QP_UPDATE – Update matrices/vectors of quadratic programming

Block SymbolLicensing group: ADVANCED

Function Description
The QP_UPDATE function block cooperates with the QP_MPC2QP block which converts the MPC problem described by equations (15.1)–(15.4) with prediction horizon $n_{p}$ and control horizon $n_{c}$ (inputs np and nc), to quadratic programming and pre-computes the Hessian matrix $H$ , parts of the gradient vector $G_{x}$ , $G_{v}$ , $G_{w}$ , matrices determining state constraints $S_{u} L$ , $S_{v}$ , $T$ , and matrices determining output constraints $S_{c u} L$ , $S_{c v}$ , $T_{c}$ . Besides the constant Hessian matrix $H$ , the other vectors and matrices are connected to input references uGx, uGv, uGw, uSuL, uSv, uT, uScuL, uScv and uTc.

For detailed information, see the PDF version of this manual.

The output references yx0, yxmin, yxmax, yymin, yymax,yV, yGx, yGv, yGw, ySuL, ySv, yT, yScuL, yScv, yTc, yG, yCA, yLBA and yUBA are always set to the corresponding input ux0, uxmin, uxmax, uymin, uymax,uV, uGx, uGv, uGw, uSuL, uSv, uT, uScuL, uScv, uTc, uG, uCA, uLBA and yUBA.

If HLD = on then nothing is computed.

The error flag E is set to on if:

the prediction horizon np < 1 or control horizon nc < 1, or nc > np,
the reference ux0 is not defined or the element type of the array it references is not Double (F64),
the internal variable bStateConstr = on and at least one of the references uxmin, uxmax is not defined, or the element type of at least one of the arrays they reference is not Double (F64),
the internal variable bOutputConstr = on and the reference uymin is defined and the element type of the array it references is not Double (F64),
the internal variable bOutputConstr = on and the reference uymax is defined and the element type of the array it references is not Double (F64),
the reference uV is defined and the element type of the array it references is not Double (F64),
the reference uG is defined and at least one of the references uGx, uGv, uSuL, uSv or uT is not defined,
the reference uG is defined and the element type of the array it references is not Double (F64), or the reference uGx is defined and the element type of the array it references is not Double (F64), or the reference uGv is defined and the element type of the array it references is not Double (F64), or the reference uGw is defined and the element type of the array it references is not Double (F64),
the reference uSuL is defined and the element type of the array it references is not Double (F64), or the reference uSv is defined and the element type of the array it references is not Double (F64), or the reference uT is defined and the element type of the array it references is not Double (F64),
the reference uScuL is defined and the element type of the array it references is not Double (F64), or the reference uScv is defined and the element type of the array it references is not Double (F64), or the reference uTc is defined and the element type of the array it references is not Double (F64),
the reference uCA or uLBA or uUBA or the element type of at least one of the arrays they reference is not Double (F64),
the arrays referenced by defined references are too small or have incompatible dimensions.

If E = on, see the system log for details.

Inputs

np	Prediction horizon $↓$ 1 $↑$ 1000000	Long (I32)
nc	Control horizon $↓$ 1 $↑$ 1000000	Long (I32)
ux0	Input reference to initial condition vector x0 of the state vector x	Reference
uxmin	Input reference to vector of low limits of the state vector elements	Reference
uxmax	Input reference to vector of high limits of the state vector elements	Reference
uymin	Input reference to vector of low limits of the output inequalities	Reference
uymax	Input reference to vector of high limits of the output inequalities	Reference
uV	Input reference to vector predicted disturbancies	Reference
uGx	Input reference to part of gradient vector G corresponding to state vector x	Reference
uGv	Input reference to part of gradient vector G corresponding to disturbance vector v	Reference
uGw	Intput reference to part of gradient vector G corresponding to vector W	Reference
uSuL	Input reference to work matrix Su*L	Reference
uSv	Input reference to work matrix Sv	Reference
uT	Input reference to work matrix T	Reference
uScuL	Input reference to work matrix Scu*L	Reference
uScv	Input reference to work matrix Scv	Reference
uTc	Input reference to work matrix Tc	Reference
uG	Input reference to gradient vector G	Reference
uCA	Input reference to QP constraints matrix CA	Reference
uLBA	Input reference to lower constraints’ bound vector LB	Reference
uUBA	Input reference to upper constraints’ bound vector LB	Reference
HLD	Hold	Bool

Outputs

yx0	Output reference to initial condition vector x0 of the state vector x	Reference
yxmin	Output reference to vector of low limits of the state vector elements	Reference
yxmax	Output reference to vector of high limits of the state vector elements	Reference
yymin	Output reference to vector of low limits of the output inequalities	Reference
yymax	Output reference to vector of high limits of the output inequalities	Reference
yV	Output reference to vector predicted disturbancies	Reference
yGx	Output reference to part of gradient vector G corresponding to state vector x	Reference
yGv	Output reference to part of gradient vector G corresponding to disturbance vector v	Reference
yGw	Output reference to part of gradient vector G corresponding to vector W	Reference
ySuL	Output reference to work matrix Su*L	Reference
ySv	Output reference to work matrix Sv	Reference
yT	Output reference to work matrix T	Reference
yScuL	Output reference to work matrix Scu*L	Reference
yScv	Output reference to work matrix Scv	Reference
yTc	Output reference to work matrix Tc	Reference
yG	Output reference to gradient vector G	Reference
yCA	Output reference to QP constraints matrix CA	Reference
yLBA	Output reference to lower constraints’ bound vector LB	Reference
yUBA	Output reference to upper constraints’ bound vector LB	Reference
E	Error indicator	Bool

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