Self-oscillating chaotic behavior and induced oscillations of a continuous stirred tank reactor with nonlinear control

► Control signals obtained through the reactor input volumetric flows. ► Detailed analysis of self-oscillating and chaotic behavior for the reactor. ► A nonlinear control law is used in conjunction with the chaotic behavior. ► A nonlinear control law generates induced oscillations with prescribed amplitudes. ► Induced oscillations and chaotic behavior allow to obtain small control signals. We analyze the dynamical properties of a continuous stirred tank reactor (CSTR) to produce propylene glycol from propylene oxide with an excess of water containing sulfur acid and methanol assuming an exothermic pseudo-first order reaction. The self-oscillation behavior is briefly treated, and when this state is achieved, it is shown that a sinusoidal variation of the reactor coolant flow rate may produce chaotic behavior. The chaotic oscillations are researched from the bifurcation diagrams, whereas sensitive dependence, Lyapunov exponents and power spectral density and surrogate computations allow to corroborate the presence of chaos. The chaotic behavior is used in connection with a nonlinear control law (based on differential geometry methods) which is applied to reach an arbitrary set point with very small control signals, even in the presence of random noise. On the basis of the nonlinear control law, new control signals are deduced to obtain induced oscillations both in the concentration and reactor temperature. In this case two new dynamical behaviors have been obtained by means of two different strategies: choosing an oscillation frequency with arbitrary amplitude or choosing the amplitude with arbitrary frequency.