The purpose of this work is to evaluate characteristics of a respiratory model, RS1, in the presence of the following stimuli: exercise, hypercapnia and hypoxia. RS1 has a controller where the driving signal optimizes alveolar ventilation and respiratory frequency to minimize the respiratory work output. A comparative study of the steady-state and transient responses with other three models is performed by simulation. Alternative equations to calculate the optimum frequency are evaluated during exercise and a linear average of two of them is proposed and tested for a healthy subject and with restrictive-obstructive pathology. Additionally, the circulatory time delay in gas transport that produces periodic breathing is calculated.