Dynamic Matrix Control
Unconstrained Optimization
Quadratic Functions
Vector Case
Necessary and sufficient optimality conditions
Norms
Least Squares Problem
Least Squares Problem
Prediction with Linear Time Invariant
State Space Models
Discrete Time
Linear Time Invariant
State Space Model
Prediction with Linear Time Invariant
State Space Models
Prediction with Linear Time Invariant
State Space Models
Prediction with Linear Time Invariant
State Space Models
Prediction with Linear Time Invariant
State Space Models
Prediction with Linear Time Invariant
State Space Models
Impulse Response
Coefficients
(Markov Parameters)
Define Vector
Output Prediction
Output Prediction
Impulse Response
Coefficients
(Markov Parameters)
Output Prediction
Impulse Response
Coefficients
(Markov Parameters)
Output Regulation Problem
z
r
Controller
u
Process
x
y
Output Regulation Problem
z
r
Controller
u
Process
x
y
Output Regulation Problem
Output Regulation Problem
Output Regulation Problem
Define / Simplify Notation
Define / Simplify Notation
Result
Weighted Least Squares Problem
Expressed as a QP
Parameters of the QP
Expressed as a QP
The Optimal Control Law
Output Regulation Problem
z
r
Controller
u
Process
x
y
Computation of the Gains
Matlab Implementation
[R,p]=chol(H); %Cholesky Factorization
if (p>0)
error(’H not pos.def’)
end
Lx0 =-(R\(R’\Mx0));
LR = -(R\(R’\MR));
Numerical / Computational Observation
Output Regulation Problem
Regularization
z
r
Controller
u
Process
x
y
Regularization
Regularized
Output Regulation Problem
Optimal Solution
Computation of the Gains
Output Regulation Problem
z
r
Controller
u
Process
x
y
Feedforward-Feedback Control
d
z
r
Controller
u
Process
x
y
Prediction in a Model with Disturbances
Prediction in a Model with Disturbances
The Objective Function
The Objective Function
The Feedforward-Feedback Problem
Computation of the Gains
Feedforward-Feedback Control
d
z
r
Controller
u
Process
x
y
Tasks in Computer Controlled Systems
d
z
r
Controller
u
Process
x
y
Tasks in Computer Controlled Systems
d
z
r
Controller
u
Process
x
y