EP0196417A2
Expired / Lapsed
EP
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Controller for multidegree of freedom nonlinear mechanical system
Assignee: Toshiba Corp
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Filing: 1986-01-29
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Granted: —
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Expires: 2006-01-29
Abstract
Abstract A controller (20) for multidegree of freedom nonlinear mechanical system is for applying adaptive model following control to a nonlinear mechanical system (18) with time-varying parameters which has multidegrees of freedom and a driving source for each of the degree of freedom, and is described by a differential equation of q-th degree. The controller (20) is equipped with a model section (22) that has a built-in reference model with desired response characteristics, a first subtracter for obtaining the difference in the internal states between the mechanical system and the reference model, the detectors for detecting signals for the position and its i-th derivative (1≦i≧q) of the mechanical system, an adaptor (30) for determining the time-varying parameters of the mechanical system based on the difference in the internal states between the mechanical system and the reference model, the input that is applied to the control system, the signals for the position and its i-th derivative (1≦i≦q) of the mechanical system, and the nonlinear structure of the mechanical system, a nonlinear force computation section (34), a non-interference section (36) for computing a compensating input for cancelling the nonlinear forces in the mechanical system as well as the interferential forces between the degrees of freedom of the mechanical system, based on the determined parameter signals from the adaptor (30), the signals for the position and its q-th derivative mechanical system, and a second subtractor and a first adder for additively synthesizing the compensating input, for bringing the output of the mechanical system to coincide with the output of the reference model in the course of the time, and the input that is applied to the control system.
Inventors
- 👤 Koichi Osuka
Bibliographic Details
Application Number
—
Jurisdiction
EP
Data Source
google_patents
Last Synchronized
2026-10-30 18:16
CPC Classifications
G; G05; G05B; G05B19/00; G05B19/02; G05B19/18; G05B19/19; G05B13/00; G05B13/02; G05B13/04; G05B2219/00; G05B2219/30; G05B2219/42; G05B2219/42064; G05B2219/42155
Claims Analysis
Total Claims: 27
Claim 1
Independent Claim
49 words
A controller for multidegree of freedom nonlinear mechanical system which carries out adaptive model following control for a nonlinear mechanical system with multiple degrees of freedom that can be described by a q-th degree differential equation and with driving sources for each of its degree of freedom, characterized by
Claim 2
Dependent Claim
49 words
A controller for multidegree of freedom nonlinear mechanical system which carries out adaptive model following control for a nonlinear mechanical system with multiple degrees of freedom that can be described by a q-th degree differential equation and with driving sources for each of its degree of freedom, characterized by
Claim 3
Dependent Claim
225 words
(a) a model section having a built-in reference model that has predetermined response characteristics; (b) a first synthesizing means for obtaining the difference of the internal states between the mechanical system and the reference model; (c) means for detecting signals for the position and its i-th derivative (1≤i≤q) of the mechanical system; (d) an adaptor for determining the time-varying parameters of the mechanical system, in accordance with the difference in the internal states between the mechanical system and the reference model obtained from said synthesizing means, the input applied to the control system, the signals for the position and its i-th derivative (1≤i≤q) of the mechanical system, and the nonlinear structure of the mechanical system; (e) computing means for computing a compensating input to cancel the nonlinear forces in the mechanical system and the interferential forces between the degrees of freedom of the mechanical system, in accordance with the determined parameter signals obrtained from said adaptor, the signals for the position and its i-th derivative (1≤i≤q) of the mechanical system, and the nonlinear structure of the mechanical system; and (f) a second synthesizing means for synthesizing the compensating input from said computing means and the input that is applied to the control system in order to coincide the output of the mechanical system with the output of the reference model in the course of time.
Claim 4
Dependent Claim
225 words
(a) a model section having a built-in reference model that has predetermined response characteristics; (b) a first synthesizing means for obtaining the difference of the internal states between the mechanical system and the reference model; (c) means for detecting signals for the position and its i-th derivative (1≤i≤q) of the mechanical system; (d) an adaptor for determining the time-varying parameters of the mechanical system, in accordance with the difference in the internal states between the mechanical system and the reference model obtained from said synthesizing means, the input applied to the control system, the signals for the position and its i-th derivative (1≤i≤q) of the mechanical system, and the nonlinear structure of the mechanical system; (e) computing means for computing a compensating input to cancel the nonlinear forces in the mechanical system and the interferential forces between the degrees of freedom of the mechanical system, in accordance with the determined parameter signals obrtained from said adaptor, the signals for the position and its i-th derivative (1≤i≤q) of the mechanical system, and the nonlinear structure of the mechanical system; and (f) a second synthesizing means for synthesizing the compensating input from said computing means and the input that is applied to the control system in order to coincide the output of the mechanical system with the output of the reference model in the course of time.
Claim 5
Dependent Claim
175 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 1, wherein said computing means comprises: a nonlinear force computation section for computing a compensating input to cancel nonlinear forces other than the inertial force in the mechanical system, in accordance with the determined parameter signals from said adaptor, the signals for the position and its i-th derivative (1≤i≤q) of the mechanical system, and the nonlinearity of the mechanical system; a noninterference computation section for computing a compensating input to cancel interferential forces between the degrees of freedom of the mechanical system that are contained in the inertial term, in accordance with the determined parameter signals from said adaptor, the signals for the position and its i-th derivative (I<i<q), and the nonlinearity of the mechanical system; and an inertial term gain computation section for computing nonlinear compensating gain for the inertial term, in accordance with the determined parameter signals from said adaptor, signals for the position and its i-th derivative (1≤i≤q) of the mechanical system, and the nonlinearity of the mechanical system.
Claim 6
Dependent Claim
66 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 2, wherein said first synthesizing means comprises a first subtractor which outputs the position deviation signal and the velocity deviation signal for each degree of freedom, by subtractively synthesizing the position signal and the velocity signal of the real mechanical system and the position signal and the velocity signal of said reference model.
Claim 7
Dependent Claim
74 words
A controller for.multidegree of freedom nonlinear mechanical system as claimed in Claim 3, wherein said second synthesizing means comprises a second subtractor for subtractively synthesizing the output from said nonlinear force computation section and the output from said noninterference computation section, and a first adder for additively synthesizing the output from the second subtractor and the output from said inertial term gain computation section for outputting the result to the nonlinear real mechanical system.
Claim 8
Dependent Claim
43 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 2, wherein said detecting means comprises a position sensor, a velocity sensor, and an acceleration sensor for detecting the position, the velocity, and the acceleration, respectively, of the mechanical system.
Claim 9
Dependent Claim
62 words
A controller for multidegree of freedom nonlinear mechanical system as. claimed in Claim 4, characterized by further comprising a stabilizer for computing a stabilizing input u Si from the position and its i-th derivative (1≤i≤q) of the mechanical system, the output u Si of said stabilizer is added to the input U to the control system by means of a second adder.
Claim 10
Dependent Claim
172 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 6, wherein the real mechanical system has a driving source for each degree of freedom, and is described by the following equation of motion: where x T (x 1 T , x 2 T ) = (x 11 , ..., X 1n , X 21 , ..., x 2n ), X 1 : position of the system, X2: velocity of the system, a ij o , ... , a ij mij ; b i 1 , ..., b i pi , (1≤i, j≤n): unknown parameters or time-varying parameters, J ij o (x), ... , J ij m.. ij (x) ; F i 1 (x), ... , F i p .(x), (1≦i, j≦n): nonlinear bounded known functions that do not containn unknown parameters, u : nxl input vector applied to the nonlinear real mechanical system, O : nxn zero matrix, I : nxn unit matrix, a ii o J ii o (x) ≠0 , and a ii > 0. 0
Claim 11
Dependent Claim
93 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 7, wherein said reference model section includes a reference model which is represented by the following equation: where x T M (x T M1 x T M2 ) (x M11 , ..., x M1n , x M21 , ..., x M2n ), U : new vector input after construction of the control system, K 1 : diag [k 11 , ... , k 1n ], and K 2 : d i ag [k 21 , ... , k 2n ].
Claim 12
Dependent Claim
194 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 8, wherein said adaptor computes the following quantities by using the position signal x 1 , the velocity signal x 2 , and the acceleration signal x 2 for each degree of freedom of the real mechanical system detected by the position sensor, the velocity sensor, and the acceleration sensor, respectively, the position deviation signal, the velocity deviation signal between the reference model and the real mechanical system detected by the subtractor, the nonlinear functions J ij o (x), ... , J ij m . (x); F i 1 (x), ... , F i p (x), (1≦i, j≦n), the vectors x 1 and x 2 , and the input U . where V i = d T i (x M1i - x 1i , x M2i x 2i ) T , (1≦i ≦n), a ii o (0), a ii ii (0). 'b i k (0) : arbitrary d 1 : 2x1 vector that is chosen to make the transfer function W i (s) = d T i (sI - A Mi ) -1 b i to be strictly positive real, and
Claim 13
Dependent Claim
94 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 9, wherein the noninterference computation section computes an output u Di given below by using the position signal x 1 , the velocity signal x 2 , and the acceleration signal x 2 that are detected by the sensors, the nonlinear functions J ij k (x) (excluding J ii o (x)) and the parameters a ij k (excluding a ii o ) that are determined by the adaptor. where δ ij 1 if i = j 0 if i ≠ j
Claim 14
Dependent Claim
70 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 10, in which the nonlinear force computation section computes a part u Ci of the compensating input given below by using the position signal x 1 and the velocity signal x 2 that are detected by the sensors, the nonlinear functions F 1 k (x), and the parameters b 1 k that are determined by the adaptor.
Claim 15
Dependent Claim
62 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 11, wherein the inertial term gain computation section computes a gain G i given below by using the position signal x l and the velocity signal x 2 that are detected by the sensors, the nonlinear functions Jo (x), and the parameters a that are determined by the adaptor.
Claim 16
Dependent Claim
51 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 12, said stabilizer computes an input u Si given below by using the position signal x 1 and the velocity signal x 2 that are detected by the sensors, and the constants k 1 and k 2 .
Claim 17
Dependent Claim
153 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 1, wherein said computing means comprises: a nonlinear force computing section for computing a compensating input to cancel nonlinear forces other than the inertial force in the mechanical system, in accordance with the determined parameter signals from said adaptor, the values of the position and its i-th derivative (1≤i≤q) of the mechanical system, and the nonlinear structure-of the mechanical system; and a noninterference computation section for computing a compensating input to cancel the interferential forces between the degrees of freedom of the mechanical system that are contained in the inertial force, as well as to compensating for the variations in the value of the inertial term due to nonlinearity, in accordance with the signals from said adaptor, the .. values of the position and the i-th derivative (1≤i≤q) of the mechanical system, and the nonlinear structure of the mechanical system.
Claim 18
Dependent Claim
66 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 14, wherein said first synthesizing means comprises a first subtractor for outputting the position deviation signal and the velocity deviation signal for each degree of freedom by subtractively synthesizing the position signal and the velocity signal of the real mechanical system and the position signal and the velocity signal from said reference model.
Claim 19
Dependent Claim
72 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 15, wherein said second synthesizing means comprises a second subtractor for subtractively synthesizing the output from said nonlinear force computation section and the output from said noninterference computation section, and a first adder for additively synthesizing the output from the second subtractor and the input to the control system to output the result to the nonlinear real mechanical system.
Claim 20
Dependent Claim
43 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 14, wherein said detecting means comprises a position sensor, a velocity sensor, and an acceleration sensor for detecting the position, the velocity, and the acceleration, respectively, of the mechanical system.
Claim 21
Dependent Claim
64 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 16, characterized by further comprising a stabilizer for computing a stabilizing input u Si from the velues of the position and its i-th derivative (1≦i≦q) of the mechanical system, the output u Si of said stabilizer is added to the output from the second subtractor by means of a second adder.
Claim 22
Dependent Claim
83 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 18, wherein the real mechanical system has a driving source for each degree of freedom, and is described by the following equation of motion: where X T = (X 1 T , X 2 T ) = (X 11 , ... , X 1n , X 21 , ... , X 2n ) , X 1 : position of the system, X 2 : velocity of the system, For Vx,
Claim 23
Dependent Claim
69 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 19, wherein said reference model section includes a reference model that is represented by the following equation: where x T M = (x T M1 x T M2 ) = (x M11 , ... x M1n , x M21 , ..., x M2n ), and U : new vector input after construction of the control system.
Claim 24
Dependent Claim
174 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 20, wherein said adaptor carries out the following computation by using the position signal x 1 , the velocity signal x 2r and the acceleration signal x 2 for each degree of freedom of the real mechanical system that are detected by the position sensor, the velocity sensor, and the acceleration sensor, respectively, the position deviation signal and the velocity deviation signal for each degree of freedom between the reference model and the real mechanical system that are detected by the subtractors, and the nonlinear functions: where -Z=[(J 1 (x)x 2 -F 1 (x))/λ ---|(J m (x)x 2 -F m (x))/λ, |-F m+1 (x)/λ, |--- -F P (x)/λ V = De λ ≧ ε + nmM J √Γmax M θ (ε : appropriate positive number) the matrix P being the positive definite symmetric solution of Lyapunov.equation. with and where D is chosen to make the transfer function W(s) = D(sI - A M ) -1 B to be strictly positive real.
Claim 25
Dependent Claim
69 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 21, wherein said noninterference computation section computes an output u D given below by using the position signal x l , the velocity signal x 2 , and the acceleration signal x 2 that are detected by said sensors, said nonlinear functions J k (x), and the parameters a k that are determined by the adaptor.
Claim 26
Dependent Claim
67 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 22, wherein said nonlinear force computation section computes a part u C of the compensating input given below by using the position signal x i and the velocity signal x 2 that are detected by said sensors, said nonlinear functions F k (x), and the parameters a k that are determined by the adaptor.
Claim 27
Dependent Claim
59 words
A controller for multidegree of freedom nonlinear mechanical system as claimed in Claim 23, in which said stabilizer computes an input u S given below by using the position signal x 1 and the velocity signal x 2 and the acceleration signal x 2 that are detected by said sensors and the constants k 1 and k 2 .
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