Robust Control

Jürgen Ackermann studied Control Engineering under the guidance of Prof. Oppelt in Darmstadt, and Control Theory under the guidance of Prof. Jury in Berkeley, California. He is well known for his contributions to the theory of control systems, as treated in his books on sampled-data [7] and robust control systems [10]. Perhaps his best known result is Ackermann´s formula for pole placement [38]. J. Ackermann has a long association with DLR, the German Aerospace Center in Oberpfaffenhofen, Germany, where he was director of the Institute of Robotics and Mechatronics from 1974 to his retirement in 2001. He has attracted to the institute and supported such well known members of the international control and dynamics community as G. Hirzinger, W. Kortüm, G. Grübel, R. Schwertassek, K. Well (now Stuttgart) and G. Kreisselmeier (now Kassel). Together with them he has initiated and guided many applied research projects which include robust autopilots and jet engine control systems for aircraft; trajectory optimization of aircraft, missiles and spacecraft; control of large flexible structures; robotics for space and manufacturing application, modelling and control of trains, maglev vehicles and automobiles. He has developed a general theory of robust control for steering of vehicles. It is based on robust triangular decoupling of steering of a point mass along a desired trajectory and automatic control of undesired vehicle rotations. J. Ackermann holds six patents for robust feedback control strategies to increase the safety of car driving [1-6]. He initiated an experimental program with BMW, which has shown spectacular safety advantages in road tests with side-wind and mu-split braking [110]. The concept was transferred to flight control [146] where it resulted in a remarkable weight reduction. In both cases the advantages resulted from the fact, that an automatic control system can compensate strong disturbance torques faster than the driver orpilot. J. Ackermann was a Member of the IFAC Council (1990-1996), where he initiated the creation of a new Technical Committee on Automotive Control. He is a founding member of the European Union Control Association and was a member of the IEEE-CSS Board of Governors (1993-1995) and of the "Beirat" of GMR (the German IFAC-NMO). He served on the Editorial Boards of Automatica, IEEE Transactions on Automatic Control (as Associate Editor at Large), C-TAT, Robust and Nonlinear Control, Automatisierungstechnik and was Guest Editor for special issues on "Robust Control" and "Automotive Control". He was chairman of the IPC for the 1989 IEEE International Conference on Control and Applications (Jerusalem), and chaired an IEEE Award Committee, the IFAC Nichols medal committee and the Theory Committee of GMR. He was also a Member of the Senate of the DLR (1986-1998) and of the Advisory Board of the "Deutsches Museum" in Munich (1986-1998). From 1988 to 1995 he was elected chief reviewer for Control Engineering for the Deutsche Forschungsgemeinschaft. Presently he is chairman of the IFAC awards committee for the Nichols medal. J. Ackermann received the J. M. Boykow-Award (1970), the VDE Best Publication Award (1973), he is an Otto-Lilienthal-Fellow (1989) and an IEEE-Fellow (1992), he is recipient of the first Nichols medal of IFAC "for robust control design methods and their use to improve automobile safety" (1996). Also in 1996 he received the Bode Prize of IEEE. In 2005 he was appointed IFAC Fellow "for outstanding and extraordinary contributions to the field of automatic control and involvement in IFAC activities in the promotion of the field". He is adjunct professor at the Technical University Munich and has held visiting appointments at Urbana-Champaign, Canberra, Irvine, Berkeley and Stanford. He was invited for numerous plenary keynote lectures at international conferences [11-26].

1 Parametric Plants and Controllers.- 1.1 State Space Model, Linearization, Eigenvalues.- 1.2 The Leverrier-Faddejew Algorithm.- 1.3 Transfer Function.- 1.4 Robust Controllability, Observability, Feedback Structures.- 1.5 Output Feedback, Closed-loop Characteristic Polynomial.- 1.6 Hurwitz-stability, Stabilizing Controller Parameters.- 1.7 Controller Structures for Partially Known Inputs.- 2 Hurwitz-stability Boundary Crossing and Parameter Space Approach.- 2.1 Critical Stability Conditions.- 2.2 The Parameter Space Approach.- 2.3 Pole Placement.- 2.4 Sequential Pole Shifting.- 2.5 Singular Frequencies.- 2.6 Hurwitz-stability Regions for PID-controllers.- 2.7 Hurwitz-stability Regions for a Compensator or Plant Subpolynomial.- 3 Eigenvalue Specifications.- 3.1 Poles, Zeros and Step Responses.- 3.2 Root Sets, Gamma-stability.- 3.3 Physical Meaning of Closed-loop Poles.- 3.4 Remarks on Existence of Robust Controllers.- 3.5 Further Potential of the Parameter Space Approach.- 4 Gamma-boundary Mapping into Parameter Space.- 4.1 Algebraic Problem Formulation.- 4.2 Parameter Space Mapping.- 4.3 Generalized Singular Frequencies.- 4.4 Gamma-stable PID-control.- 4.5 Non-linear Coefficient Functions.- 5 Frequency Domain Analysis and Design.- 5.1 Frequency Loci Specifications (Theta-stability).- 5.2 Mapping of Frequency Loci Margins into Parameter Space.- 5.3 Frequency Response Magnitude Specifications (Beta-stability).- 5.4 Mapping of Frequency Response Magnitude Specifications into Parameter Space.- 5.5 MIMO Systems.- 6 Case Studies in Car Steering.- 6.1 Tires, Braking, and Steering.- 6.2 The Two Steering Tasks.- 6.3 The Non-linear Single-track Model and its Robust Unilateral Decoupling.- 6.4 The Linearized Single-track Model.- 6.5 Linear Analysis of Robust Decoupling.- 6.6 Skidding Avoidance Based on Robust Decoupling.- 6.7 Skidding Avoidance Based on the Disturbance Observer.- 6.8 Rollover Avoidance.- 6.9 Patents.- 6.10 Automatic Car Steering.- 7 Case Studies in Flight Control.- 7.1 Aircraft Load Alleviation in case of an Engine Out by Robust Yaw-lateral Decoupling.- 7.2 Robust and Fault-tolerant Gamma-stabilization of an F4-E.- 7.3 Large Envelope Flight Control of a High Performance Aircraft.- 8 Robustness Analysis by Value Sets.- 8.1 Mikhailov Plot.- 8.2 Value Sets and Zero Exclusion.- 8.3 Interval Polynomials, Kharitonov Theorem.- 8.4 Affine Coefficients: Edge Theorem.- 8.5 Edge Theorem for Gamma-stability.- 8.6 Singularity of Value Sets.- 9 Value Sets for Non-linear Coefficient Functions.- 9.1 A Warning Example.- 9.2 Desoer Mapping Theorem.- 9.3 Tree-structured Value Set Construction.- 9.4 Computer-aided Execution of Value Set Operations.- 9.5 Tree-structured Transfer Functions.- 9.6 The Stability Profile.- 9.7 Synopsis of Parametric Robustness Analysis.- 10 The Stability Radius.- 10.1 Tsypkin-Polyak Loci.- 10.2 Affine Dependence: The Largest Hypersphere in Parameter Space.- 10.3 Polynomial Dependence.- 11 Robustness of Sampled-data Control Systems.- 11.1 Plant and Controller Discretization.- 11.2 Discrete-time Controllers.- 11.3 Eigenvalue Specifications.- 11.4 Classical Stability Tests.- 11.5 Edge Test.- 11.6 Construction of Value Sets.- 11.7 Real Radius of Stability.- 11.8 Single-loop Feedback Structures.- 11.9 Circle Stability.- A Polynomials and Polynomial Equations.- B PARADISE: Parametric Robustness Analysis and Design Interactive Software Environment.