Glenohumeral Joint Control System

The present simulator’s control system was predicated on the use of previously validated

in-vivo muscle loading ratios as an a-priori set of data to be modulated by a series of Closed-Loop PID controllers running in parallel. This would achieve real-time control of the glenohumeral joint’s three rotational DOF.

5.2.2.1

A-Priori Muscle Loading Ratios

A number of muscle loading ratio data sets exist in the literature. Some prescribe equal loads to all muscle groups (Apreleva et al., 1998; Debski et al., 1995), others consider the physiological cross-sectional area (pCSA) to apportion load based on muscle size (Halder et al., 2001; Itoi et al., 1994; Sharkey, Marder, & Hanson, 1994; Wuelker et al., 1995), and still others combine pCSA with electromyographic (EMG) activation data, averaged over a motion, to describe loading ratios based on the muscle’s capacity and behaviour during motion (Hsu, Luo, Cofield, & An, 1997). However, the most physiologically accurate set of ratios has come from the evaluation of pCSA, and EMG while it varies throughout a motion, rather than averaged over a motion (Kedgley, Mackenzie, Ferreira, Drosdowech, King, Faber, & Johnson, 2007b). In the literature, these data were only recorded for abduction in the scapular plane with neutral axial rotation, and as such, PID controllers are required to modulate these ratios, thereby allowing control of motions in other planes of elevation and levels of axial rotation (Table 5.1) (Kedgley, Mackenzie, Ferreira, Drosdowech, King, Faber, & Johnson, 2007b).

Table 5.1: Muscle Loading Ratios.

This table illustrates the physiologic muscle loading ratios, at various levels of humeral abduction, utilized by the simulator to achieve accurate joint loading. These ratios are modulated by the PID controllers based on real time kinematic feedback.

5.2.2.2 Nested-Parallel Closed-Loop PID Controllers

In designing the glenohumeral joint active motion control system, three inputs were identified: (1) the setpoints – target rotation angles for each of the three rotational DOF; (2) the process variables – the instantaneous joint angles taken from real-time kinematic data; and (3) the muscle loading ratios corresponding to the real-time abduction angle. The first input is defined as a desired motion profile or constant joint angle for the

secondary DOF, and the third input is drawn from a-priori muscle loading ratio data.

However, because the second input is drawn from real-time kinematic data, a custom LabView (National Instruments, Austin, TX) program was written to acquire humerus and scapula marker data from the Optotrak Certus and convert it to three joint rotations using the previously defined local bone coordinate systems and the ISB recommended YXY Euler angle rotation sequence (Wu, van der Helm, Veeger, Makhsous, Van Roy, Anglin, Nagels, Karduna, McQuade, Wang, Werner, Buchholz, & International Society of Biomechanics, 2005b). The output from this system is a load command for each muscle group.

The three inputs allowed the control of the glenohumeral joint’s rotational DOF through independent PID controllers running in a combined cascade-parallel structure, each using one Euler angle rotation corresponding to its respective DOF (FGIURE). Each PID controller was configured to control the loading of an individual or set of muscles which,

from previous in-vivo investigations, have been found to be primarily responsible for

movement in the PID’s respective DOF.

The three heads of the deltoid are the primary elevators of the shoulder in-vivo; therefore,

the PID controlling abduction angle was configured to output the total deltoid force. This PID was considered the primary controller because its force output had to be sufficient to actively overcome the gravitational load of the arm during glenohumeral abduction, and to maintain the level of abduction during extension motions.

The other two DOF were each controlled by an independent PID. These controllers ran in parallel to each other but cascaded below the primary abduction PID controller. The total

Figure 5.2: Block Diagram of Shoulder Active Motion Control System.

The above block diagram illustrates the control algorithm implemented including the inputs, outputs, and intermediate data within the controller. Green arrows represent setpoints and real-time feedback; blue arrows represent a-priori muscle ratio data or intermediate output from PID controllers; red arrows represent load commands to be sent to actuators and in some cases to other parts of the controller.

force applied to the muscles controlling each of these two DOF was dictated by the sum of the physiologic ratios of each muscle forming the force couple (Plane of Abduction DOF: ∑Anterior and Posterior Deltoid, Axial Rotation DOF: ∑Subscapularis and Infraspinatus/Teres Minor) relative to the middle deltoid at the instantaneous abduction angle (Table 5.1). This total force was then redistributed between the muscles forming the force couple for each DOF using the corresponding Euler angle kinematics as the process variable for the PID controllers. These PID controllers output a ratio ranging from -0.95 to +0.95 which was then multiplied by the total force determined earlier in order to redistribute the load between the muscles in the force couple. The output range was defined in this way to ensure that a minimum tone of 5% of the total load was maintained

on both muscles. This method of using a-priori loading ratios ensured that the two

secondary controllers did not apply non-physiologic forces while still leveraging the control provided by the PID algorithm to produce smooth accurate motion.

Finally, the supraspinatus was actuated based on the magnitude of middle deltoid load, and its physiologic loading ratio with respect to the middle deltoid. This ratio varies with abduction angle since the supraspinatus functions as a primary abductor in early motion, with a decreasing role later on. The supraspinatus was the only muscle not directly controlled by a PID algorithm because while its primary function is to abduct, its role is secondary to that of the middle deltoid (Kedgley, Mackenzie, Ferreira, Drosdowech, King, Faber, & Johnson, 2007a).

5.2.2.3 Control System Tuning

Following implementation of the control system, a tuning procedure was undertaken for each of the three PIDs controlling an individual DOF. Each PID was tuned for two distinct forms of operation: (1) to follow a smooth predefined motion profile; and (2) to maintain a constant rotation angle when a predefined motion profile is being followed in

another DOF (e.g. maintaining an axial rotation angle during an abduction motion). The

abduction PID – the primary controller – was tuned first, since its output cascades to the others. The secondary PIDs were then tuned, and a heuristic process was applied to the primary PID to account for any effect this secondary PID tuning had on its performance.

The initial tuning procedure undertaken for the primary and secondary DOF followed the Ziegler–Nichols method (Ziegler & Nichols, 1942); first, a proportional only controller is

implemented, then its gain is increased until oscillation is initiated (Ku). 45% of this gain

is then used to achieve a desirable Quarter Amplitude Decay Response (Kp). The

estimated oscillation period (Tu) from the first step was then used to select an initial

integral time value (inverse action of gain) (Ti) using the formula:

𝑇𝑖 = 0.83_𝐾𝑇𝑢 𝑝

Equation 5.1: Ziegler-Nichols equations for determination of Integral Time PID parameter initial guess.

Eq. 5.1

The derivative time (Td) was then increased from zero in a heuristic manner until the

resulting profile was sufficiently responsive. Through these tuning procedures, it was determined that the optimal PID gains required for following an abduction profile and for maintaining a constant abduction level were equal. This was also the case for the plane of elevation PID controller (Table 5.2). However, for controlling internal-external rotation, the tuning procedures produced two different sets of gains (Table 5.2). An example of the continuously variable muscle loads produced by this tuned control system can be seen in Figure 5.2.