Hello Emmanuel,
The Integral of Squared Error (ISE) performance index is commonly used in control theory to evaluate the quality of a control system. For a continuous-time system, the ISE is defined as:
where ( e(t) ) is the error signal, which is the difference between the desired output (reference) and the actual output of the system at time ( t ).
In a discrete-time setting, such as when working with a Model Predictive Control (MPC) system, the continuous integral is replaced by a summation over all time steps, since the system is evaluated at discrete intervals. The discrete-time ISE can be expressed as:
or, if the system is evaluated over a finite number of samples ( N ):
where:
( e[k] ) is the error at the kth time step,
( Ts ) is the sampling period (the time interval between successive samples).
For realizing the above equation, we can use a Discrete-Time Integrator block or a Sum block with enabled state to accumulate the squared error over time.
Please refer to the following link for more information on Discrete-Time Integrator block - https://www.mathworks.com/help/simulink/slref/discretetimeintegrator.html
Hope this helps.
Best Regards,
Sachin
