Position control system including a quick response control

A position control system comprising:

• position command generating means for generating a position command at a prescribed sampling time k for a time k+M which is at least one sampling cycle M ahead of the prescribed sampling time;
• a controlled object including a speed control loop, and control means for generating a control input value determined by determining a weight coefficient of each of position commands at sampling times k+l, (l=1, 2, . . . , M) and a weight coefficient for the position and speed which are outputs of the controlled object in order to minimize the value of an evaluation function so that the position command at said prescribed sampling time k and the position of the controlled object will be equalized, while the position commands produced by said position command generating means at the sampling times k+l (l=1, 2, . . . M), the position and speed of the controlled object, and a control input to be applied to said controlled object are being used as variables, wherein the state equation of said controlled object in a discrete-time system is expressed by:
• X.sub.(k+1) =.PHI..multidot.X.sub.(k) +G.multidot.U.sub.(k),
• and a control input vector for minimizing the evaluation function:
• ##EQU8## which evaluates the difference between a status variable vector X.sub.(k) of said controlled object and a position command vector R.sub.0(k) is generated at the prescribed sampling time k, while the position command vectors R.sub.0(k+1), R.sub.0(k+2), . . . , R.sub.0(k+M) generated by said position command generating means from a sampling time k+1 to a sampling time k+M which is M steps ahead of the sampling time k+1 are being used as variables,
• where
• X.sub.(k) :
• the status variable vector (n.times.1) of the system,
• .PHI.:
• the coefficient matrix (n.times.n) of the controlled object,
• G:
• the input matrix (n.times.m),
• U.sub.(k) :
• the control input vector (m.times.i),
• R.sub.0(k) :
• the enlarged position command signal (n.times.1), F.sub.M :
• the final matrix (n.times.n),
• Q:
• the positive semi-definite symmetric matrix (n.times.n),
• H.sub.(i) :
• the positive definite symmetric matrix (m.times.m),
• i=1, . . . , M (M is a predictive period, i.e., the number of sampling times).