Date of publication: 2017-09-05 00:50
Through this derivation of the transfer function matrix, we have shown the equivalency between the Laplace methods and the State-Space method for representing systems. Also, we have shown how the Laplace method can be generalized to account for MIMO systems. Through the rest of this explanation, we will use the Laplace and State Space methods interchangeably, opting to use one or the other where appropriate.
For SISO systems, the Transfer Function matrix will reduce to the transfer function as would be obtained by taking the Laplace transform of the system response equation.
These are named because if there is no input to the system (zero-input), then the output is the response of the system to the initial system state. If there is no state to the system, then the output is the response of the system to the system input. The complete response is the sum of the system with no input, and the input with no state.
Systems with more than one input and/or more than one output are known as Multi-Input Multi-Output systems, or they are frequently known by the abbreviation MIMO. This is in contrast to systems that have only a single input and a single output (SISO), like we have been discussing previously.
SIMO has the advantage that it is relatively easy to implement although it does have some disadvantages in that the processing is required in the receiver. The use of SIMO may be quite acceptable in many applications, but where the receiver is located in a mobile device such as a cellphone handset, the levels of processing may be limited by size, cost and battery drain.
GRAHAM GOODWIN has over 85 years of experience in the area of control engineering covering research, education and industry. He is the author of seven books, 555 papers and holds four patents. He was the foundation Chairman of a spin-off company and is currently Directory of a special research center dedicated to systems and control research.
We can combine these two equations into a single difference equation using the coefficient matrices A , B , C , and D. To do this, we find the ratio of the system output vector, Y[n] , to the system input vector, U[n] :
STEFAN GRAEBE 's career spans both academic and industrial positions. He was previously research coordinator in the Centre for Industrial Control Science at the University of Newcastle. He is currently head of the Department of Optimization and Automation for the Schwechat refinery of OMV--Austria.
MARIO SALGADO received a Maters degree in Control from Imperial College and a . from the University of Newcastle. He is currently an academic in the Department of Electronics at the Universidad Tecnica Frederico Santa Maria, Valpara so--Chile. His interests include signal processing and control systems design.
There is a number of different MIMO configurations or formats that can be used. These are termed SISO, SIMO, MISO and MIMO. These different MIMO formats offer different advantages and disadvantages - these can be balanced to provide the optimum solution for any given application.