An improved integrator for use in physical analog-computing systems is disclosed, featuring real-time dynamic amplitude scaling schemas that make use of an injected correction factor responsive to a contemporaneous change in an input dynamic-amplitude-scaling compensation factor. The injected correction factor is designed to reduce or eliminate transient output perturbations due to the amplitude scaling change. The disclosures discussed have real-world applications for physical analog computers and hybrid computers used to control and manage many types of industrial-control systems.