MPC Fundamentals NOTE: One may also specify bounds on y. These constraint-handling properties are a distinguishing feature of MPC and can be particularly valuable when one has multiple control objectives to be achieved via multiple adjustments In reality, however, model imperfections, plant limitations, and unmeasured disturbances cause the measurement, y, to deviate from its expected value. Thus, MPC uses the output measurement and a"disturbance model"(d->y)to predict future changes in y. It then uses its u>y model to calculate appropriate adjustments(a form of feedback compensation). This calculation also considers the known constraints Various types of "noise" can corrupt the measurement. The signal z in Figure 1-1 represents such effects. They may vary randomly about a zero mean or exhibit a non-zero, drifting bias.MPC uses a :>y model in combination with its d-j model to remove the estimated noise component of the measurement("filtering") The above feedforward/feed back actions are mPC's"regulator mode. MPC also has a servo" mode, i.e., it adjusts u such that y tracks a time-varying setpoint. The tracking accuracy depends on the plant characteristics(including constraints), the accuracy of the l-y model, and whether or not future setpoint variations can be anticipated, i.e., known Details: siso case Sampling period and sampling instants MPC operates at discrete intervals of Af time units, the"sampling period. " Suppose that MPC starts at time t=0. The "sampling instants"are the times at which MPC adjusts the manipulated variable, u. They are integer multiples of the sampling period: 0, 4t, 24t, 341, kAt, where the integer index, k, represents the current sampling instant.MPC Fundamentals 1-7 NOTE: One may also specify bounds on . These constraint-handling properties are a distinguishing feature of MPC and can be particularly valuable when one has multiple control objectives to be achieved via multiple adjustments. In reality, however, model imperfections, plant limitations, and unmeasured disturbances cause the measurement, y, to deviate from its expected value. Thus, MPC uses the output measurement and a “disturbance model” ( ) to predict future changes in . It then uses its model to calculate appropriate adjustments (a form of “feedback” compensation). This calculation also considers the known constraints. Various types of “noise” can corrupt the measurement. The signalz in Figure 1-1 represents such effects. They may vary randomly about a zero mean or exhibit a non-zero, drifting bias. MPC uses a model in combination with its model to remove the estimated noise component of the measurement (“filtering”). The above feedforward/feedback actions are MPC’s “regulator” mode. MPC also has a “servo” mode, i.e., it adjusts u such that tracks a time-varying setpoint. The tracking accuracy depends on the plant characteristics (including constraints), the accuracy of the model, and whether or not future setpoint variations can be anticipated, i.e., known in advance. Details: SISO case Sampling period and sampling instants MPC operates at discrete intervals of Dt time units, the “sampling period.” Suppose that MPC starts at time t = 0. The “sampling instants” are the times at which MPC adjusts the manipulated variable, u. They are integer multiples of the sampling period: 0,Dt, 2Dt, 3Dt, ..., kDt, where the integer index, k, represents the current sampling instant. y d y ® y u y ® z y ® d y ® y u y ®