Why do some mental activities feel harder than others? Despite decades of study, the answer to this question is surprisingly controversial. In a recent article, we explained cognitive effort by bringing together concepts from dynamical systems analysis, control theory in engineering, artificial neural networks, cognitive psychology and neurophysiology. That article introduced the concept of the "controllosphere," an energy-inefficient region of neural state space associated with high cognitive control. Here we will apply the controllosphere theory in a series of simulations that achieve 3 objectives. First, we will demonstrate the viability of the approach by showing that cognitive control processes are effortful because they inject energy into the system, thereby driving brain states into the controllosphere. Second, we will provide a unifying account of seemingly disparate cognitive phenomena by showing that processes related to working memory and task switching increase effort levels. Third, we will make novel predictions about human brain activity that can be tested in future experiments. By applying the theory to a variety of computational models, these experiments will demonstrate that the predictions follow from the principles of the theory rather than from the particulars of their instantiation. Success will impact basic research on cognitive effort in humans, clinical research on psychiatric disorders, and studies of neurodynamics in non-human animals.