Multi-objective optimisation is a proven, well-known parameter tuning technique in engineering design. It is especially suited to solve complex, multidisciplinary design problems with emphasis on control system design.
MOPS (Multi-Objective Parameter Synthesis) is a software environment, which supports the design engineer in setting up his design problem as a properly formulated multi-objective optimisation task. To this end, MOPS offers a basic control system criteria library, a generic multi-model structure for multidisciplinary problems and a generic multi-case structure for robust control law design, as well as visualisation tools for monitoring the design progress. Several additional features for dealing with large amounts of parameters and criteria, parallelisation of time consuming applications and the use of external simulation and analysis servers for distributed computation are also provided. MOPS also supports parameter estimation in identification problems. Robustness assessment can be performed by optimisation based worst case search, Monte-Carlo analysis or simple parameter studies. The user is provided with a clear application program interface and a graphical user interface both implemented in MATLAB. To solve the underlying optimisation problem different powerful optimisation procedures are available.
MOPS is currently applied to various design and evaluation problems at DLR and in industry. The main fields of application are industrial robotics, flight control, power-optimised aircraft systems, and vehicle dynamics. Development and maturation of MOPS is an ongoing process.
Realistic control law design is a multi-disciplinary task, involving the simultaneous minimisation of many design criteria in the presence of various constraints. Typically, the different criteria and constraints are evaluated using computational models developed for different engineering disciplines or resulting from different modelling formalisms. MOPS explicitly supports the usage of different models from multiple disciplines (multi-models) to compute the design criteria. To each analysis model (e.g. non-linear simulation model, frequency domain models, etc.) a set of criteria is associated.
Robust controller design can be achieved in several ways by appropriately mapping the robustness requirements onto design criteria. A kind of 'global' robustness can be achieved by using the multi-case approach. For example, for analysis models depending on uncertain physical parameters, the robustness against parameter variations can be achieved by trying to apply a unique controller to a whole set of model instantiations, corresponding to different values of physical parameters.
Such a set of model instantiations is called a multi-case model and ideally characterises the whole range of dynamics variations over the parameter range. MOPS explicitly supports the multi-case approach for robust controller design, by automatic generation of multi-case models from a given parameterised analysis model.
In MOPS a multi-objective/multi-model/multi-case design problem is usually mapped to a weighted min-max optimisation problem, which is then solved by using one of several available powerful optimisers, implementing local and global search strategies. Besides very efficient gradient-based solvers (well-suited primarily for smooth problems, especially identification problems), more robust gradient-free direct-search based solvers are available to address problems with non-smooth or noisy criteria. To overcome the problem of local minima to some extent, global solvers based on stochastic, evolutionary or branching strategies can be alternatively used.
Besides solving the weighted min-max single objective optimisation problem, MOPS explicitly supports multi-objective optimisation by detection of Pareto-fronts.
During a multi-objective parameter tuning performed with MOPS, all intermediate iteration steps can be visualised to allow the user a maximum insight into the tuning process. The criteria values are simultaneously displayed in a normalised parallel co-ordinate plot. This plot gives an overview of all (normalised) criteria values at successive iterations, allowing the user to quickly figure out which criteria are easy to be fulfilled, or in contrast, are hard to be satisfied. By just watching this plot, it is often easy to detect conflicting criteria which need to be compromised during the design process. In addition, the user is able to conveniently specify own graphical output of interest related to the criteria computation, such as simulation responses, pole maps, frequency responses etc. All curves belonging to the same design iteration automatically get the same colour. Clicking on any visualised curve or point causes all other graphical outputs at the same iteration to be also highlighted.
Monte Carlo simulation (MCS) is a well known and established technique for modelling and quantification of uncertainties of complex engineering systems. Since robust design of engineering systems with uncertainties is a major concern of MOPS, see for instance multi-model/multi-case models or worst case anti-optimisation, it stands to reason to support MCS within MOPS. Two ways of applying MCS are supported:
The idea of optimisation based worst robustness analysis is to use available and efficient optimisation methods to find those parameter conditions for which the (design) criteria are violated or poorly satisfied. Worst-case search based robustness analysis can be performed by anti-optimisation automatically derived from a design problem set-up in MOPS.
The computation of the criteria may require the use of existing simulation/analysis programs running on specific hardware architectures. An easy to use application program interface (API) has been implemented to facilitate the interfacing of such simulation tools with MOPS. Especially for Modelica models in Dymola the MOPS problem setup can be generated automatically.
Criteria evaluations may be very time consuming, especially when long simulations or complicated analyses are involved. Distributed computation, allowing parallel evaluation of criteria, can alleviate this problem. The underlying parameter variations (e.g. populations in genetic algorithms, gradient approximation by finite differences or even the physical parameter variations in a multi-model/multi-case formulation of the design problem) are well suited to a natural parallelisation of criteria evaluations. MOPS supports
MOPS automatically ensures the synchronisation of the parallel processes and distributed tasks.