Stability of viscoelastic control systems

The paper adapts the classical root locus plot analysis to some one-dimensional, controlled, distributed, viscoelastic structures. The constitutive law that is used for the viscoelastic material may be modeled with fractional order derivatives provided the control law(s) involve similar derivatives. Two sample one-dimensional structures and control systems are used to introduce the approach. A partial differential equation representation of each structure is used as well as a Ritz approximation. The effect of error due to approximation upon stability conclusions is discussed in the context of this comparison.