SELF-TUNING REGULATION OF MUSCLE GENERATED MOMENT INDUCED BY ELECTRICAL STIMULATION

M. Ponikvar, M. Munih

Faculty of Electrical Engineering,

University of Ljubljana, Slovenia

SUMMARY

This paper presents the development, implementation, and experimental evaluation of adaptive feedback system for control of the muscle generated moment. The control system, which utilizes self-tuning regulator (STR) and real-time estimation of local muscle model parameters triggered the stimulator and muscle contractions. Design of such moment controller represents the base stage leading toward the construction of a position controller. In order to simplify in vivo experiments with FES, we focused only on gastrosoleus muscles under isometric conditions.

The stimulated subject stood in mechanical rotating frame (MRF), which prevented rotation of knee, hip and lumbosacral joints. MRF is locked, meaning that also ankle joint is stiff. The moment in the ankle as output of the standing human was measured separately for left and right foot with two force plates. The STR was then used to automatize the muscle model identification and the calculation of controller parameters. The fidelity of muscle models was estimated on-line with least square recursive method, which enables the implementation of adaptive control. Adaptive control of electrically stimulated muscle can in real-time embrace the changes caused by time-varying muscle behavior such as fatigue. On-line identification does not require any advance identification procedures and stimulation. The control law was based on the pole placement design that gives desired closed-loop poles. The STR was realized with program Matlab Simulink by using program blocks for identification part, controller, force plates and computer controlled electrical stimulator. The linear controller operation was then tested in three activation regions between stimulation threshold and saturation to exclude nonlinear activation effects. For all three activation regions were utilized different controller configurations with advance adjustment of tuning parameters that indirectly reflect the desired closed-loop transfer function. Sinusoidally shaped moment trajectories included oscillation frequencies between 0.1 Hz and 1.5 Hz. The muscles were stimulated with controlled repetition pulses at 20 Hz. The controller tracking demonstrated to be satisfactory, however due to simple adaptive constitution not enough robust to attenuate well larger disturbances.

STATE OF THE ART

We are interested in studying of the control of paraplegic standing, including standing up and sitting down, by using closed-loop functional electrical stimulation (FES). The method used by nature to enable precise positioning of body parts and achieve body stability is to simultaneously control many synergistic muscles with feedforward and feedback commands. To efficiently investigate the artificial control we want to simplify the demanding body stabilisation conditions and avoid the problem of muscle redundancy. For this reason we try to restrict the arbitrary body motion with the MRF and focus on ankle plantarflexor muscles only. In this study is presented simple single-input single-output controller of the FES generated muscle moment that accounts for slow changes of muscle properties.

MATERIAL AND METHODS

Development of a control system involves many tasks such as modeling, design of a control law, implementation, and validation. The STR attempts to automate several of these tasks /1/. This is illustrated in Fig. 1, which shows a Matlab Simulink block diagram of a process with a STR.

There are many possible choices of model and controller structures. In our study was the process, electrically stimulated muscle, presented with a linear second order discrete transfer function with a pure time delay z^-1 /2/:

(1)

The model sampling time was fixed at 0.05 s, which was also the stimulation rate. The linear model is only valid for a limited region of stimulation levels and was estimated with recursive least squares identification method (RARX) /3/. A simple pole placement method was selected to define a discrete-time domain controller that gives desired closed-loop poles /1/. In addition it is required that the system follows the reference signal u_c in a specified manner.

The controller was described by

(2)

where R, S, and T are polynomials, u is the muscle stimulation level and y is generated moment. This control law represents a negative feedback with the transfer operator –S/R and a feedforward with the transfer operator T/R. The controller was utilized by using two custom discrete transfer functions with adjustable parameters as is shown in Fig. 1, Controller. After the model (1) parameters were identified, was the control law defined according to pole placement controller specifications.

The pole placement procedure for reference model-following was designed to operate without cancellation of the process model zero to avoid unstable operation in the case of biased model parameter estimates. Since the process model is of second order, the minimum-degree solution has polynomials R, S, and T of first order and the closed-loop system is of third order /1/. The reference model, which implements the controller specifications thus needs to be a third order transfer function.

RESULTS

The described controller was tested in moment tracking experiments with intact subjects. The moment reference signals u_c were sinusoidally shaped and included oscillation frequencies between 0.1 Hz and 1.5 Hz, Fig. 2. The effect of varying the parameters of reference model was studied for signals around three output levels: 37.5 %, 62.5 % and 87.5 % where the 100 % stands for the generated moment at maximal (saturation) stimulation level. The sine amplitude was app. 10 % of the maximal generated moment measured in advance tests. At all stimulation levels were achieved the best tracking results if the selected reference model (controller specifications) was a second order transfer function with equivalent damping factor of 0.8 and natural frequency 10 rad^-1s. The initial values of the process parameters were and reached the stationary values after app. 1.5 s, Fig 3. The self-tuning of the controller was therefore started after 1 s of stimulation control with nonadaptive poleplacement controller. The control signal (stimulation level) oscillations arose due to the identified parameter oscillations and due to the initial commutation between constant and adaptive controller parameters.

DISCUSSION

The controllers used in this work are linear and can only adjust to relatively slow changes in muscle properties. The local model approach used here is a possible stage in a process of nonlinear controller design. By using a linear controller we can simplify the validation of adaptive properties of the closed-loop system. Nonlinear control can be afterwards designed by switching between the linear controllers, where the switching can be such as gain scheduling between controllers or fuzzy switching between single controller parameters.

Moment tracking results show time delays of controlled moment after the reference signal. The delays were induced by the slow closed-loop program and will be reduced in our future work. Such delays additionally reduce the system robustness.

REFERENCES

/1/ Astrom K. J., Bjorn W., Adaptive Control, Addison-Wesley Publishing Company, Inc., 1995, 90 – 137

/2/ Hunt K. J., Munih M., Donaldson N., Barr F., Investigation of the Hammerstein Hypothesis in the Modeling of Electrically Stimulated Muscle, IEEE Trans Rehab Eng, Vol. 5, No. 4, Dec. 1997, 998 – 1009

/3/ Ponikvar M., Munih M., Setup and Procedure for On-line Identification of Electrically Stimulated Muscle with Matlab Simulink, accepted for IEEE Trans Neural Rehab Eng, Vol. 9, No. 3, Sep. 2001

ACKNOWLEDGEMENTS

The authors acknowledge the financial support of the Ministry of Science and Technology of the Republic of Slovenia.