2 MPC Based on Step Response Models Step Response Models Step response models are based on the following idea. Assume that the system is at rest. For a linear time-invariant single-input single-output (SISO) system let the output change for a unit input change Av be given by 0,S1,S2,……,SSm:} Here we assume that the system settles exactly after nsteps. The step response Sn) constitutes a complete model of the system, which allows us to compute the system output for any input sequence Kk) vk-1+s,wk-n-1 Step response models can be used for both stable and integrating processes. Fc an integrating process it is assumed that the slope of the response lcu nor 2 For a multi-input multi-output(MIMO)process with n, inputs and ny outputs one obtains a series of step response coefficient matrices where Smi is the ith step response coefficient relating the mh input to the th 2-22 MPC Based on Step Response Models 2-2 Step Response Models Step response models are based on the following idea. Assume that the system is at rest. For a linear time-invariant single-input single-output (SISO) system let the output change for a unit input change ∆v be given by {0, s1, s2,..., sn, sn, . . .} Here we assume that the system settles exactly after n steps. The step response {s1, s2,..., sn} constitutes a complete model of the system, which allows us to compute the system output for any input sequence: Step response models can be used for both stable and integrating processes. For an integrating process it is assumed that the slope of the response remains constant after n steps, i.e., sn – sn – 1 = sn + 1 – sn = sn + 2 – sn + 1 =... For a multi-input multi-output (MIMO) process with nv inputs and ny outputs, one obtains a series of step response coefficient matrices where sl,m,i is the i th step response coefficient relating the mth input to the l th output. y k( ) si ∆v( ) k i – i = 1 n
sn = + vk n ( ) – – 1 Si s1 1, , i s1 2, , i … s1 nv , , i s2 1, , i sny, , 1 i sny, , 2 i … sny nv , , i = …