steady state, PI-type fuzzy logic control at transient state, and a simple switching mechanism between steady and transient states, to achieve satisfied performance under steady and transient conditions. The features of the presented new hybrid fuzzy controller are highlighted by comparing the performance of various control approaches, including PI control, PI-type fuzzy logic control (FLC), proportional-derivative (PD) type FLC, and combination of PD-type FLC and I control, for DTC-based induction motor drives. The pros and cons of these controllers are demonstrated by intensive experimental results. It is shown that the presented induction motor drive is with fast tracking capability, less steady state error, and robust to load disturbance while not resorting to complicated control method or adaptive tuning mechanism. Experimental results derived from a test system are presented confirming the above-mentioned claims.     

Tuning of a nonanalytical hierarchical control system for reachingwith FES

Point-to-point functional movements involve simultaneous shoulder and elbow joint rotations. In able-bodied subjects these movements are fully automatic, and feed-forward control ensures the synergistic activity of many muscles. Synergy between joint rotations was defined and described as a scaling between joint angular velocities (M. Popovic and D. Popovic, J. Electromyog. Kinesiol., vol. 4, p. 242-53, 1994). Similarly, subjects who can control their shoulder movements may be assisted in reaching tasks by functional electrical stimulation (FES) of elbow extensor muscles. The synergistic control paradigm can be implemented in real-time by employing a hierarchically structured production-rules method. The use of production-rules necessitates the acquisition of knowledge and the assembly of a rule-base. A nonparametric technique was designed for the identification of the rules. The identification process was divided into two phases: determination of the scaling parameters, and determination of the stimulation parameters. The scaling parameters, needed for the coordination of movements, were determined in able-bodied subjects. Those depend exclusively on the initial and target positions of the hand. The number of scalings could be reduced by dividing the workspace into 12 zones. The stimulation parameters, needed for the execution of movements, were determined in subjects with paralyzed elbow extensor muscles by identifying triplets: elbow angular velocity, elbow angular acceleration (velocity increments), and the corresponding pulse durations for various classes of movements and loads attached to the hand     

Closed-Loop Positioning of Hemiplegic Patient''s Joint by Means of Functional Electrical Stimulation

We report about the results on positioning of the ankle joint of a hemiplegic patient and of normal experimental subjects, using functional electrical stimulation (FES) of antagonistic muscle groups and position feedback. Such a controller is intended to be used as the execution level of a multilevel orthotic system. The synthesis of the controller has been made with the aid of the components of an analog hybrid computer. Experimental results show that the static and dynamic properties of regulated movements are not essentially inferior to the properties of voluntary movements. There are stated technological problems that will have to be solved before the controller can be clinically applied for rehabilitation purposes. At the present state of the art, the poor technology of FES, the unsolved problem of fatigue with FES muscles, size, price, and bad cosmetic effect prevent the position controller from being clinically applicable.     

Design and test of a novel closed-loop system that exploits the nociceptive withdrawal reflex for swing-phase support of the hemiparetic gait

A novel closed-loop system for improving gait in hemiparetic patients by supporting the production of the swing phase using electrical stimulations evoking the nociceptive withdrawal reflex was designed. The system exploits the modular organization of the nociceptive withdrawal reflex and its stimulation site- and gait-phase modulation in order to evoke movements of the hip, knee, and ankle joints during the swing phase. A modified model-reference adaptive controller (MRAC) was designed to select the best stimulation parameters from a set of 12 combinations of four electrode locations on the sole of the foot and three different stimulation onset times between heel-off and toe-off. It was hypothesized that the MRAC system would result in a better walking pattern compared with an open-loop preprogrammed fixed pattern of stimulation (FPS) controller. Thirteen chronic or subacute hemiparetic subjects participated in a study to compare the performance of the two control schemes. Both control schemes resulted in a more functional gait compared to no stimulation (P < 0.05) with a weighted joint angle peak change of 4.0 ± 1.6 (mean ± Standard deviation) degrees and 3.1 ± 1.4 degrees for the MRAC and FPS schemes, respectively. This indicates that the MRAC scheme performed better than the FPS scheme (P < 0.001) in terms of reaching the control target.     

Control of end-point forces of a multijoint limb by functionalneuromuscular stimulation

A multivariable feedback controller was designed and tested for regulating the magnitude and orientation of the force vector at the end point of a multijoint limb in contact with an isometric load. The force vector was produced by electrical stimulation of muscles. To achieve arbitrary control of end-point force magnitude and orientation, two coupling issues must be dealt with by the control system. First, there is a geometric coupling between the end-point force vector and joint torques. The amplitude and orientation of the force vector depend on the limb geometry. Second, torques at two joints may be coupled due to activation of muscles that cross them (biarticular coupling). To eliminate the geometric coupling, a transformation of controller error from the Cartesian space to the joint space was employed. A multivariable proportional-plus-integral (PI) control law was used to calculate muscle activation based on the transformed controller error. Centralized and decentralized controls were investigated for decoupling the effects of biarticular muscles. The results obtained from cat experiments showed that the magnitude and orientation of the end-point forces of the cat hindlimb could be regulated by this controller. In the presence of strong biarticular coupling, centralized control yielded better performance than decentralized control during transient responses. Both control strategies could decouple the biarticular muscle at steady state. When no biarticular coupling was present, centralized control sometimes performed worse than decentralized control. This is the first step in the simultaneous control of multiple joints by functional neuromuscular stimulation (FNS). The controller has broad potential applications in FNS neural prostheses.     

Feedback regulation of hand grasp opening and contact force duringstimulation of paralyzed muscle

A fixed-parameter, discrete-time, first-order, feedback control system is described for regulating grasp during electrical stimulation of paralyzed muscles of the hand. The stiffness of the grasp (relationship between grasp force and grasp opening) is kept constant by linearly combining force and position feedback signals. Thus, a single continuous command signal can control the size of the grasp opening prior to object acquisition and both grasp force and opening after contact. The controller achieves this change in controlled variables by scaling and summing the force and position feedback signals, rather than by a discrete switch in control strategy. Experimental tests of the control system in quadriplegic subjects show that control can be obtained over conditions ranging from unloaded position regulation to isometric force regulation, as well as in the transition between these conditions. The robustness of the control system was evaluated during force regulation with isometric loads. Step response rise time and overshoot were much more dependent on system gain than on the location of the controller zero. Responses with rise time less than two seconds and overshoot less than 30% were obtained over a gain range up to ten, indicating good robustness to muscle gain reductions such as might be caused by fatigue.     

Control of functional neuromuscular stimulation systems forstanding and locomotion in paraplegics

The authors adopt a control-systems perspective in reviewing past applications of functional neuromuscular stimulation for providing lower extremity motor function in paralyzed individuals. Specifically, their approach emphasizes direct computer-controlled electrical stimulation of paralyzed muscle rather than triggering reflexes. In experimental settings it provides paralyzed individuals with the ability to do functional tasks while standing, to walk short distances on varying surfaces, to negotiate obstacles, and to climb and descend stairs     

Fuzzy sliding-mode control of a human arm in the sagittal plane with optimal trajectory

Patients with spinal cord injuries cannot move their limbs using their intact muscles. A suitable controller can be used to move their arms by employing the functional electrical stimulation method. In this article, a fuzzy exponential sliding-mode controller is designed to move a musculoskeletal human arm model to track an optimal trajectory in the sagittal plane. This optimal arm trajectory is obtained by developing a policy for the central nervous system. In order to specify the optimal trajectory between two points, two dynamic and static optimal criteria are applied simultaneously. The first dynamic objective function is defined to minimize the joint torques, and the second static optimization is offered to minimize the muscle forces at each moment. In addition, fuzzy logic is used to tune the sliding-surface parameter to enable an appropriate tracking performance. Simulation results are evaluated and compared with experimental data for upward and downward movements of the human arm.     

Tetanic responses of electrically stimulated paralyzed muscle atvarying interpulse intervals

The influence of stimulus interpulse interval (IPI) on torque output during electrically-evoked contractions was investigated for the knee extensor muscles of paralyzed subjects. The parameters measured were the rise time, magnitude, and relaxation time of the contraction at stimulus IPI's ranging from 62 to 7 ms. Torque output increased as IPI's were decreased from 62 to 15 ms. Peak torques were recorded at IPI's of 12-15 ms; IPI's less than these resulted in an insignificant loss of torque. Rise times decreased as IPI's were decreased. Relaxation time generally increased as IPI's were decreased with the longest relaxation times occurring with stimulation at an IPI of 12 ms. To demonstrate the influence of IPI on muscle fatigue, the effect of prolonged stimulation at short (12 ms) and long (50 ms) IPI's was also compared. After 30 s of stimulation with an IPI of 12 ms, mean torque had declined to 5 +/- 3 percent and after 30 s of stimulation with an IPI of 50 ms, mean torque had declined to 82 +/- 4 percent of the initial value. Knowledge of how stimulus IPI influences the response of paralyzed muscle to electrical stimulation may assist in the development of rehabilitation devices which utilize these technologies.     

Fuzzy-PI-based centralised control of semi-isolated FP-SEPIC/ZETA BDC in a PV/battery hybrid system

Multiport converters with centralised controller have been most commonly used in stand-alone photovoltaic (PV)/battery hybrid system to supply the load smoothly without any disturbances. This study presents the performance analysis of four-port SEPIC/ZETA bidirectional converter (FP-SEPIC/ZETA BDC) using various types of centralised control schemes like Fuzzy tuned proportional integral controller (Fuzzy-PI), fuzzy logic controller (FLC) and conventional proportional integral (PI) controller. The proposed FP-SEPIC/ZETA BDC with various control strategy is derived for simultaneous power management of a PV source using distributed maximum power point tracking (DMPPT) algorithm, a rechargeable battery, and a load by means of centralised controller. The steady state and the dynamic response of the FP-SEPIC/ZETA BDC are analysed using three different types of controllers under line and load regulation. The Fuzzy-PI-based control scheme improves the dynamic response of the system when compared with the FLC and the conventional PI controller. The power balance between the ports is achieved by pseudorandom carrier modulation scheme. The response of the FP-SEPIC/ZETA BDC is also validated experimentally using hardware prototype model of 500 W system. The effectiveness of the control strategy is validated using simulation and experimental results.     

An adaptive fuzzy logic controller: its VLSI architecture andapplications

Most previous work about the hardware design of a fuzzy logic controller (FLC) intended to either improve its inference performance for real-time applications or to reduce its hardware cost. To our knowledge, there has been no attempt to design a hardware FLC that can perform an adaptive fuzzy inference for the applications of on-line adaptation. The purpose of this paper is to present such an adaptive memory-efficient FLC and its applications. Taking advantage of the adaptability provided by a symbolic fuzzy rule format and the dynamic membership function generator, as well as the high-speed integration capability afforded by VLSI, the proposed adaptive fuzzy logic controller (AFLC) can perform an adaptive fuzzy inference process using various inference parameters, such as the shape and location of a membership function, dynamically and quickly. Three examples are used to illustrate its applications, and the experimental results show the excellent adaptability provided by AFLC     

High-Speed Control of IPMSM Drives Using Improved Fuzzy Logic Algorithms

This paper presents an improved fuzzy logic controller (FLC) for an interior permanent magnet synchronous motor (IPMSM) for high-performance industrial drive applications. In the proposed control scheme for high-speed operations above the rated speed, the operating limits of IPMSM are expanded by incorporating the maximum torque per ampere operation in constant torque region and the flux-weakening operation in constant power region. The power ratings of the motor and the inverter are considered in developing the control algorithm. A new and simple FLC is utilized as a speed controller. The FLC is developed to have less computational burden, which makes it suitable for real-time implementation, particularly at high-speed operating conditions. The complete drive is implemented in real-time using digital signal processor (DSP) controller board DS 1102 on a laboratory 1-hp IPM motor. The efficiency of the proposed control scheme is evaluated through both experimental and computer simulation results. The proposed controller is found to be robust for high-speed applications     

Breaking the fixed-arrival-time restriction in reaching movements of neural prosthetic devices

We routinely generate reaching arm movements to function independently. For paralyzed users of upper extremity neural prosthetic devices, flexible, high-performance reaching algorithms will be critical to restoring quality-of-life. Previously, algorithms called real-time reach state equations (RSE) were developed to integrate the user's plan and execution-related neural activity to drive reaching movements to arbitrary targets. Preliminary validation under restricted conditions suggested that RSE might yield dramatic performance improvements. Unfortunately, real-world applications of RSE have been impeded because the RSE assumes a fixed, known arrival time. Recent animal-based prototypes attempted to break the fixed-arrival-time assumption by proposing a standard model (SM) that instead restricted the user's movements to a fixed, known set of targets. Here, we leverage general purpose filter design (GPFD) to break both of these critical restrictions, freeing the paralyzed user to make reaching movements to arbitrary target sets with various arrival times and definitive stopping. In silico validation predicts that the new approach, GPFD-RSE, outperforms the SM while offering greater flexibility. We demonstrate the GPFD-RSE against SM in the simulated control of an overactuated 3-D virtual robotic arm with a real-time inverse kinematics engine.     

An accurate and cost-effective fuzzy logic controller with a fastsearching of moment equilibrium point

This paper proposes a cost-effective architecture of fuzzy logic controller (FLC) that works in an accurate and fast manner. The accuracy of the proposed FLC is obtained by using the center of gravity (COG) defuzzifier that considers both membership values and spans of membership functions in calculating a crisp value. The cost effectiveness of the proposed FLC is obtained by restructuring the conventionally simplified FLC in the following ways. Firstly, the MAX-MIN inference is replaced by a read-modify-write operation that can be implemented economically in the structure of register files. Secondly, the division in the COG defuzzifier is avoided by finding the moment equilibrium point. The proposed COG defuzzifier has two disadvantages, in that it requires additional multipliers and it takes a lot of computation time to find the moment equilibrium point. The first disadvantage is overcome by replacing the multipliers with stochastic AND operations and the second disadvantage is alleviated by using a coarse-to-fine searching algorithm. The hardware complexity of the proposed FLC is analyzed in terms of the number of building blocks. Simulation of the proposed FLC to the truck backer-upper control problem is performed in VHDL, and the control performance of the proposed FLC is compared with that of the conventionally simplified FLC in terms of average tracing distance     

Polymer Fiber Probes Enable Optical Control of Spinal Cord and Muscle Function In Vivo

Restoration of motor and sensory functions in paralyzed patients requires the development of tools for simultaneous recording and stimulation of neural activity in the spinal cord. In addition to its complex neurophysiology, the spinal cord presents technical challenges stemming from its flexible fibrous structure and repeated elastic deformation during normal motion. To address these engineering constraints, we developed highly flexible fiber probes, consisting entirely of polymers, for combined optical stimulation and recording of neural activity. The fabricated fiber probes exhibit low‐loss light transmission even under repeated extreme bending deformations. Using our fiber probes, we demonstrate simultaneous recording and optogenetic stimulation of neural activity in the spinal cord of transgenic mice expressing the light sensitive protein channelrhodopsin 2 (ChR2). Furthermore, optical stimulation of the spinal cord with the polymer fiber probes induces on‐demand limb movements that correlate with electromyographical (EMG) activity.     

Advancing step by step

Restoring movement to paralyzed limbs by means of electrical stimulation has been a research goal for over 30 years. Recently, those efforts have borne commercial fruit in a system that gives some people who are paralyzed limited use of their legs. Still, before a large number of paralyzed people can achieve full dexterity and mobility, much work has yet to be done. Formidable multidisciplinary problems remain, challenging the diverse teams of engineers, physicians, and therapists who are at work on them     

Attenuation of eye movements evoked by a vestibular implant at the frequency of the baseline pulse rate

We are developing a vestibular implant to electrically stimulate vestibular neurons in the semicircular canals in order to alleviate vertigo, which is a commonly occurring problem. However, since electrical stimulation causes synchronous (phase-locked) neural responses, such electrical stimulation might also cause inappropriate vestibuloocular eye movements, which might, in turn, cause visual blurring. We investigated the eye movements evoked in the guinea pig using electric stimulation with a constant rate of 250 pulses per second (pps), and measured 0.010(°) peak-to-peak eye movements on an average at 250 Hz, with an average peak velocity amplitude of 8.1(°)/s, which might cause visual blurring. However, after half an hour of stimulation, that component reduced to 1.6(°)/s (0.0020(°) peak-to-peak). The average time constant for this reduction was 5.0 min. After one week of constant stimulation, the 250-Hz response component was only slightly smaller, at 1.2(°)/s (0.0015(°) peak-to-peak). We conclude that although an electrical prosthesis with a resting rate of 250 pps may cause some visual blurring when first turned on, such blurring is very likely to attenuate and be imperceptible within several minutes.     

Hybrid fuzzy proportional-integral plus conventional derivativecontrol of linear and nonlinear systems

This paper presents a new approach toward the optimal design of a hybrid proportional-integral-derivative (PID) controller applicable for controlling linear as well as nonlinear systems using genetic algorithms (GAs). The proposed hybrid PID controller is derived by replacing the conventional PI controller by a two-input normalized linear fuzzy logic controller (FLC) and executing the conventional D controller in an incremental form. The salient features of the proposed controller are as follows: (1) the linearly defined FLC can generate nonlinear output so that high nonlinearities of complex systems can be handled; (2) only one well-defined linear fuzzy control space is required for both linear and nonlinear systems; (3) optimal tuning of the controller gains is carried out by using a GA; and (4) it is simple and easy to implement. Simulation results on a temperature control system (linear system) and a missile model (nonlinear system) demonstrate the effectiveness and robustness of the proposed controller     

Fuzzy control of dc–dc converters based on user friendly design

The aim of this paper is to show how to build a fuzzy controller and its membership functions automatically. In a fuzzy logic controller (FLC), the proposed method allows one easily to construct a set of membership functions, called shrinking-span membership functions (SSMFs). The FLC uses Mamdani-type fuzzy controllers for the defuzzification strategy and inference operators. The FLC hardware implementation is performed on an 8-bit microcontroller. Simulation results and experimental results demonstrate that the converter can be regulated with good performance even when subjected to input disturbance and load variation. The presented approach is generally valid for the design of an FLC, and can be applied to any dc–dc converter topologies.