Brief Theoretical Information

1. What physiological and pathological factors influence the pH of the urine?

2. In which diseases does protein present in the urine?

3. In what pathologies are hematuria and hemoglobinuria observed?

4. Which states lead to glycosuria?

Laboratory work № 3

DISCRETE-TIME SYSTEMS

 

Brief Theoretical Information

Discrete-time systems evolve as approximate representations of continuous-time systems at specific points in time. The numerical integrators already considered as well as those to come are predicated on some form of discrete-time approximation to the derivative function. Digital processors that manipulate streams of sampled numerical data are likewise discrete time in nature. Indeed, much of the first part of this book deals with methods for obtaining discrete-time model approximations of continuous-time systems. In the case of linear time-invariant (LTI) discrete-time systems, methods for finding solutions to specific inputs were presented as well.

Alternatively, some discrete-time systems process information, which by its very nature is allowed to change only at discrete instants of time. In that case, the systems are inherently discrete time. The difference equations are solved either recursively or by the use of a general solution (if one exists), resulting in an output sequence of numbers defined solely at discrete times 0, T, 2T, 3T,....

Simulink is well suited to obtain solutions of discrete-time system models regardless of whether they are approximations of continuous-time systems or inherently discrete time to begin with. The procedure for obtaining a Simulink diagram of a discrete-time system is similar to the way Simulink diagrams of continuous-time systems were developed.

With discrete-time systems, the goal is to express the highest order difference term as an explicit function of the lower order terms. For example, suppose an nth-order discrete-time system with output and input is modelled by the nth-order difference equation,

(3.1)

with initial condition Oftentimes it is possible to solve Equation (3.1) explicitly for , giving

(3.2)

Starting with and , delayed signals and are generated using the ‘‘Unit Delay’’ block and combined according to Equation (3.2) to complete the simulation diagram of the discrete-time system.