Os procedimentos para obtenção de soluções exatas dos parâmetros ótimos de um sistema de controle com atraso impõem dificuldades algébricas e de aplicação da teoria envolvida. Neste trabalho são comparadas soluções aproximadas com as exatas para sistemas de primeira e segunda ordem. O termo transcendental que representa o atraso no domínio da transformada de Lplace e aproximado por funções polinomiais racionais. São tratados sistemas do tipo siso e mimo. Para sistemas siso foi utilizado o truncamento da expansão em serie do termo exponencial e procedida à otimização com critério de desempenho baseado em funções do erro entre entrada e saída. Nos sistemas do tipo mimo foram usadas as aproximações de Padé com critério quadrático de otimização. Resultados satisfatórios foram observados para aproximações de Padé de ordem igual ou superior a três.

The procedures to estabilish the exact solutions for the optimal parameters of a control system with time-delay dynamics add significant algebraical and theory understanding difficulties. Due to this the exact solutions for the optimal parameters for first and second order systems as well as the solutions with a substitution of the time-delay dynamics by others, easier to perform algebraically, were obtained in order to analyse the diferences of their results. The time-delay dynamics introduces exponential terms when represented in the Laplace domain. The approximations employed to substitute the time-delay dynamics correspond to analytical approximations to the exponential term represented by rational polynomial functions. This work divides the solution analysis into classes of systems, one with single input and single output and the other with multiple input and multiple output. For systems with single input and single output the approximation employed resulted from the first order trancation of Taylor series and, as an object of optimizations, the performance indexes based on linear combinations of error functionals. From the approximations studied, one particularly, which presented one pole in the left side and a zero in the right side of the imaginary axis, showed the closest results to the exact values of the optimal parameters. For systems with multiple input and multiple output the approximations employed were based on the Padé binomy and as an object of optimization the quadratic criterium involving the states and the control function. Satisfactory results were only obtained for Padé approximations of third order or superior.